EGM-20-001

EGM-20-001

# Reconstruction of decays to merged photons using end-to-end deep learning
with domain continuation in the CMS detector

###### Abstract

A novel technique based on machine learning is introduced to reconstruct the
decays of highly Lorentz-boosted particles. Using an end-to-end deep learning
strategy, the technique bypasses existing rule-based particle reconstruction
methods typically used in high energy physics analyses. It uses minimally
processed detector data as input and directly outputs particle properties of
interest. The new technique is demonstrated for the reconstruction of the
invariant mass of particles decaying in the CMS detector. The decay of a
hypothetical scalar particle $\mathcal{A}$ into two photons,
$\mathcal{A}\to\gamma\gamma$, is chosen as a benchmark decay. Lorentz boosts
$\gamma_{\mathrm{L}}=60$–600 are considered, ranging from regimes where both
photons are resolved to those where the photons are closely merged as one
object. A training method using domain continuation is introduced, enabling
the invariant mass reconstruction of unresolved photon pairs in a novel way.
The new technique is validated using $\Pgpz\to\gamma\gamma$ decays in LHC
collision data.

##  0.1 Introduction

Since the standard model (SM) of particle physics continues to show excellent
agreement with measurements performed at particle colliders, such as the CERN
LHC, the search for physics beyond the standard model (BSM) has led
experiments, such as CMS, to look beyond simple decay topologies toward more
exotic, potentially overlooked ones. An important class of such exotic
signatures is composed of Lorentz-boosted particles that are sufficiently
energetic to induce collimation of their decay products [1]. An important
consideration in developing a robust search program for such phenomena is
understanding whether existing particle reconstruction algorithms are
sensitive to the decays of boosted particles.

Particle-flow (PF) algorithms [2, 3] are widely used frameworks for the
reconstruction of particle decays in the LHC detectors. These algorithms
reconstruct and identify each individual particle in an event using an
optimized combination of information from the various detector elements.
Although PF algorithms have been successfully used in previous CMS analyses,
they lean heavily on the assumption that particle decays are well resolved and
well isolated, a feature not generally true for boosted particle decays that
often exhibit some degree of merging.

In its loosest sense, merging may refer to the collimation of particles that
are otherwise individually resolved but are in overlapping ensembles. For
instance, in the hadronic decay of a boosted high-mass resonance to jets, the
jets overlap to form a single, large-radius jet. In such cases, there is an
ambiguity in how to group the decays so as to consistently reconstruct the
properties of the parent particle. Although such ensemble merging may be
mitigated, the corresponding analyses require a fine-tuned strategy for
clustering, often at the cost of losing reconstruction efficiency in some
regions of phase space. Therefore, attempts to directly probe the mass of
exotic resonances are rarely pursued in the boosted regime, unlike for the
reconstruction of known SM resonances [4, 5, 6, 7].

At higher boosts, a more experimentally challenging form of merging arises
when the separation between the decay products approaches the detector
resolution. Consider, for instance, decay products interacting with the CMS
electromagnetic calorimeter (ECAL). At separations approaching the Molière
radius of the calorimeter material, the particle showers of the decay products
begin to overlap. This effect can cause the merged decay products to be
misreconstructed as a single-particle candidate. Such shower merging, if
within a few Molière radii, might still be discernible by current dedicated
shower clustering tools, even in regimes inaccessible to PF. The $3{\times}3$
clustering algorithm, used for reconstructing low-energy
$\Pgpz\to\gamma\gamma$ decays [8], is a notable example. However, at
separations approaching the Molière radius, such clustering tools are unable
to discern distinct clusters and begin to lose their sensitivity. Thus, they
are difficult to adapt to exotic searches that typically probe a wide range of
particle masses and Lorentz boosts.

A special case of shower merging occurs when the decay products are collimated
to the point of depositing their energy within the same calorimeter cell, or
less than the Molière radius. In this limit of fully overlapping particle
showers, the resulting shower pattern is nearly indistinguishable from that of
a true, single-particle shower. The only distinction in such cases is the
slightly greater spreading in the particle shower along the principal axis
connecting the points where the decay products enter the calorimeter.
Reconstructing such an instrumentally merged decay remains a challenge for
existing experimental tools. Such a tool must discern subtle differences in
the energy distribution of the fully merged particle shower.

As a concrete example of such a signature, we consider the exotic decay
$\PH/\PX\to\mathcal{A}\mathcal{A}$ of the Higgs boson $\PH$ with a mass of
about 125, or some new resonance $\PX$, to a pair of hypothetical scalar
particles $\mathcal{A}$. Such decays are well motivated in extended Higgs
sectors or BSM models involving two-Higgs doublets, an additional singlet, or
axionlike particle production [9, 10, 11]. Depending on the mass and decay
mode of the $\mathcal{A}$, one or more forms of shower or instrumental
merging, as described above, may occur in its decay. In particular, for decays
to diphotons $\mathcal{A}\to\gamma\gamma$ [12], since photons are massless,
the particle $\mathcal{A}$ can be arbitrarily light and the resulting diphoton
system correspondingly merged. For the mass of the $\mathcal{A}$ satisfying
$m_{\mathcal{A}}\lesssim 0.4\GeV$, the $\PH\to\mathcal{A}\mathcal{A}\to
4\gamma$ signal is increasingly dominated by events where both
$\mathcal{A}\to\gamma\gamma$ decays experience shower or instrumental merging.
When this occurs, each $\mathcal{A}\to\gamma\gamma$ decay is misreconstructed
as a single photonlike cluster, burying the $\PH\to\mathcal{A}\mathcal{A}\to
4\gamma$ signal in existing SM $\PH\to\gamma\gamma$ events [13, 14]. Moreover,
in this $m_{\mathcal{A}}$ regime, the decay modes of the $\mathcal{A}$ into
more massive particles become inaccessible. This feature further emphasizes
the importance of the diphoton decay mode at low $m_{\mathcal{A}}$.

In this paper, we introduce a novel particle reconstruction strategy based on
a modern machine learning (ML) approach also known as deep learning. We show
that such a strategy addresses the above merging challenges associated with
reconstructing boosted particle decays over a wide range of boosts. We
describe the concept of end-to-end particle reconstruction using ML algorithms
that bypass PF [15] and train directly on minimally processed detector data to
reconstruct a particle property of interest. To benchmark our technique, we
reconstruct the invariant mass of simulated $\mathcal{A}\to\gamma\gamma$
decays for masses in the range $m_{\mathcal{A}}=0.1$–1.0and for boost regimes
where the diphotons are barely resolved to instrumentally merged. For particle
$\mathcal{A}$ boosts $\gamma_{\mathrm{L}}=E_{\mathcal{A}}/m_{\mathcal{A}}$,
where $E_{\mathcal{A}}$ is the energy of the $\mathcal{A}$, these correspond
to boosts of $\gamma_{\mathrm{L}}=60$–600. A single end-to-end ML mass
regressor is used, where regressor refers to the output mass of the ML
algorithm. For instrumentally merged diphotons, we further develop a novel ML
technique called domain continuation. This technique involves extending the
training domain to nonphysical values, to include the learning of masses below
the detector resolution. Using both end-to-end particle reconstruction and
domain continuation, we are able to reconstruct the invariant mass of
instrumentally merged diphotons in the CMS detector, a first for a particle
reconstruction method. The technique is validated using $\Pgpz\to\gamma\gamma$
decays in LHC collision data collected by the CMS experiment in 2017. We
achieve a substantial sensitivity gain over existing benchmark algorithms,
allowing previously inaccessible boost regimes to be probed.

##  0.2 The CMS detector

The central feature of the CMS apparatus is a superconducting solenoid of 6m
internal diameter, providing a magnetic field of 3.8T. Within the solenoid
volume are a silicon pixel and strip tracker, a lead tungstate crystal ECAL,
and a brass and scintillator hadron calorimeter, each composed of a barrel and
two endcap sections. Forward calorimeters extend the pseudorapidity ($\eta$)
coverage provided by the barrel and endcap detectors. Muons are detected in
gas-ionization chambers embedded in the steel flux-return yoke outside the
solenoid.

The ECAL consists of 75 848 lead tungstate crystals, which provide a coverage
of $\abs{\eta}<1.48$ in the barrel region (EB) and $1.48<\abs{\eta}<3.00$ in
the two endcap regions. The full azimuthal range $\abs{\phi}<\pi$ is covered
for all regions.

In the barrel section of the ECAL, which is the focus of this paper, an energy
resolution of about 1% is achieved for photons in the tens of energy range,
for those that do not convert to an $\Pep\Pem$ pair before reaching the EB.
The energy resolution for photons converting in the EB is about 1.3% up to
$\abs{\eta}=1$, rising to about 2.5% at $\abs{\eta}=1.48$ [8]. Each EB crystal
has dimensions of $2.18\times 2.18\times 23\,\cm^{3}$. This corresponds to an
angular resolution of $\Delta\eta\times\Delta\varphi=0.0174\times 0.0174$ in
the direction of the collision. The crystal Molière radius is comparable to
the crystal width, leading to more than 90% of the energy of photons
converting only in the ECAL to be laterally contained within a $3{\times}3$
crystal matrix [8].

The material structure of the inner tracking detectors changes with
pseudorapidity. As a result, the number of radiation lengths ($X_{0}$) that a
photon traverses before reaching the EB surface varies from $0.4\,X_{0}$ along
the central plane ($\eta\approx 0$) up to $1.8\,X_{0}$ on the forward edge
($\eta\approx 1.4$). Correspondingly, the amount of energy that a photon
loses, and its probability to convert into an $\Pep\Pem$ pair before reaching
the ECAL crystals, varies with $\eta$.

Finally, an important feature of the proton collisions at the LHC is the
presence of additional, soft collisions concurrent with the primary hard-
scattering event. Such additional proton-proton interactions within the same
or nearby bunch crossings, known as pileup (PU), can contribute additional
energy depositions in the ECAL. Since these energy deposits may potentially be
misidentified as photons, appropriate pileup mitigation techniques are applied
[16].

A more detailed description of the CMS detector, together with a definition of
the coordinate system used and the relevant kinematic variables, is reported
in Ref. [17].

##  0.3 End-to-end ML particle reconstruction

A number of LHC-related studies have attempted to use ML techniques to
reconstruct boosted particle decays, particularly for heavy-resonance decays
exhibiting ensemble merging. These included the use of jet images [18, 19],
graphs [20, 21, 22], and other physics-inspired structures [23, 24, 25, 26,
27]. The large majority of these, however, rely on PF candidates as inputs.
Although such attempts show promise over traditional rule-based selection
algorithms, they are ultimately constrained by the PF information itself. In
their current form, such PF-based techniques would not be sensitive to shower-
merged decays since information about the individual decay products is not
present.

The powerful feature-learning capabilities of modern ML algorithms provide an
alternative. Using inputs that are as unfiltered and informationally rich as
possible, such algorithms have been shown to outperform cut-based or even ML-
based methods utilizing input variables modeled by hand [28, 29, 30, 31, 32,
33, 34]. This is expected if the input variables are difficult to model by
hand or if their correlations are difficult to extract. Moreover, by
encompassing the majority of the reconstruction workflow into the
functionality of the ML algorithm, potential information loss due to stepwise
optimizations is avoided. Such end-to-end ML algorithms are thus trained
directly on minimally processed detector data with the objective of predicting
the desired quantity of interest. This motivates an end-to-end ML-based
particle reconstruction strategy for the challenges of shower merging. We
accomplish this by transforming the detector data into high-fidelity images
[35, 15, 36], and using these to train a convolutional neural network (CNN)
that outputs the final parent particle property of interest. Similar
applications in the literature have employed order-invariant graph-based ML
models as well [37, 38].

The end-to-end ML approach has specific advantages for boosted particle
decays. The first is the gain in information granularity offered by detector
data for features that cannot easily be reduced to a particle-level, or
shower-shape-type representation. Second, the choice of a CNN, or any similar
hierarchical ML architecture like a graph-based network, allows detector
features to be learned across several length scales. Features from the crystal
level to the cluster level and beyond are learned in a complementary way. This
is particularly advantageous for boosted particle decays that may exhibit
merging at multiple scales. Third, by training on minimally processed data
rather than heavily filtered or clustered data, the ML algorithm may learn to
adapt to more varied, higher-dimensional changes in the data, potentially
developing a greater robustness to evolving data-taking conditions. Finally,
there is the computational simplicity of using a single ML algorithm versus a
hierarchy of algorithms each with its own intermediate optimizations.
Admittedly, transitioning to a fully end-to-end ML-based particle
reconstruction framework would involve an extensive overhaul of the workflows
employed by the LHC experiments such as CMS. Moreover, to what extent the
entire particle reconstruction workflow can or should be reduced to a single
ML algorithm remains an open question.

Although a comprehensive end-to-end particle reconstruction framework is a
long-term undertaking, its benefits can already be demonstrated through
targeted applications. In this paper, we test the potential of this technique
by investigating a previously inaccessible boost regime, namely the merged
$\mathcal{A}\to\gamma\gamma$ decay. We train an ML regression algorithm to
reconstruct the generated mass $m_{\mathcal{A}}$ using only the
electromagnetic shower pattern of the merged diphoton decay in the CMS ECAL.
This enables us to exploit subtle differences in the energy distribution of
the ECAL shower pattern [39] to analyze even extremely merged decays.

We parametrize the diphoton merging in terms of the Lorentz boost of the
particle $\mathcal{A}$. Figure 1 illustrates the typical merging regimes at
three different boosts. Samples of $\mathcal{A}\to\gamma\gamma$ decays
misreconstructed by PF as single photons passing candidate selection criteria
(discussed in Sec. 0.5) are used. The $\mathcal{A}\to\gamma\gamma$ samples are
derived from simulated $\PH\to\mathcal{A}\mathcal{A}$ events in which the true
positions of the diphoton decays are known. The distribution of the opening
angles between the higher-$\pt$ (leading, $\gamma_{1}$) and lower-$\pt$
(subleading, $\gamma_{2}$) photons from the simulated particle $\mathcal{A}$
decay is shown in Fig. 1 (left column). The angles are expressed in number of
ECAL crystals in the $\eta$ direction,
$\Delta\eta(\gamma_{1},\gamma_{2})^{\mathrm{gen}}$, versus the $\phi$
direction, $\Delta\varphi(\gamma_{1},\gamma_{2})^{\mathrm{gen}}$. Typical ECAL
energy deposition patterns from a single $\mathcal{A}\to\gamma\gamma$ decay
are also displayed in Fig. 1 (right column). The diphoton particle showers are
resolved in the ECAL for boosts of $\gamma_{\mathrm{L}}\lesssim 50$ (Fig. 1,
upper row), they are shower merged for $50\lesssim\gamma_{\mathrm{L}}\lesssim
250$ (Fig. 1, middle row), and instrumentally merged for
$\gamma_{\mathrm{L}}\gtrsim 250$ (Fig. 1, lower row). Note that the same
$\gamma_{\mathrm{L}}$ value can lead to considerably different merging,
depending on the opening angle between the diphotons.

The barely resolved decays ($\gamma_{\mathrm{L}}\approx 50$) represent the
challenge of ensemble merging. First, rule-based methods may fail to
categorize the $\mathcal{A}\to\gamma\gamma$ shower pattern as either one or
two photon objects, potentially causing the event to be discarded. Second,
resolved $\mathcal{A}\to\gamma\gamma$ decays can resemble both a photon
conversion to an $\Pep\Pem$ pair and low-energy deposits from pileup. For
these latter two possibilities, track information, if present, can potentially
be exploited to distinguish between energy deposits from
$\mathcal{A}\to\gamma\gamma$ decays where the photons do not convert before
reaching the ECAL and those arising from single photons converting before
reaching the ECAL and from pileup, as is done in PF. For the shower-merged
regime, not even dedicated shower clustering tools have the sensitivity to
reconstruct the invariant mass of the $\mathcal{A}\to\gamma\gamma$ system. As
we will show in this paper, only the end-to-end ML approach can effectively
operate in all three regimes. The $\mathcal{A}\to\gamma\gamma$ decay thus
provides a simple but comprehensive test case for all the merging regimes
occurring in the decays of boosted particles.

Figure 1: Simulation results for the decay chain
$\PH\to\mathcal{A}\mathcal{A}$, $\mathcal{A}\to\gamma\gamma$ at various
boosts: (upper plots) barely resolved, $m_{\mathcal{A}}=1.0\GeV$,
$\gamma_{\mathrm{L}}=50$; (middle plots) shower merged,
$m_{\mathcal{A}}=0.4\GeV$, $\gamma_{\mathrm{L}}=150$; and (lower plots)
instrumentally merged, $m_{\mathcal{A}}=0.1\GeV$, $\gamma_{\mathrm{L}}=625$.
The left column shows the normalized distribution of opening angles between
the leading ($\gamma_{1}$) and subleading ($\gamma_{2}$) photons from the
particle $\mathcal{A}$ decay, expressed by the number of crystals in the
$\eta$ direction, $\Delta\eta(\gamma_{1},\gamma_{2})^{\mathrm{gen}}$, versus
the $\phi$ direction, $\Delta\phi(\gamma_{1},\gamma_{2})^{\mathrm{gen}}$. Note
that the distributions include contributions outside of the plotted ranges and
thus may not sum to unity within the displayed ranges. The right column
displays the ECAL energy shower pattern for a single
$\mathcal{A}\to\gamma\gamma$ decay, plotted in relative ECAL crystal index
coordinates and color-coded by energy. In all cases, only decays reconstructed
as a single PF photon candidate passing selection criteria are used.

##  0.4 Detector images

Since the photons from $\mathcal{A}\to\gamma\gamma$ decays deposit energy
primarily in the ECAL, for simplicity, we use an image construction strategy
that consists of only ECAL information. We take a $32{\times}32$ matrix of
ECAL crystals around the most energetic (seed) crystal of the reconstructed
photon candidate and create an image array. This corresponds to an angular
cone of $\sqrt{\smash[b]{(\Delta\eta)^{2}+(\Delta\phi)^{2}}}\approx 0.3$, and
ensures the subleading photon in the $\mathcal{A}\to\gamma\gamma$ decay is
fully contained in the image. Although generous, our results are not strongly
sensitive to the size of the image. Each pixel in the image exactly
corresponds to the energy deposited in a single ECAL crystal. These energy
depositions represent the actual interaction of the incident photon with the
detector material (Fig. 1, right column). This approach is distinct from those
that use PF candidates, in which case the $\mathcal{A}\to\gamma\gamma$ decay,
reconstructed as a single particle, would be displayed as a single image
pixel, by construction. No rotation is performed on the images since
electromagnetic showers are not rotationally symmetric. In addition to the
$\eta$-$\phi$ symmetry being broken by the CMS magnetic field, general
rotations of square pixels are destructive operations that distort the
particle shower pattern.

For simplicity, only photons depositing energy in the barrel section of the
ECAL are used in this paper. For general particle decays, the ECAL images can
be combined with additional subdetector images [35], or parsed into a multi-
subdetector graph if one is using such an architecture. Including such
tracking images, even as a complement to the $\mathcal{A}\to\gamma\gamma$ ECAL
images, could enable a better accounting of contributions from $\Pep\Pem$
conversions and pileup. However, they were not included in this study.

As noted in Sec. 0.2, because of the $\eta$-dependent material structure of
the inner tracker, electromagnetic shower development varies significantly
with $\eta$. Once the $32{\times}32$ crystal matrix of the particle shower is
taken, the resulting image no longer contains explicit information about where
in the ECAL the shower was located. We thus perform two modifications to
recover this information during the training of our ML algorithm. The first is
to split the ECAL images described above into a two-layer image that contains
the transverse and longitudinal components of the crystal energy, which are
defined as $E\sin\theta$ and $E\abs{\cos\theta}$, respectively, where $E$ is
the crystal energy and $\theta$ is the polar angle of the crystal energy
deposit position. The second is to include the crystal seed coordinates.

The calibrated ECAL detector data exist at various levels of processing: from
minimally processed to the filtered and clustered version more easily
accessible at the analysis level. Since the clustered detector data are
historically optimized for the needs of PF, it is worth revisiting this choice
for the end-to-end ML technique. As discussed in Appendix .11.1, training on
minimally processed instead of clustered data significantly improves our
results. We thus emphasize our earlier statement that using minimally
processed detector data is critical in realizing the full potential of ML. We
make exclusive use of minimally processed detector data in this paper. One
caveat is that accessing such data is becoming logistically challenging
because of the trend toward more compact CMS file formats, necessitated by the
growing volume of LHC data.

##  0.5 Candidate selection and datasets

To address the most challenging diphoton particle decays, we require that the
diphoton system be misreconstructed by the PF algorithm as a single photon
candidate, labeled $\Gamma$. As a consequence of the PF ambiguities in
categorizing low-boost $\mathcal{A}\to\gamma\gamma$ decays
$(\gamma_{\mathrm{L}}\lesssim 50)$ as either one- or two-photon objects, this
requirement does not necessarily imply that the diphotons are merged. For
diphotons that are barely resolved, if one of the photons is too low in energy
($\pt<10\GeV$), it is not reconstructed by PF as a separate photon even if it
is sufficiently separated from the other photon. Acceptance of this
information results in a range of boost regimes. Reconstructed photons are
also required to pass shower shape and isolation criteria that would accept
single photons with $>90$% efficiency. These photon selection criteria are
similar to those used by CMS in the SM $\PH\to\gamma\gamma$ analysis [13],
which emphasizes how a merged signal might be buried in such events. For each
selected photon candidate $\Gamma$, a single detector image is constructed
(described in Sec. 0.4), which is then passed to the ML algorithm for either
training or inference.

For training, we use a sample of simulated $\mathcal{A}\to\gamma\gamma$ decays
in which the particle $\mathcal{A}$ decays promptly. The sample includes
pileup but otherwise no additional particles. An ensemble of continuously
distributed masses $m_{\mathcal{A}}$ is used, such that the ML model described
in Sec. 0.6 does not learn the discretization of the mass points. These
samples are generated with $p_{\mathrm{T,\,\mathcal{A}}}=$ 20–100,
$m_{\mathcal{A}}=$ 0–1.6, and $\abs{\eta_{\mathcal{A}}}<1.4$. This corresponds
to Lorentz boosts with $\gamma_{\mathrm{L}}$ in the approximate range 10–1000
and adequately covers the regimes of interest (discussed in Sec. 0.3). After
applying photon selection criteria, samples with closely merged photons
($\gamma_{\mathrm{L}}\gtrsim 150$) are preferentially selected over samples
with resolved photons ($\gamma_{\mathrm{L}}\lesssim 50$), since the latter are
more likely to fail single-photon shower-shape criteria. This tends to sculpt
the phase space in $(p_{\mathrm{T,\,\mathcal{A}}},\,m_{\mathcal{A}})$, which
can result in the mass regressor preferring to output masses in regions with
higher populations. To prevent this from happening, the training samples are
generated to ensure that the
$(p_{\mathrm{T,\,\mathcal{A}}},\,m_{\mathcal{A}})$ phase space is uniformly
distributed after the photon selection criteria have been applied. After
applying these requirements, approximately 780,000
$\mathcal{A}\to\gamma\gamma$ decays are available for training, a sample of
about 26,000 decays for validation, and another 26,000 for testing. In
addition, as explained in Sec. 0.6.2, the training samples are augmented with
true, single-photon samples with similar kinematic properties. After the
selection requirements, there are 150,000, 26,000, and 26,000 simulated single
photons for training, validation, and testing, respectively. The validation
set is used to optimize the ML model hyperparameters, and the test set is used
to assess the performance of the chosen model on a statistically independent
sample.

To benchmark the ML technique, we use both simulated and actual CMS collision
data. The benchmark studies are described further in Sec. 0.6.4. In addition
to pileup, underlying events are included in the simulated
$\mathcal{A}\to\gamma\gamma$ samples to make them more realistic. The
simulated samples are obtained from $\PH\to\mathcal{A}\mathcal{A}\to 4\gamma$
events generated at fixed masses of $m_{\mathcal{A}}=0.1$, 0.4, and 1.0, all
with prompt $\mathcal{A}$ decays. The decays correspond to median boosts of
$\langle\gamma_{\mathrm{L}}\rangle=600$, 150, and 60, respectively, covering a
similar boost range as used for training. The collision data contain events
enriched in $\Pgpz\to\gamma\gamma$ decays selected from the 2017 and 2018 CMS
data-taking periods [40], corresponding to an integrated luminosity of 41.5
and 56.9 $\fbinv$, respectively. To enrich the data sample with
$\Pgpz\to\gamma\gamma$ decays from hadronic jets, as explained in Sec. 0.8.2,
only reconstructed photon candidates with $\pt=$ 20–35are used. Shower-shape
and isolation requirements, which are slightly tighter than for the
$\mathcal{A}\to\gamma\gamma$ analysis described above, are applied.

To study the robustness of the ML technique as a function of various
parameters, as described in Sec. 0.9, events enriched with electrons from
$\PZ\to\Pep\Pem$ decays are used. The electrons are obtained from 2017 data
and simulation using the “tag-and-probe” method [41]. The selected electron is
required to coincide with a photon candidate passing the photon selection
criteria described earlier.

For all simulated samples, events are generated with corresponding 2017 data-
taking pileup conditions and fully simulated CMS geometry and detector
response [17].

##  0.6 Mass regression model and training

A ResNet CNN architecture [42] forms the basis of our mass regression model.
Although other ML architectures exist, including those that use graph-based
techniques, the emphasis in this paper is placed on the general reconstruction
method rather than the optimization of the ML model.

The energy deposits in the ECAL detector images are first scaled by a sample-
wide constant so that the sample-wide energy distribution is approximately
within the $[0,1]$ interval. Each image associated with a reconstructed photon
candidate $\Gamma$ is then passed to the ResNet model, which outputs to a
global maximum pooling layer. A more detailed description of the ResNet model
used is presented in Ref. [15]. The outputs are then concatenated with the
crystal seed coordinates of the photon candidate. The seed coordinates are
also scaled to lie within the $[0,1]$ interval. The concatenated outputs are
then fully connected to a final output node that gives the predicted or
regressed value of the scalar-particle mass $m_{\mathcal{A}}$ for that photon
candidate. The above ML mass regressor contains 89k trainable parameters.

To train the mass regressor, the regressed mass $m_{\Gamma}$ is compared with
the true (generated) $m_{\mathcal{A}}$ by calculating the absolute error loss
function $\abs{m_{\Gamma}-m_{\mathcal{A}}}$, averaged over the training batch.
Other loss functions are equally performant. This loss function is then
minimized using the ADAM optimizer [43]. To facilitate convergence, the mass
values are also scaled to lie within $[0,1]$ before they are passed to the
optimizer. This procedure represents our basic training strategy.

###  0.6.1 Performance limitations when $m_{\mathcal{A}}\to 0$

Relying solely on this basic training strategy has significant performance
limitations. As shown in Fig. 2 (left), naively training the mass regressor as
described above results in a nonlinear response near either boundary of the
mass regression range. At the high-$m_{\mathcal{A}}$ boundary, this issue can
be resolved by trivially extending the training mass range. Thus, if one
wanted to obtain a usable regression range up to $m_{\mathcal{A}}\approx
1.2\GeV$, one would train with a sample including higher masses, as we have,
up to $m_{\mathcal{A}}\approx 1.6\GeV$, depending on the mass resolution at
the upper mass range. Predictions in the extended mass range are then
discarded during the physics analysis. This approach cannot, however, be used
in any obvious way for the low-$m_{\mathcal{A}}$ boundary, since it is
constrained by the physical requirement $m_{\mathcal{A}}>0$. The mass region
$m_{\Gamma}\lesssim 200\MeV$, of considerable theoretical interest for the
diphoton decay mode in BSM models (discussed in Sec. 0.1), would therefore be
inaccessible. The use of the mass regressor as a tool for reconstructing
$\Pgpz\to\gamma\gamma$ decays would also be lost. Moreover, significant biases
in the regressed masses of true photons would arise. As illustrated in Fig. 2
(right), photons would be regressed as a peak around $m_{\Gamma}\lesssim
200\MeV$, reducing even further the usable range of the mass regressor when
single-photon backgrounds are included.

Figure 2: Left: the regressed mass $m_{\Gamma}$ vs. the generated
$m_{\mathcal{A}}$ value for simulated $\mathcal{A}\to\gamma\gamma$ decays
generated uniformly in $(\pt,\,m_{\mathcal{A}})$ before domain continuation is
implemented. The regressed $m_{\Gamma}$ is normalized in 0.025vertical slices
of the generated $m_{\mathcal{A}}$. The color scale to the right of the plot
gives the normalized number of events per vertical slice in 0.025bins of
$m_{\Gamma}$. Right: the regressed $m_{\Gamma}$ distribution for simulated
single-photon samples only, before domain continuation, resulting in a
distinct peak in the low-$m_{\Gamma}$ region. The distribution is normalized
to unity with the vertical bars on the points indicating the statistical
uncertainty.

###  0.6.2 Domain continuation to negative masses

Fundamentally, the above boundary problem arises because, when training the
mass regressor, the physically observable $\mathcal{A}\to\gamma\gamma$
invariant mass distribution becomes underrepresented for samples with
$m_{\mathcal{A}}<\sigma(m_{\mathcal{A}})$, where $\sigma(m_{\mathcal{A}})$ is
the mass resolution. This issue is illustrated in Fig. 3 (left). For samples
where $m_{\mathcal{A}}\approx\sigma(m_{\mathcal{A}})$, the full, physically
observable mass distribution ($\mathrm{f}_{\mathrm{obs}}$), visualized as a
Gaussian distribution, is barely represented in the training set. As
$m_{\mathcal{A}}\to 0$, shown in Fig. 3 (middle), only half of the mass
distribution is now observable. For these underrepresented samples, the mass
regressor defaults to the closest mass value whose observable distribution is
well represented, $m_{\mathcal{A}}\approx\sigma(m_{\mathcal{A}})$, since this
will appear most similar. This results in a gap above $m_{\Gamma}\approx 0$
and an accumulation of masses at $m_{\Gamma}\approx 200\MeV$. More generally,
this boundary problem manifests itself when regressing a quantity $q$, with
resolution $\sigma(q)$, over the range $(a,b)$, for samples with $q\lesssim
a+\sigma(q)$ or $q\gtrsim b-\sigma(q)$. This effect only becomes negligible at
either boundary in the limit $\sigma(q)\ll a,b$.

Figure 3: Pictorial representation of the $m_{\mathcal{A}}\to 0$ boundary
problem occurring when attempting to regress below the mass resolution. Left:
the distribution of physically observable $\mathcal{A}\to\gamma\gamma$
invariant masses ($\mathrm{f}_{\mathrm{obs}}$) vs. the generated
$m_{\mathcal{A}}$. When $m_{\mathcal{A}}\approx\sigma(m_{\mathcal{A}})$, the
left tail of the mass distribution becomes underrepresented in the training
set. Middle: As $m_{\mathcal{A}}\to 0$, only half of the mass distribution is
represented. The regressor subsequently defaults to the last full mass
distribution at $m_{\mathcal{A}}\approx\sigma(m_{\mathcal{A}})$. Right: with
domain continuation, the generated mass distribution of the original training
samples ($\mathcal{A}\to\gamma\gamma$, red region) is augmented with
topologically similar samples that are randomly assigned nonphysical masses
($\gamma$, blue region). This allows the regressor to see a full mass
distribution over the entire region of interest (unhatched region).
Predictions in the black hatched regions are discarded.

This motivates a solution for the low-$m_{\mathcal{A}}$ boundary problem by
extending the regression range below $m_{\mathcal{A}}=0$, into the nonphysical
domain. These are then populated with “topologically similar” samples. We thus
augment the training set with samples artificially and randomly labeled with
negative masses. During inference, we remove the nonphysical predictions
$m_{\Gamma}<0$. As a topologically similar sample, either a sample of decays
with a fixed mass $m_{\mathcal{A}}\approx 0.001\MeV$ or a sample of single
photons can be used. In this paper, we use the latter, although we find either
method works well. If we require that the “negative mass” samples have the
same mass density as the “positive mass” samples in the training set (cf. Fig.
3, right), then only a single hyperparameter is needed, the minimum artificial
mass value, $\mathrm{min}(m_{\mathcal{A}})$. This can be set by choosing the
negative value with the smallest magnitude that closes the
low-$m_{\mathcal{A}}$ gap (cf. Fig. 2, left) and linearizes the mass response
in the physical domain, $m_{\Gamma}>0$. We find a value of
$\mathrm{min}(m_{\mathcal{A}})=-0.3\GeV$ to be sufficient. Other applications
may seek to optimize both the minimum artificial mass value and the number
density of the augmented samples. Note that having the augmented samples carry
negative mass values is simply a consequence of the low-$m_{\mathcal{A}}$
boundary coinciding with $m_{\Gamma}=0$. Had the boundary coincided with a
positive mass, positive artificial mass values would be involved as well.

The above procedure effectively tricks the mass regressor into seeing a full
invariant mass distribution for all physical $\mathcal{A}\to\gamma\gamma$
decays, even when they reside below the detector mass resolution. As a result,
the full low-$m_{\mathcal{A}}$ regime becomes accessible. In addition, this
procedure provides a simple way for suppressing single-photon backgrounds by
requiring $m_{\Gamma}>0$. Since single photons will tend to be regressed with
negative masses, removing samples with $m_{\Gamma}<0$ reduces single-photon
contributions in a mass decorrelated way. The only trade-off is that
low-$m_{\mathcal{A}}$ samples incur a selection efficiency to be regressed
within $m_{\Gamma}>0$. However, this is expected for most
$\mathcal{A}\to\gamma\gamma$ merged cases that cannot be distinguished from
true photons.

By analogy to complex analysis, we denote the above procedure as domain
continuation. Similar procedures, however, all occur in the statistical tests
used in high energy physics [44]. Our final training strategy implements
domain continuation on top of the basic training strategy described at the
beginning of this section.

###  0.6.3 Out-of-sample response

An important feature of ML-based regression algorithms is that their
predictions are bound by the regression range on which they were trained. This
is true even when out-of-sample decays, or decays not represented in the
training set, are given to the mass regressor. If this fact is not addressed,
unexpected peaks and features in the regressed mass spectrum can potentially
appear. Although hadronic jets are indeed out of sample, it is desirable not
to reject them at the stage of the mass regressor in order to enable the
reconstruction of, , embedded $\Pgpz\to\gamma\gamma$ decays. If desired, these
can instead be suppressed by modifying the photon selection criteria, for
instance, as described in Sec. 0.8.2.

Furthermore, $\mathcal{A}\to\gamma\gamma$ decays from more massive
$\mathcal{A}$ particles than those used during training are a potential issue.
These will be regressed as a false mass peak near the upper $m_{\mathcal{A}}$
boundary. For this and other reasons stated earlier, when addressing the
boundary problem at the upper mass range, we ignore predictions above
$m_{\Gamma}>1.2\GeV$ (Fig. 3, right). Lastly, to suppress single photons, as
noted above, we ignore predictions with $m_{\Gamma}<0$. During inference, the
use of the mass regressor is thus limited to samples regressed within the
region of interest (ROI): $m_{\mathcal{A}}\text{-ROI}$ $\in[0,1.2]\GeV$. The
impact of this method on the sample selection efficiency is estimated in Sec.
0.7.

###  0.6.4 Evaluation

In Sec. 0.7, we validate the ML training using a number of figures of merit.
We primarily use the mean absolute error,
$\mathrm{MAE}=\langle\abs{m_{\mathcal{A}}-m_{\Gamma}}\rangle$ over the test
set, but also consider its normalized counterpart, the mean relative error,
$\mathrm{MRE}=\langle\abs{m_{\mathcal{A}}-m_{\Gamma}}/m_{\mathcal{A}}\rangle$.
The MAE (MRE) approximately corresponds to the mean absolute (relative) mass
resolution. If treating the mass distribution at a fixed $m_{\mathcal{A}}$ as
a signal model, a lower MRE, similar to a lower relative mass resolution,
implies a better signal significance assuming some fixed background
contribution. The regression efficiency, or the number of samples regressed
within $m_{\mathcal{A}}\text{-ROI}\in[0,1.2]\GeV$, divided by the total number
of samples considered, is also used as a figure of merit. Similarly, if
treating the mass distribution at a fixed $m_{\mathcal{A}}$ as a signal model,
a higher regression efficiency implies a higher signal significance for a
given background contribution.

In Sec. 0.8, we benchmark the physics performance of the end-to-end ML mass
regressor (end-to-end) by comparing its response with both a traditional
neural network-based mass regressor (photon NN) and a shower cluster-based
algorithm used for mass reconstruction ($3{\times}3$ algorithm). The photon NN
is trained on a mix of 11 shower-shape and isolation variables, identical to
those used by CMS for multivariate photon tagging [13]. These variables are
passed to a fully connected neural network of 128 nodes and three hidden
layers that regresses the scalar-particle mass. For a fair comparison, it is
also trained with domain continuation. The resulting performance was
insensitive to small increases or decreases in network size. The $3{\times}3$
algorithm is similar to that used by CMS for the reconstruction of low-energy
$\Pgpz\to\gamma\gamma$ decays in the calibration of the ECAL [8]. It first
identifies a local crystal energy maximum (seed). If the seed energy is above
some energy threshold, then a $3{\times}3$ crystal matrix (cluster) around the
seed is formed. If a pair of nearby clusters is found, the reconstructed mass
is calculated as the invariant mass of the two clusters. If a pair of clusters
cannot be found, a default mass value outside of the
$m_{\mathcal{A}}\text{-ROI}$ range is passed.

Lastly, in Sec. 0.9, to assess the robustness and generalizability of the end-
to-end mass regressor, we compare its mass response versus various kinematic
and detector quantities of interest. We conclude with a comparison of the
regressed mass spectrum in data versus simulation.

##  0.7 Training validation

To validate the training of the mass regressor and to characterize its
performance, we use a test sample of $\mathcal{A}\to\gamma\gamma$ decays with
a continuous uniform $m_{\mathcal{A}}$ distribution. The regressed versus
generated mass is shown in Fig. 4 (upper). We observe a linear and well-
behaved mass response throughout the $m_{\mathcal{A}}\text{-ROI}$ range. Since
the regressed mass range spans more than an order of magnitude, some variation
can be seen in the mass resolution, and thus in the shape of the regressed
$m_{\Gamma}$ versus $m_{\mathcal{A}}$ response. Notably, the mass regressor is
able to probe the low-$m_{\mathcal{A}}$ regime where it exhibits a gentle and
gradual loss in resolution upon approaching the $m_{\Gamma}=0$ boundary. As
discussed in Sec. 0.6, this behavior is the result of using domain
continuation. This performance confirms the ability of the end-to-end ML
technique to access the highest boost regimes, where shower and instrumental
merging are present, yet maintain performance into the high-$m_{\mathcal{A}}$
regime, where the particle showers become resolved.

The MAE and MRE as functions of the generated mass are displayed in Fig. 4
(lower left). The MAE varies from 0.14 (0.20) for $m_{\mathcal{A}}$ in the
range 0.1 (1.2) , corresponding to mean boosts of
$\langle\gamma_{\mathrm{L}}\rangle=$ 600 (50), respectively. In general, the
absolute mass resolution worsens with increasing $m_{\mathcal{A}}$, as
reflected in the MAE trend. However, the relative mass resolution tends to
improve with mass, as is evident in the MRE values, converging to about $20\%$
for $m_{\mathcal{A}}=1.2\GeV$. If the $\mathcal{A}\to\gamma\gamma$ mass
distribution is used as a signal model, then, for a fixed regression
efficiency, a lower relative resolution implies better signal significance,
given some fixed background contribution. Notably, as shown in Fig. 4 (lower
left), for $m_{\mathcal{A}}\lesssim 0.3\GeV$, the MAE starts worsening with
decreasing mass. This can be attributed to the gradual deterioration of the
mass regressor below the detector’s mass resolution.

These figures of merit are achieved with a regression efficiency between 70
and 95%, as shown in Fig. 4 (lower right). The regression efficiency for a
given sample as a function of $m_{\mathcal{A}}$ is defined as the number of
events in a particular $m_{\mathcal{A}}$ bin that has $m_{\Gamma}$ within
$m_{\mathcal{A}}\text{-ROI}$, divided by the total number of samples in that
bin. If the $\mathcal{A}\to\gamma\gamma$ mass distribution is used as a signal
model, then, for a fixed mass resolution, a higher regression efficiency
implies better signal significance, for some fixed background contribution.
The efficiency is primarily driven by how much of the mass peak can fit within
$m_{\mathcal{A}}\text{-ROI}$. Thus, it is highest at the midway point of
$m_{\mathcal{A}}\text{-ROI}$ and falls off to either side. The relatively
poorer mass reconstruction at low $m_{\mathcal{A}}$ causes the efficiency to
fall off more steeply than it does at high $m_{\mathcal{A}}$. About $50\%$ of
single photons are rejected by the $m_{\mathcal{A}}\text{-ROI}$ requirement,
as seen by the hatched region in Fig. 4 (lower right). Photons with
$m_{\Gamma}>0$ are primarily due to $\Pep\Pem$ conversions.

Figure 4: Mass regression performance for simulated
$\mathcal{A}\to\gamma\gamma$ samples generated uniformly in
$(\pt,m_{\mathcal{A}})$, corresponding to mean boosts in the range
$\langle\gamma_{\mathrm{L}}\rangle=$ 600–50 for $m_{\mathcal{A}}=$ 0.1–1.2
GeV. Upper: regressed $m_{\Gamma}$ vs. generated $m_{\mathcal{A}}$. The
regressed $m_{\Gamma}$ is normalized in 0.025vertical slices of the generated
$m_{\mathcal{A}}$. The color scale to the right of the plot gives the
normalized number of events per vertical slice in 0.025bins of $m_{\Gamma}$.
Lower left: the MAE (blue circles, use left scale) and MRE (red squares, use
right scale) vs. the generated $m_{\mathcal{A}}$. For clarity, the MRE for
$m_{\mathcal{A}}<0.1\GeV$ is not shown since its value diverges as
$m_{\mathcal{A}}\to 0$. Lower right: the $m_{\mathcal{A}}$ regression
efficiency as a function of the generated $m_{\mathcal{A}}$. The hatched
region shows the efficiency for single photons. The vertical bars on the
points show the statistical uncertainty in the simulated sample.

##  0.8 Physics validation

To validate the physics performance of the end-to-end mass regressor, we
compare it with two traditional reconstruction strategies: a photon NN-based
mass regressor trained on shower-shape and isolation variables, and a
$3{\times}3$ shower clustering algorithm (described in Sec. 0.6.4). Although
the figures of merit from the previous section provide a high-level
characterization of the reconstruction performance, the ultimate physical
quantity of interest is the regressed mass spectrum itself, which is the focus
of this section.

###  0.8.1 Simulation

The validation on simulated data compares the mass spectra for
$\mathcal{A}\to\gamma\gamma$ decays for various fixed-mass values. As
described in Sec. 0.5, we use $\mathcal{A}\to\gamma\gamma$ samples obtained
from simulated $\PH\to\mathcal{A}\mathcal{A}\to 4\gamma$ events with masses
$m_{\mathcal{A}}=0.1$, 0.4, and 1.0. In these events, the particle
$\mathcal{A}$ energy is distributed around a median of $E_{\mathcal{A}}$
$\approx m_{\PH}/2\approx 60\GeV$, corresponding to median boosts of
$\langle\gamma_{\mathrm{L}}\rangle\approx 600$, $150$, and $60$ for the
respective $m_{\mathcal{A}}$ masses. In addition to the photon selection
criteria, event selection criteria similar to those used in the CMS
$\PH\to\gamma\gamma$ analysis are applied. The reconstructed mass spectra are
shown in Fig. 5 for the different algorithms and $m_{\mathcal{A}}$ mass
values. For each mass value, representing a different median boost regime, the
samples are further broken down by ranges of reconstructed
$p_{\mathrm{T},\,\Gamma}$, to highlight the stability of the mass spectrum
with energy. These $p_{\mathrm{T},\,\Gamma}$ ranges are:

  * (i)

low-$p_{\mathrm{T},\,\Gamma}$: $30<p_{\mathrm{T},\,\Gamma}<55\GeV$,

  * (ii)

mid-$p_{\mathrm{T},\,\Gamma}$: $55<p_{\mathrm{T},\,\Gamma}<70\GeV$,

  * (iii)

high-$p_{\mathrm{T},\,\Gamma}$: $70<p_{\mathrm{T},\,\Gamma}<100\GeV$, and

  * (iv)

ultra-$p_{\mathrm{T},\,\Gamma}$: $p_{\mathrm{T},\,\Gamma}>100\GeV$.

Some overlap in the boost values across different $m_{\mathcal{A}}$ masses is
to be expected. Note that the mass regressor has been trained on samples with
$p_{\mathrm{T},\,\Gamma}<100\GeV$ and that reconstructed candidates only in
the range $\abs{\eta_{\Gamma}}<1.44$ are used.

Figure 5: Reconstructed mass spectra for end-to-end (left column), photon NN
(middle column), and $3{\times}3$ algorithms (right column) for
$\mathcal{A}\to\gamma\gamma$ decays with $m_{\mathcal{A}}=1.0\GeV$ (upper
row), $m_{\mathcal{A}}=0.4\GeV$ (second row), $m_{\mathcal{A}}=0.1\GeV$ (third
row), and for isolated single photons (lower row). For each panel, the mass
spectra are separated by reconstructed $p_{\mathrm{T},\,\Gamma}$ value into
ranges of 30–55 GeV (red circles, low-$p_{\mathrm{T},\,\Gamma}$), 55–70 GeV
(gray triangles, mid-$p_{\mathrm{T},\,\Gamma}$), 70–100(blue squares,
high-$p_{\mathrm{T},\,\Gamma}$), and $>$100(green inverted triangles,
ultra-$p_{\mathrm{T},\,\Gamma}$). The vertical bars on the points give the
statistical uncertainties. All the mass spectra are normalized to unity,
including samples outside $m_{\mathcal{A}}\text{-ROI}$. The vertical dotted
line shows the input $m_{\mathcal{A}}$ value.

For boosts $\langle\gamma_{\mathrm{L}}\rangle\approx 60$ and
$m_{\mathcal{A}}=1.0\GeV$, only the end-to-end algorithm (Fig. 5, upper left)
consistently reconstructs a mass peak for all $p_{\mathrm{T},\,\Gamma}$
ranges. The position of the mass peak remains stable, with the resolution
improving in the high-$p_{\mathrm{T},\,\Gamma}$ category. The end-to-end
regression performs best when the $\mathcal{A}\to\gamma\gamma$ decay products
are moderately merged, and neither fully resolved nor fully merged. The mass
peak in the ultra-$p_{\mathrm{T},\,\Gamma}$ category is well reconstructed
despite being outside the trained phase space. This demonstrates that the
phase space extrapolation is effective for internally learned quantities like
$p_{\mathrm{T},\,\Gamma}$.

For $m_{\mathcal{A}}=1.0\GeV$, the photon NN (Fig. 5, upper middle) has
difficulty reconstructing the mass peak, except at the
higher-$p_{\mathrm{T},\,\Gamma}$ categories. This can be understood in terms
of the information content of the input variables on which the algorithm was
trained. At higher $p_{\mathrm{T},\,\Gamma}$, the two photons are more likely
to be moderately merged so that their showers are contained within the
$5{\times}5$ crystal block where the shower-shape variables are defined. At
lower $p_{\mathrm{T},\,\Gamma}$, the two photons are more often resolved so
that the lower-energy photon shower falls outside the $5{\times}5$ crystal
block. The photon NN must then rely on the isolation variables, which are
defined much more coarsely over a cone of
$\sqrt{\smash[b]{(\Delta\eta)^{2}+(\Delta\phi)^{2}}}<0.3$ about the seed
crystal. Since these variables have much less discriminating power, this
results in a steep falloff in reconstruction performance. To improve the
performance, the photon NN could be augmented with the momentum components of
the lower-energy photon, in instances where the PF is able to reconstruct it.

Lastly, for $m_{\mathcal{A}}=1.0\GeV$, the $3{\times}3$ algorithm (Fig. 5,
upper right) is the only one competitive with the end-to-end method for lower
$p_{\mathrm{T},\,\Gamma}$. As the photon clusters become resolved, the
$3{\times}3$ method thus becomes an effective tool for mass reconstruction.
However, as soon as the clusters begin to merge at higher
$p_{\mathrm{T},\,\Gamma}$, a sudden dropoff in reconstruction efficiency
occurs since the $3{\times}3$ algorithm is unable to compute a mass for a
single cluster. A spurious peak develops at $m_{\Gamma}\approx 0.5\GeV$ for
decays with sufficient showering prior to the ECAL. The $3{\times}3$ method is
thus only useful for a limited range of low boosts. The comparatively weaker
performance of the end-to-end method to the $3{\times}3$ one at
low-$p_{\mathrm{T},\,\Gamma}$ is attributable to the underrepresentation of
relevant boosts in the training sample. The optimization of the end-to-end
technique for these lower boosts is beyond the scope of this paper.

For boosts $\langle\gamma_{\mathrm{L}}\rangle\approx 150$ and
$m_{\mathcal{A}}=0.4\GeV$, the end-to-end method (Fig. 5, second row, left) is
able to reconstruct the mass peak with full sensitivity across most of the
$p_{\mathrm{T},\,\Gamma}$ ranges. Only at the highest
$p_{\mathrm{T},\,\Gamma}$ range does the mass peak significantly degrade,
although it is still reasonably well behaved. Training with higher
$p_{\mathrm{T},\,\Gamma}$ could potentially improve this behavior. The photon
NN performs its best in this regime (Fig. 5, second row, middle) because a
majority of the photon showers fall within the $5{\times}5$ crystal block.
However, the mass resolution is still significantly worse compared with the
end-to-end method. The $3{\times}3$ algorithm (Fig. 5, second row, right) is
barely able to reconstruct a mass peak for these boosts. We recall that, if
the $3{\times}3$ algorithm is unable to find a pair of clusters, an invariant
mass cannot be calculated, and a default mass value outside
$m_{\mathcal{A}}\text{-ROI}$ is instead passed.

For boosts $\langle\gamma_{\mathrm{L}}\rangle\approx 600$ and
$m_{\mathcal{A}}=0.1\GeV$, the end-to-end method (Fig. 5, third row, left)
reaches the limits of its sensitivity, although it is still usable. We
attribute the performance of the end-to-end method to its ability to discern
subtle differences in the energy distribution of the fully merged particle
shower, which we expect to have more smearing along the principal axis
connecting the $\mathcal{A}\to\gamma\gamma$ diphotons. Notably, even at these
boosts, the position of the mass peak measured with the end-to-end method
remains stable with $p_{\mathrm{T},\,\Gamma}$. This is not the case for the
photon NN (Fig. 5, third row, middle) whose peak becomes erratic and displaced
with increasing $p_{\mathrm{T},\,\Gamma}$. The $3{\times}3$ method is not able
to calculate a mass at this level of merging for the same reasons stated
earlier.

For reference, the regressed mass spectrum for single, isolated photons from
$\PH\to\gamma\gamma$ decays is shown in Fig. 5 (lower row). Both the end-to-
end (left) and photon NN (middle) methods are able to regress to the
$m_{\Gamma}\approx 0\GeV$ boundary, with a smoothly falling distribution since
they were trained with domain continuation (cf. Fig. 2, right). The remaining
photons within $m_{\mathcal{A}}\text{-ROI}$ come from photon conversions that
acquire an effective mass because of nuclear interactions.

Summarizing the validation performance on simulated data, the end-to-end ML
technique is the only one that is able to robustly and consistently probe
boost regimes ranging from resolved to instrumentally merged showers.

###  0.8.2 Data

To validate the findings described above from simulated events, we perform a
cross-check using $\gamma+\text{jet}$ events from CMS data, where the jet is
reconstructed as a photon candidate. The CMS dataset was acquired in 2017 at
the LHC with proton-proton collisions at $\sqrt{s}=$ 13\. In Sec. 0.9.2, we
also compare the results from this dataset with a similar one acquired in the
2018 LHC running. These two datasets correspond to integrated luminosities of
41.5 and $56.9\fbinv$, respectively. If the jet contains an energetic,
collimated neutral-meson decay ($p_{\mathrm{T},\,\Gamma}\gtrsim 20\GeV$),
typically a $\Pgpz\to\gamma\gamma$ or $\Pgh\to\gamma\gamma$, it will be
misreconstructed as a single photon $\Gamma$ and the event will pass a
diphoton trigger. Since the energy of the jet will, in general, be shared
among several constituent particles, the $\Pgpz$ is more likely to be
reconstructed as the lower-energy photon in the event. Thus, a data sample
enriched in merged photons is obtained by selecting events passing a diphoton
trigger and selecting the lower-energy reconstructed photon, which we
additionally require to pass our photon selection criteria. The selected
sample is then given to the $m_{\Gamma}$ regressor, whose output we study
below. Further details about the trigger and photon selection criteria can be
found in the $\PH\to\gamma\gamma$ analysis [13]. We emphasize that the mass
regressor is being used to regress the $m_{\Gamma}$ of individual
reconstructed photon candidates, which we assume to be merged photons, not the
invariant mass of the reconstructed diphoton event itself. As before, only
reconstructed candidates in the range $\abs{\eta_{\Gamma}}<1.44$ are used.

An important caveat in regressing the $m_{\Gamma}$ of energetic photons
($p_{\mathrm{T},\,\Gamma}\gtrsim 20\GeV$) within jets is the presence of other
hadrons within the jet. At these energies, we emphasize that it is no longer
the case that neutral-meson decays are well isolated in jets, a main point of
distinction compared with the isolated $\mathcal{A}\to\gamma\gamma$ decays
used to train the mass regressor. In general, the neutral-meson decay will be
collimated with other hadrons, including, potentially, several merged $\Pgpz$
decays. The effect of these additional hadrons is to smear and distort the
resulting $m_{\Gamma}$ spectrum and introduce an energy dependence in the
$m_{\Gamma}$ value. We therefore restrict our study to
$20<p_{\mathrm{T},\,\Gamma}<35\GeV$ and require tighter shower-shape criteria,
to increase the contribution from well-isolated $\Pgpz\to\gamma\gamma$ decays
that more closely resemble the $\mathcal{A}\to\gamma\gamma$ decay. The
low-$\pt$ threshold is dictated by the chosen diphoton trigger. Although these
tighter criteria mitigate the stated effects, the impact of these effects
remains visible.

Within the above restricted $p_{\mathrm{T},\,\Gamma}$ range, the $\Pgpz$ is
boosted to the approximate range $\gamma_{\mathrm{L}}=$ 150–250, putting its
invariant mass reconstruction out of reach of all but the end-to-end mass
regressor. Also present is the higher-mass $\Pgh$, which, though produced with
a much lower cross section, is boosted to only about the range
$\gamma_{\mathrm{L}}=$ 30–60, just within reach of the $3{\times}3$ algorithm.

As clearly seen in Fig. 6, the end-to-end method is able to reconstruct a
prominent $\Pgpz$ peak. Indeed, it is the only algorithm able to do so. The
$\Pgpz$ peak appears more prominent than the corresponding $\mathcal{A}$ peak
at $m_{\mathcal{A}}=0.1\GeV$ (cf. Fig 5, third row, left) because of the
higher mass and lower boost of the $\Pgpz$ in this case. The photon NN
exhibits an erratic response, suggesting it does not have the data granularity
needed to probe this regime. Likewise, the $3{\times}3$ method is unable to
reconstruct the $\Pgpz$ peak at all. It is, however, able to reconstruct the
$\Pgh$ peak, as expected. We attribute the weaker $\Pgh$ peak in the end-to-
end method to the aforementioned smearing effect of additional hadrons in the
jet, as discussed further in Appendix .11.2. The $3{\times}3$ method is less
sensitive to this effect because of the restriction on the ECAL energy
clusters being in the smaller $3{\times}3$ window.

Whether the sensitivity of the end-to-end method to the effects of jet
hadronization represents an advantage or disadvantage depends on the
application. For an analysis searching for isolated
$\mathcal{A}\to\gamma\gamma$ decays [45], background processes from neutral
mesons in jets will be smeared in mass, providing a distinct advantage for
separating their mass spectra from that of true $\mathcal{A}\to\gamma\gamma$
decays peaking at similar masses. The optimization of the end-to-end technique
for the mass regression of neutral mesons in jets is beyond the scope of this
paper.

The unique capability of the end-to-end technique to reconstruct highly
boosted particle decays thus opens the door to physics searches in boost
regimes previously inaccessible to existing reconstruction algorithms.
Additionally, because of the difficulty of obtaining low-energy $\Pgpz$ decays
($E\approx 1\GeV$) with increasing luminosity, the ability to reconstruct the
more abundantly available high-energy ($E\approx 10\GeV$) $\Pgpz$ decays
instead offers the possibility of improving the reach of existing CMS ECAL
intercrystal calibration methods, which rely on such decays [8].

Figure 6: Reconstructed mass $m_{\Gamma}$ for end-to-end (red circles), photon
NN (blue squares), and $3{\times}3$ (gray triangles) algorithms for hadronic
jets from data enriched with $\Pgpz\to\gamma\gamma$ decays. All distributions
are normalized to the same number of events, including those outside
$m_{\mathcal{A}}\text{-ROI}$. The statistical uncertainties in the
distributions are negligible.

##  0.9 Robustness of the algorithm

To further assess the robustness and generalizability of the end-to-end ML-
based mass regressor, we study how the regressed mass varies with respect to a
number of key quantities of interest. Such studies are useful in revealing
potential biases of the mass regressor technique to kinematic regions and
detector conditions for which it was not trained. These mass dependence
studies are performed on data using both $\Pgpz\to\gamma\gamma$ events and
electrons from events enriched with $\PZ\to\Pep\Pem$ decays.

###  0.9.1 Mass dependence on kinematic quantities

We first measure the dependence of the regressed mass on reconstructed
kinematic quantities such as $p_{\mathrm{T},\,\Gamma}$ and $\eta_{\Gamma}$.
These studies have the caveat outlined in Sec. 0.8.2 concerning the
distortions in the regressed $\Pgpz$ invariant mass distribution coming from
jet hadronization. Figure 7 (left) shows a two-dimensional plot of the
regressed mass versus $p_{\mathrm{T},\,\Gamma}$ for
$20<p_{\mathrm{T},\,\Gamma}<35\GeV$. A clear band is observed that is
independent of $p_{\mathrm{T},\,\Gamma}$. We attribute this band to well-
isolated $\Pgpz\to\gamma\gamma$ decays, which are more prominent in this
relatively low-$p_{\mathrm{T},\,\Gamma}$ range. This is consistent with our
earlier results from simulated $\mathcal{A}\to\gamma\gamma$ decays, shown in
Fig. 5, albeit for a narrower $p_{\mathrm{T},\,\Gamma}$ range. A broadening of
the mass distribution for $p_{\mathrm{T},\,\Gamma}\gtrsim 30\GeV$ is also
visible in Fig. 7 (left). However, this is likely an artifact of the
discontinuous increase in the photon population of the selected sample, due to
the turn-on of the leading-$\pt$ threshold for the diphoton trigger.

Next, we study the dependence of the regressed mass on the reconstructed
$\eta_{\Gamma}$. As discussed earlier, the number of radiation lengths
traversed by an electromagnetic particle entering the ECAL barrel at
$\eta\approx 1.4$ is nearly fivefold that at $\eta\approx 0$ because of
differences in the underlying tracker material structure (described in Sec.
0.2). Thus, this study is a useful check on the sensitivity of the regressed
mass to the level of electromagnetic shower development in the
$\mathcal{A}\to\gamma\gamma$ energy deposits. As seen in Fig. 7 (right), the
regressed mass has noticeably better resolution in the central region
($\abs{\eta_{\Gamma}}\lesssim 0.5$) than in the forward regions
($\abs{\eta_{\Gamma}}\gtrsim 1$), as expected. The regressed mass distribution
also shows good continuity with respect to $\eta_{\Gamma}$. The dependence of
the regressed mass on the same kinematic quantities for simulated
$\PH\to\mathcal{A}\mathcal{A}\to 4\gamma$ events is presented in Appendix
.11.3, with similar conclusions.

Figure 7: Regressed mass from $\Pgpz\to\gamma\gamma$ data events vs.
$p_{\mathrm{T},\,\Gamma}$ (left) and $\eta_{\Gamma}$ (right). For both plots,
the regressed mass distributions are normalized in vertical slices of the
accompanying kinematic quantity to highlight the intrinsic dependence on the
quantity. The relative contribution over each vertical slice is given by the
color scale to the right of each plot.

###  0.9.2 Mass dependence on detector conditions

A critical question surrounding the end-to-end ML technique is how well it
accommodates mismodeled detector conditions, or even conditions unseen in the
training set; in particular, whether exposure to the full granularity of the
detector data results in an algorithm that is overly dependent on detector
conditions or the amount of pileup.

To address these questions using the same $\Pgpz\to\gamma\gamma$ data, we
study the regressed mass versus the mean number of interactions per bunch
crossing. Importantly, because of challenges with the LHC during the data-
taking period used in this study, the proton bunch scheme was significantly
altered in the latter half of the year. This resulted in the pileup
distribution being significantly skewed toward a higher number of interactions
per bunch crossing. This effect was not fully modeled in the simulated data
used to train the mass regressor. In spite of this, as shown in Fig. 8
(upper), we observe that both the peak and width of the regressed masses are
stable versus the amount of pileup. For various slices of data in the pileup
range from 15 to 50, we fit the regressed mass distribution in each slice to a
Gaussian-plus-quadratic function in the vicinity of the mass peak. The
variation in the position and width of the fitted mass peaks is less than 3%
and 9%, respectively.

We next investigate the stability of the regressed mass with respect to
changing detector conditions by comparing the regressed $\Pgpz\to\gamma\gamma$
mass spectrum at different times. In Fig. 8 (lower left), the mass spectrum is
plotted for the start, middle, and end of the 2017 data-taking period. During
these time segments, the electronic noise in the ECAL barrel increased by 25%.
Using the same fitting procedure described earlier, the positions and widths
of the peak in the latter two time segments are within 1 (middle) and 4%
(end). These differences are similar to those measured in these datasets using
established calibration techniques. As an additional check, in Fig. 8 (lower
right), we show the invariant mass spectrum separately for the entire 2017 and
2018 data-taking periods. Between the ends of these two data-taking periods,
the electronic noise in the ECAL barrel increased by about 10%. The positions
and widths of the $\Pgpz$ peak are consistent within uncertainties using a
similar fitting procedure.

Robustness to changes in detector conditions is thus a principal strength of
the end-to-end ML technique when using minimally processed detector data.
However, such robustness is notably degraded when training on clustered data,
as discussed in Appendix .11.1.

Figure 8: Upper: two-dimensional plot of the regressed mass for
$\Pgpz\to\gamma\gamma$ data events vs. the amount of pileup (PU). The mass
distribution is normalized in vertical slices of the amount of pileup. The
relative contribution over each vertical slice is given by the color scale to
the right of the plot. Lower left: the regressed mass distributions for the
start (gray circles), middle (blue squares), and end (red triangles) of data
taking during the year 2017. Lower right: the regressed mass distributions for
the 2017 (gray circles) and 2018 (blue squares) data-taking periods. The lower
two plots are normalized to unity and the vertical bars on the points show the
statistical uncertainties. The lower panel for the lower left plot gives the
ratio of distributions for the middle to the start (blue squares) and the end
to the start (red triangles) of the 2017 data-taking period. The lower panel
for the lower right plot gives the ratio (blue squares) for the 2018 and 2017
data-taking periods. The vertical bars on the points in both lower panels show
the statistical uncertainties in the numerator quantity, and the gray bands
give the similar uncertainty in the denominator quantity.

###  0.9.3 Mass dependence on data versus simulation

Finally, we compare the dependence of the mass regressor for events from data
versus simulation. If the relative mass resolution in data is worse than it is
in simulation, the significance of an observed mass peak in data would be
adversely affected. If there is a bias in the position of the mass peak in
data versus simulation, an inaccurate mass measurement would be made unless
the bias is corrected.

First, it is important to decouple data-versus-simulation mismodeling caused
by detector-related effects from that attributable to the collimation of jets
described in Sec. 0.8.2. An unbiased assessment of the mass regressor requires
a measurement of the detector-related mismodeling alone. Because of the
computational and logistical challenge of obtaining minimally processed
simulated QCD events with energetic $\Pgpz\to\gamma\gamma$, we analyze instead
the agreement between data and simulation using electrons from
$\PZ\to\Pep\Pem$ events. Electrons from $\PZ\to\Pep\Pem$ decays are produced
in abundance, and are reconstructed with good isolation and high purity. The
tag-and-probe method is used to select the electrons for both data and
simulation within the range $\abs{\eta_{\Pe}}<1.44$.

Although the electron is effectively massless in this energy regime, radiation
is produced from its bending in the CMS magnetic field. This causes the energy
in the seed crystal of the electron shower to be slightly smeared toward
neighboring crystals in the shower [39], similar to the pattern seen in
instrumentally merged $\mathcal{A}\to\gamma\gamma$ decays. As a result, the
regressed electron mass spectrum displays a peak at $m_{\Gamma}\approx
0.1\GeV$ that can be used to measure differences in the mass spectrum.

We parametrize the differences between data and simulation in terms of a
Gaussian relative mass scale $s_{\text{scale}}$ and smearing difference
$s_{\text{smear}}$. A scan is performed over different ($s_{\text{scale}}$,
$s_{\text{smear}}$) hypotheses, in steps of ($\Delta s_{\text{scale}}=4\times
10^{-3}$, $\Delta s_{\text{smear}}=0.4\MeV$). At each hypothesis, the value of
$m_{\Gamma,\,\mathrm{i}}$ for each electron candidate in the simulated sample
is then smeared using the probability distribution
$\mathcal{N}(s_{\text{scale}}\times
m_{\Gamma,\,\mathrm{i}},\,s_{\text{smear}})$, where $\mathcal{N}(\mu,\sigma)$
is a Gaussian function parametrized by mean $\mu$ and standard deviation
$\sigma$. The best fit mass scale and smearing between data and simulation is
then defined as the ($s_{\text{scale}}$, $s_{\text{smear}}$) hypothesis for
which the chi-square ($\chi^{2}$) test statistic between the mass distribution
in data and the transformed simulated sample is at a minimum. The definition
$\chi^{2}=\sum_{i}(h_{\mathrm{data,i}}-h_{\mathrm{MC,i}})^{2}/h_{\mathrm{MC,i}}$
is used, where $h_{\mathrm{data,i}}$ and $h_{\mathrm{MC,i}}$ denote the
normalized data and transformed simulation counts, respectively, at bin $i$ of
$m_{\Gamma}$. We determine the best fit value for the relative mass scale to
be $1.040$ and the best fit value for the mass difference is less than $\Delta
s_{\text{smear}}$. The contours of the $\chi^{2}$ scan over the scale and
smearing hypotheses are displayed in Fig. 9 (left). The resulting regressed
mass distributions for electrons in data versus simulation under the best fit
hypothesis are shown in Fig. 9 (right).

After the difference in mass scale is taken into account, we find the core of
the mass distribution to be well modeled in the simulation, as seen in Fig. 9
(right). Although there are some systematic differences in the high-side tail
of the mass distribution between data and simulation, these deviations will be
less relevant in an application where data are limited in the tails and
statistical uncertainties are larger. Indeed, the significance of an observed
mass peak is primarily driven by the core of the peak and not the tail
contribution. Thus, the lack of any significant mass smearing implies the full
mass resolution of the regressor is preserved in data.

Figure 9: The agreement in the regressed $m_{\Gamma}$ spectrum between
electrons in data versus simulation. Left: contours of 68% (solid line) and
95% (dotted line) confidence level () in the $\chi^{2}$ test statistic as a
function of the ($s_{\text{scale}}$, $s_{\text{smear}}$) hypothesis. The best
fit point ($s_{\text{scale}}=1.040$, $s_{\text{smear}}=0\MeV$) is indicated by
the red diamond. Right: the regressed mass distributions in data (points) and
the best fit Monte Carlo (MC) simulation (blue region) for electrons from
$\PZ\to\Pep\Pem$ events. The difference between the simulated distribution
under the null scale and smearing hypothesis versus the best fit hypothesis
(Syst) is plotted as a green band. Each of the distributions are normalized to
unity, including samples outside $m_{\mathcal{A}}\text{-ROI}$. Statistical
uncertainties in the data distribution are negligible. The lower panel shows
the ratio of the data to the simulation under the best fit hypothesis
(points). The statistical uncertainties in the latter are plotted as a blue
band. The ratio of the simulated distribution for the null to the best fit
hypothesis is displayed as a green band.

##  0.10 Summary

A novel end-to-end particle reconstruction technique is introduced that is
able to serve as a general strategy for reconstructing decays of boosted
particles. The method involves the use of deep learning algorithms that do not
rely on particle-flow objects, but are trained directly on minimally processed
detector-level data to reconstruct particle properties of interest. Using
simulated $\mathcal{A}\to\gamma\gamma$ decays in the CMS electromagnetic
calorimeter, where $\mathcal{A}$ is a hypothetical scalar particle, the
technique is used to reconstruct the diphoton invariant mass over a wide range
of photon-merging scales, corresponding to Lorentz boosts
$\gamma_{\mathrm{L}}=$ 60–600. Furthermore, when domain continuation is
incorporated in the training, the most challenging parts of the
$\mathcal{A}\to\gamma\gamma$ phase space ($\gamma_{\mathrm{L}}>150$) are made
accessible. The resulting end-to-end mass regressor, in addition to being a
highly sensitive tool, also has a robust response. Based on studies using
simulated samples and collision data, a stable mass response is observed in
various kinematic, beam, and detector conditions.

Studies are under way to employ the end-to-end mass regressor in
$\Pgpz\to\gamma\gamma$ reconstruction and in searches for new physics, such as
$\PH/\PX\to\mathcal{A}\mathcal{A}\to 4\gamma$, where $\PH$ is the Higgs boson
and $\PX$ is some new heavy resonance. Furthermore, although demonstrated for
the specific case of mass reconstruction of a boosted particle decaying to
photons, the end-to-end deep learning technique can be used for arbitrary
decay modes by including additional subdetector information. The technique is
not restricted to mass reconstruction; other particle properties, particularly
those that are currently resolution constrained, such as the lifetime of
particles in long-lived decays, stand to benefit significantly. It can
potentially be used instead of particle-flow techniques to reconstruct the
four-momenta of resolved decays. Sensitivity gains in these cases, however,
are likely to be more modest, and must be balanced against the challenges of
accessing the wider event content of the CMS datasets.

The technique of training via domain continuation can be exploited
independently of the end-to-end method. Indeed, it is applied to the training
of the photon neural network used as a benchmark. The application of this
technique is not specific to high energy physics. It should be applicable in
any machine learning regression task that seeks to regress a quantity near a
boundary, physical or otherwise, that is close in scale to its resolution.

When end-to-end particle reconstruction is combined with domain continuation,
diphoton showers that are completely unresolved can now be reconstructed. This
is a regime inaccessible to existing reconstruction techniques, and it is the
first time a technique has been developed to achieve this important goal.

###### Acknowledgements.

We congratulate our colleagues in the CERN accelerator departments for the
excellent performance of the LHC and thank the technical and administrative
staffs at CERN and at other CMS institutes for their contributions to the
success of the CMS effort. In addition, we gratefully acknowledge the
computing centers and personnel of the Worldwide LHC Computing Grid and other
centers for delivering so effectively the computing infrastructure essential
to our analyses. Finally, we acknowledge the enduring support for the
construction and operation of the LHC, the CMS detector, and the supporting
computing infrastructure provided by the following funding agencies: BMBWF and
FWF (Austria); FNRS and FWO (Belgium); CNPq, CAPES, FAPERJ, FAPERGS, and
FAPESP (Brazil); MES and BNSF (Bulgaria); CERN; CAS, MoST, and NSFC (China);
MINCIENCIAS (Colombia); MSES and CSF (Croatia); RIF (Cyprus); SENESCYT
(Ecuador); MoER, ERC PUT and ERDF (Estonia); Academy of Finland, MEC, and HIP
(Finland); CEA and CNRS/IN2P3 (France); BMBF, DFG, and HGF (Germany); GSRI
(Greece); NKFIH (Hungary); DAE and DST (India); IPM (Iran); SFI (Ireland);
INFN (Italy); MSIP and NRF (Republic of Korea); MES (Latvia); LAS (Lithuania);
MOE and UM (Malaysia); BUAP, CINVESTAV, CONACYT, LNS, SEP, and UASLP-FAI
(Mexico); MOS (Montenegro); MBIE (New Zealand); PAEC (Pakistan); MES and NSC
(Poland); FCT (Portugal); MESTD (Serbia); MCIN/AEI and PCTI (Spain); MOSTR
(Sri Lanka); Swiss Funding Agencies (Switzerland); MST (Taipei); MHESI and
NSTDA (Thailand); TUBITAK and TENMAK (Turkey); NASU (Ukraine); STFC (United
Kingdom); DOE and NSF (USA). Individuals have received support from the Marie-
Curie program and the European Research Council and Horizon 2020 Grant,
contract Nos. 675440, 724704, 752730, 758316, 765710, 824093, 884104, and COST
Action CA16108 (European Union); the Leventis Foundation; the Alfred P. Sloan
Foundation; the Alexander von Humboldt Foundation; the Belgian Federal Science
Policy Office; the Fonds pour la Formation à la Recherche dans l’Industrie et
dans l’Agriculture (FRIA-Belgium); the Agentschap voor Innovatie door
Wetenschap en Technologie (IWT-Belgium); the F.R.S.-FNRS and FWO (Belgium)
under the “Excellence of Science – EOS” – be.h project n. 30820817; the
Beijing Municipal Science & Technology Commission, No. Z191100007219010; the
Ministry of Education, Youth and Sports (MEYS) of the Czech Republic; the
Hellenic Foundation for Research and Innovation (HFRI), Project Number 2288
(Greece); the Deutsche Forschungsgemeinschaft (DFG), under Germany’s
Excellence Strategy – EXC 2121 “Quantum Universe” – 390833306, and under
project number 400140256 - GRK2497; the Hungarian Academy of Sciences, the New
National Excellence Program - ÚNKP, the NKFIH research grants K 124845, K
124850, K 128713, K 128786, K 129058, K 131991, K 133046, K 138136, K 143460,
K 143477, 2020-2.2.1-ED-2021-00181, and TKP2021-NKTA-64 (Hungary); the Council
of Science and Industrial Research, India; the Latvian Council of Science; the
Ministry of Education and Science, project no. 2022/WK/14, and the National
Science Center, contracts Opus 2021/41/B/ST2/01369 and 2021/43/B/ST2/01552
(Poland); the Fundação para a Ciência e a Tecnologia, grant CEECIND/01334/2018
(Portugal); the National Priorities Research Program by Qatar National
Research Fund; MCIN/AEI/10.13039/501100011033, ERDF “a way of making Europe”,
and the Programa Estatal de Fomento de la Investigación Científica y Técnica
de Excelencia María de Maeztu, grant MDM-2017-0765 and Programa Severo Ochoa
del Principado de Asturias (Spain); the Chulalongkorn Academic into Its 2nd
Century Project Advancement Project, and the National Science, Research and
Innovation Fund via the Program Management Unit for Human Resources &
Institutional Development, Research and Innovation, grant B05F650021
(Thailand); the Kavli Foundation; the Nvidia Corporation; the SuperMicro
Corporation; the Welch Foundation, contract C-1845; and the Weston Havens
Foundation (USA).

## References

  * [1] A. Abdesselam et al., “Boosted objects: a probe of beyond the standard model physics”,  Eur. Phys. J. C 71 (2011) 1661, 10.1140/epjc/s10052-011-1661-y, arXiv:1012.5412.
  * [2] CMS Collaboration, “Particle-flow reconstruction and global event description with the CMS detector”,  JINST 12 (2017) P10003, 10.1088/1748-0221/12/10/P10003, arXiv:1706.04965.
  * [3] ATLAS Collaboration, “Jet reconstruction and performance using particle flow with the ATLAS detector”,  Eur. Phys. J. C 77 (2017) 466, 10.1140/epjc/s10052-017-5031-2, arXiv:1703.10485.
  * [4] CMS Collaboration, “Measurement of the jet mass distribution and top quark mass in hadronic decays of boosted top quarks in pp collisions at $\sqrt{s}=13$ TeV”,  Phys. Rev. Lett. 124 (2020) 202001, 10.1103/PhysRevLett.124.202001, arXiv:1911.03800.
  * [5] CMS Collaboration, “Inclusive search for a highly boosted Higgs boson decaying to a bottom quark-antiquark pair”,  Phys. Rev. Lett. 120 (2018) 071802, 10.1103/PhysRevLett.120.071802, arXiv:1709.05543.
  * [6] ATLAS Collaboration, “Measurements of $\ttbar$ differential cross-sections of highly boosted top quarks decaying to all-hadronic final states in pp collisions at $\sqrt{s}=13$ TeV using the ATLAS detector”,  Phys. Rev. D 98 (2018) 012003, 10.1103/PhysRevD.98.012003, arXiv:1801.02052.
  * [7] ATLAS Collaboration, “Identification of boosted Higgs bosons decaying into $\mathrm{b}$-quark pairs with the ATLAS detector at 13 TeV”,  Eur. Phys. J. C 79 (2019) 836, 10.1140/epjc/s10052-019-7335-x, arXiv:1906.11005.
  * [8] CMS Collaboration, “Performance of photon reconstruction and identification with the CMS detector in proton-proton collisions at $\sqrt{s}=8$ TeV”,  JINST 10 (2015) P08010, 10.1088/1748-0221/10/08/P08010, arXiv:1502.02702.
  * [9] D. Curtin et al., “Exotic decays of the 125 GeV Higgs boson”,  Phys. Rev. D 90 (2014) 075004, 10.1103/PhysRevD.90.075004, arXiv:1312.4992.
  * [10] N. Toro and I. Yavin, “Multiphotons and photon jets from new heavy vector bosons”,  Phys. Rev. D 86 (2012) 055005, 10.1103/PhysRevD.86.055005, arXiv:1202.6377.
  * [11] M. Bauer, M. Neubert, and A. Thamm, “Collider probes of axion-like particles”,  JHEP 12 (2017) 044, 10.1007/jhep12(2017)044, arXiv:1708.00443.
  * [12] B. A. Dobrescu, G. Landsberg, and K. T. Matchev, “Higgs boson decays to $\mathrm{CP}$-odd scalars at the Fermilab Tevatron and beyond”,  Phys. Rev. D 63 (2001) 075003, 10.1103/PhysRevD.63.075003, arXiv:hep-ph/0005308.
  * [13] CMS Collaboration, “Observation of the diphoton decay of the Higgs boson and measurement of its properties”,  Eur. Phys. J. C 74 (2014) 3076, 10.1140/epjc/s10052-014-3076-z, arXiv:1407.0558.
  * [14] CMS Collaboration, “Combined measurements of Higgs boson couplings in proton-proton collisions at $\sqrt{s}=13$ TeV”,  Eur. Phys. J. C 79 (2019) 421, 10.1140/epjc/s10052-019-6909-y, arXiv:1809.10733.
  * [15] M. Andrews, M. Paulini, S. Gleyzer, and B. Poczos, “End-to-end physics event classification with CMS open data: applying image-based deep learning to detector data for the direct classification of collision events at the LHC”,  Comput. Softw. Big Sci. 4 (2020) 6, 10.1007/s41781-020-00038-8, arXiv:1807.11916.
  * [16] CMS Collaboration, “Pileup mitigation at CMS in 13 TeV data”,  JINST 15 (2020) P09018, 10.1088/1748-0221/15/09/p09018, arXiv:2003.00503.
  * [17] CMS Collaboration, “The CMS experiment at the CERN LHC”,  JINST 3 (2008) S08004, 10.1088/1748-0221/3/08/S08004.
  * [18] G. Kasieczka, T. Plehn, M. Russell, and T. Schell, “Deep-learning top taggers or the end of QCD?”,  JHEP 05 (2017) 006, 10.1007/JHEP05(2017)006, arXiv:1701.08784.
  * [19] ATLAS Collaboration, “Performance of top-quark and $\mathrm{W}$-boson tagging with ATLAS in Run 2 of the LHC”,  Eur. Phys. J. C 79 (2019) 375, 10.1140/epjc/s10052-019-6847-8, arXiv:1808.07858.
  * [20] X. Ju and B. Nachman, “Supervised jet clustering with graph neural networks for Lorentz boosted bosons”,  Phys. Rev. D 102 (2020) 075014, 10.1103/PhysRevD.102.075014, arXiv:2008.06064.
  * [21] P. T. Komiske, E. M. Metodiev, and J. Thaler, “Energy flow networks: deep sets for particle jets”,  JHEP 01 (2019) 121, 10.1007/JHEP01(2019)121, arXiv:1810.05165.
  * [22] H. Qu and L. Gouskos, “ParticleNet: jet tagging via particle clouds”,  Phys. Rev. D 101 (2020) 056019, 10.1103/PhysRevD.101.056019, arXiv:1902.08570.
  * [23] CMS Collaboration, “Identification of heavy-flavour jets with the CMS detector in pp collisions at 13 TeV”,  JINST 13 (2017) P05011, 10.1088/1748-0221/13/05/P05011, arXiv:1712.07158.
  * [24] CMS Collaboration, “A deep neural network for simultaneous estimation of $\mathrm{b}$ quark energy and resolution”,  Comput. Softw. Big Sci. 4 (2020) 10, 10.1007/s41781-020-00041-z, arXiv:1912.06046.
  * [25] CMS Collaboration, “A deep neural network to search for new long-lived particles decaying to jets”,  Mach. Learn. Sci. Tech. 1 (2020) 035012, 10.1088/2632-2153/ab9023, arXiv:1912.12238.
  * [26] A. Butter, G. Kasieczka, T. Plehn, and M. Russell, “Deep-learned top tagging with a Lorentz layer”,  SciPost Phys. 5 (2018) 028, 10.21468/SciPostPhys.5.3.028, arXiv:1707.08966.
  * [27] G. Louppe, K. Cho, C. Becot, and K. Cranmer, “QCD-aware recursive neural networks for jet physics”,  JHEP 01 (2019) 057, 10.1007/JHEP01(2019)057, arXiv:1702.00748.
  * [28] A. Krizhevsky, I. Sutskever, and G. E. Hinton, “ImageNet classification with deep convolutional neural networks”,  Commun. ACM 60 (2017) 84, 10.1145/3065386.
  * [29] A. Esteva et al., “Dermatologist-level classification of skin cancer with deep neural networks”,  Nature 542 (2017) 115, 10.1038/nature21056.
  * [30] D. Silver et al., “A general reinforcement learning algorithm that masters chess, shogi, and Go through self-play”,  Science 362 (2018) 1140, 10.1126/science.aar6404, arXiv:1712.01815.
  * [31] A. W. Senior et al., “Improved protein structure prediction using potentials from deep learning”,  Nature 577 (2020) 706, 10.1038/s41586-019-1923-7.
  * [32] A. Aurisano et al., “A convolutional neural network neutrino event classifier”,  JINST 11 (2016) P09001, 10.1088/1748-0221/11/09/P09001, arXiv:1604.01444.
  * [33] MicroBooNE Collaboration, “Deep neural network for pixel-level electromagnetic particle identification in the MicroBooNE liquid argon time projection chamber”,  Phys. Rev. D 99 (2019) 092001, 10.1103/PhysRevD.99.092001, arXiv:1808.07269.
  * [34] L. Uboldi et al., “Extracting low energy signals from raw LArTPC waveforms using deep learning techniques – a proof of concept”,  Nucl. Instrum. Meth. A 1028 (2022) 166371, 10.1016/j.nima.2022.166371, arXiv:2106.09911.
  * [35] M. Andrews et al., “End-to-end jet classification of quarks and gluons with the CMS open data”,  Nucl. Instrum. Meth. A 977 (2020) 164304, 10.1016/j.nima.2020.164304, arXiv:1902.08276.
  * [36] L. De Oliveira, B. Nachman, and M. Paganini, “Electromagnetic showers beyond shower shapes”,  Nucl. Instrum. Meth. A 951 (2020) 162879, 10.1016/j.nima.2019.162879, arXiv:1806.05667.
  * [37] X. Ju et al., “Graph neural networks for particle reconstruction in high energy physics detectors”, in  33rd Ann. Conf. Neural Information Processing Systems.  2020\.  arXiv:2003.11603.
  * [38] S. R. Qasim, J. Kieseler, Y. Iiyama, and M. Pierini, “Learning representations of irregular particle-detector geometry with distance-weighted graph networks”,  Eur. Phys. J. C 79 (2019) 608, 10.1140/epjc/s10052-019-7113-9, arXiv:1902.07987.
  * [39] M. Andrews, M. Paulini, S. Gleyzer, and B. Poczos, “End-to-End event classification of high-energy physics data”,  J. Phys. Conf. Ser. 1085 (2018) 042022, 10.1088/1742-6596/1085/4/042022.
  * [40] CMS Collaboration, “The CMS trigger system”,  JINST 12 (2017) P01020, 10.1088/1748-0221/12/01/P01020, arXiv:1609.02366.
  * [41] CMS Collaboration, “Measurement of the inclusive $\mathrm{W}$ and $\mathrm{Z}$ production cross sections in pp collisions at $\sqrt{s}=7$ TeV”,  JHEP 10 (2011) 132, 10.1007/JHEP10(2011)132, arXiv:1107.4789.
  * [42] K. He, X. Zhang, S. Ren, and J. Sun, “Deep residual learning for image recognition”,  2016 IEEE Conf. Computer Vision and Pattern Recognition (2016) 10.1109/CVPR.2016.90, arXiv:1512.03385.
  * [43] D. P. Kingma and J. Ba, “Adam: a method for stochastic optimization”, in  3rd Int. Conf. for Learning Representations.  2015\.  arXiv:1412.6980.
  * [44] The ATLAS Collaboration, The CMS Collaboration, The LHC Higgs Combination Group, “Procedure for the LHC Higgs boson search combination in Summer 2011”, Technical Report CMS-NOTE-2011-005, ATL-PHYS-PUB-2011-11, 2011.
  * [45] GlueX Collaboration, “Search for photoproduction of axion-like particles at GlueX”, 2021. arXiv:2109.13439.

##  .11 Supplementary studies

###  .11.1 Minimally processed versus clustered data

We attribute the robustness of the end-to-end ML mass regressor (discussed in
Sec. 0.9) to the use of minimally processed (all) rather than clustered
(clustered) detector data. As shown in Fig. A.1, the PF clustering algorithm
filters out low-energy deposits and, under certain situations, may completely
remove all the deposits associated with the lower-energy photon from the
$\mathcal{A}\to\gamma\gamma$ decay. For example, in Fig. A.1 (left), showing
the minimally processed data, the lower-energy photon is visible on the lower
left of the core photon, at a distance of approximately $7$ ECAL crystals. In
the clustered data on the right plot, the deposits associated with the lower-
energy photon have been dropped, along with other, isolated low-energy
deposits.

Figure A.1: A typical $\mathcal{A}\to\gamma\gamma$ decay using minimally
processed (left) and clustered (right) data. The energy distributions are
plotted in relative ECAL crystal index coordinates of the pseudorapidity
$\eta$ versus the azimuthal angle $\phi$ and color coded by energy.

The impact of using minimally processed versus clustered data is seen in Fig.
A.2, which compares the effect of training on all (upper row) versus clustered
data (lower row). The regressed mass spectra for shower-merged and barely
resolved boosts are displayed in the left and right columns, respectively. For
each scenario, we regress the mass of a sample constructed from all (blue
circles) versus clustered (red squares) data to compare how well each mass
regressor extrapolates to the other’s domain. For the mass regressor trained
on minimally processed data (upper row), despite the differences in input
image (cf. Fig. A.1), we see no evidence of a shift in the mass peak in either
boost regime. This is not the case for the mass regressor trained on clustered
data (lower row), which exhibits a shift when applied outside of its domain.
This suggests it is desirable not to filter the detector data beforehand so
that the mass regressor learns to suppress low-energy deposits. Without this
opportunity, the mass regressor becomes more susceptible to variations in the
data.

In addition, the loss of the lower-energy photon at resolved boosts (right
column) leads to $\mathcal{A}\to\gamma\gamma$ decays being incorrectly
reconstructed as photons, causing both a drop in reconstruction efficiency at
the correct mass value ($m_{\Gamma}=1\GeV$) and a buildup of samples at the
wrong mass ($m_{\Gamma}\approx 0\GeV$). Even if minimally processed data are
presented to the mass regressor trained on clustered data (lower right, blue
circles), the lost efficiency at the correct mass value is still not
recovered. The use of minimally processed data is thus vital to maximizing the
capabilities of the end-to-end ML-based technique.

Figure A.2: Regressed mass spectra for the mass regressor trained on minimally
processed data (upper) versus clustered data (lower) at shower-merged boosts
(left) and barely resolved boosts (right). For each scenario, the mass
regressor is run on the same set of $\mathcal{A}\to\gamma\gamma$ decays,
composed either of minimally processed (blue circles, all) or clustered (red
squares, clustered) data. The vertical bars on the points give the statistical
uncertainties and the vertical dotted line shows the input $m_{\mathcal{A}}$
value.

###  .11.2 Hadronization effects

Although the end-to-end method is able to clearly reconstruct $\Pgpz$
candidates in hadronic jets, the $\Pgh$ resonance in jets appears much less
pronounced compared with that reconstructed by the $3{\times}3$ method (cf.
Fig. 6). At the particle energies that we study, the weaker $\Pgh$ resonance
from the end-to-end method is due to the presence of additional particles
collimated in the jet. As noted in Sec. 0.8.2, because the $3{\times}3$ method
uses only a window of $3{\times}3$ crystals, it is less exposed to these
effects. To illustrate this point, in Fig. A.3, we select a representative
merged photon candidate reconstructed by the $3{\times}3$ algorithm with a
mass close to the $\Pgh$ resonance.

Figure A.3: A typical hadronic jet sample reconstructed by the $3{\times}3$
algorithm with a mass near the $\Pgh$ meson peak, using minimally processed
(all, left) and $3{\times}3$ clustered ($3{\times}3$, right) data. The energy
distributions are plotted in relative ECAL crystal index coordinates of the
azimuthal angle $\phi$ versus the pseudorapidity $\eta$ and color coded by
energy.

The ECAL energy pattern associated with the minimally processed detector data
(all), as used by the end-to-end technique, is plotted on the left. The
corresponding energy pattern, after applying the $3{\times}3$ clustering
($3{\times}3$), is shown on the right. We have verified that, by applying the
end-to-end method on candidates within a mass window of the $\Pgh$ peak built
using only $3{\times}3$ clusters, we are able to reconstruct an $\Pgh$ mass
peak of similar size as for the $3{\times}3$ algorithm. The effects of
hadronization are also relevant for $\Pgpz$ reconstruction in jets. However,
the higher production rate of $\Pgpz$ mesons permits the use of tighter photon
identification criteria (cf. Sec. 0.8.2), in order to maximize the isolated
$\Pgpz$-like component.

###  .11.3 Mass dependence in simulated samples

To complement the mass dependence studies performed on data using
$\Pgpz\to\gamma\gamma$ decays and electrons, we present in Fig. A.4 similar
studies for $\mathcal{A}\to\gamma\gamma$ decays from simulated
$\PH\to\mathcal{A}\mathcal{A}\to 4\gamma$ events passing our event and photon
selection criteria. Two-dimensional plots are shown of the regressed mass
versus the generated $p_{\mathrm{T,\,\mathcal{A}}}$ (left),
$\eta_{\mathcal{A}}$ (center), and amount of pileup (right) for barely
resolved (upper), shower merged (middle), and instrumentally merged (lower)
decay products. There is good stability in the regressed mass response
throughout the explored phase space and the varying beam conditions.

Figure A.4: Regressed mass spectra vs. generated
$p_{\mathrm{T,\,\mathcal{A}}}$ (left), generated $\eta_{\mathcal{A}}$
(center), and amount of pileup (right), for $\mathcal{A}\to\gamma\gamma$
decays that are barely resolved (upper), shower merged (middle), or
instrumentally merged (lower). In all plots, the regressed mass distribution
is normalized in vertical slices of the quantity of interest. The relative
contribution over each vertical slice is given by the color scale to the right
of each plot.

##  .12 The CMS Collaboration

Yerevan Physics Institute, Yerevan, Armenia A. Tumasyan10009-0000-0684-6742

Institut für Hochenergiephysik, Vienna, Austria W. Adam0000-0001-9099-4341,
J.W. Andrejkovic, T. Bergauer0000-0002-5786-0293, S.
Chatterjee0000-0003-2660-0349, K. Damanakis0000-0001-5389-2872, M.
Dragicevic0000-0003-1967-6783, A. Escalante Del Valle0000-0002-9702-6359, R.
Frühwirth20000-0002-0054-3369, M. Jeitler20000-0002-5141-9560, N.
Krammer0000-0002-0548-0985, L. Lechner0000-0002-3065-1141, D.
Liko0000-0002-3380-473X, I. Mikulec0000-0003-0385-2746, P. Paulitsch, F.M.
Pitters, J. Schieck20000-0002-1058-8093, R. Schöfbeck0000-0002-2332-8784, D.
Schwarz0000-0002-3821-7331, S. Templ0000-0003-3137-5692, W.
Waltenberger0000-0002-6215-7228, C.-E. Wulz20000-0001-9226-5812

Universiteit Antwerpen, Antwerpen, Belgium M.R. Darwish30000-0003-2894-2377,
E.A. De Wolf, T. Janssen0000-0002-3998-4081, T. Kello4, A.
Lelek0000-0001-5862-2775, H. Rejeb Sfar, P. Van Mechelen0000-0002-8731-9051,
S. Van Putte0000-0003-1559-3606, N. Van Remortel0000-0003-4180-8199

Vrije Universiteit Brussel, Brussel, Belgium E.S. Bols0000-0002-8564-8732, J.
D’Hondt0000-0002-9598-6241, A. De Moor0000-0001-5964-1935, M.
Delcourt0000-0001-8206-1787, H. El Faham0000-0001-8894-2390, S.
Lowette0000-0003-3984-9987, S. Moortgat0000-0002-6612-3420, A.
Morton0000-0002-9919-3492, D. Müller0000-0002-1752-4527, A.R.
Sahasransu0000-0003-1505-1743, S. Tavernier0000-0002-6792-9522, W. Van
Doninck, D. Vannerom0000-0002-2747-5095

Université Libre de Bruxelles, Bruxelles, Belgium D. Beghin, B.
Clerbaux0000-0001-8547-8211, G. De Lentdecker0000-0001-5124-7693, L.
Favart0000-0003-1645-7454, K. Lee0000-0003-0808-4184, M.
Mahdavikhorrami0000-0002-8265-3595, I. Makarenko0000-0002-8553-4508, S.
Paredes0000-0001-8487-9603, L. Pétré, A. Popov0000-0002-1207-0984, N. Postiau,
E. Starling0000-0002-4399-7213, L. Thomas0000-0002-2756-3853, M. Vanden
Bemden, C. Vander Velde0000-0003-3392-7294, P. Vanlaer0000-0002-7931-4496

Ghent University, Ghent, Belgium D. Dobur0000-0003-0012-4866, J.
Knolle0000-0002-4781-5704, L. Lambrecht0000-0001-9108-1560, G. Mestdach, M.
Niedziela0000-0001-5745-2567, C. Rendón, C. Roskas0000-0002-6469-959X, A.
Samalan, K. Skovpen0000-0002-1160-0621, M. Tytgat0000-0002-3990-2074, N. Van
Den Bossche0000-0003-2973-4991, B. Vermassen, L. Wezenbeek0000-0001-6952-891X

Université Catholique de Louvain, Louvain-la-Neuve, Belgium A.
Benecke0000-0003-0252-3609, A. Bethani0000-0002-8150-7043, G.
Bruno0000-0001-8857-8197, F. Bury0000-0002-3077-2090, C.
Caputo0000-0001-7522-4808, P. David0000-0001-9260-9371, C.
Delaere0000-0001-8707-6021, I.S. Donertas0000-0001-7485-412X, A.
Giammanco0000-0001-9640-8294, K. Jaffel0000-0001-7419-4248, Sa.
Jain0000-0001-5078-3689, V. Lemaitre, K. Mondal0000-0001-5967-1245, J.
Prisciandaro, A. Taliercio0000-0002-5119-6280, T.T. Tran0000-0003-3060-350X,
P. Vischia0000-0002-7088-8557, S. Wertz0000-0002-8645-3670

Centro Brasileiro de Pesquisas Fisicas, Rio de Janeiro, Brazil G.A.
Alves0000-0002-8369-1446, C. Hensel0000-0001-8874-7624, A.
Moraes0000-0002-5157-5686, P. Rebello Teles0000-0001-9029-8506

Universidade do Estado do Rio de Janeiro, Rio de Janeiro, Brazil W.L. Aldá
Júnior0000-0001-5855-9817, M. Alves Gallo Pereira0000-0003-4296-7028, M.
Barroso Ferreira Filho0000-0003-3904-0571, H. Brandao
Malbouisson0000-0002-1326-318X, W. Carvalho0000-0003-0738-6615, J.
Chinellato5, E.M. Da Costa0000-0002-5016-6434, G.G. Da
Silveira60000-0003-3514-7056, D. De Jesus Damiao0000-0002-3769-1680, V. Dos
Santos Sousa0000-0002-4681-9340, S. Fonseca De Souza0000-0001-7830-0837, J.
Martins70000-0002-2120-2782, C. Mora Herrera0000-0003-3915-3170, K. Mota
Amarilo0000-0003-1707-3348, L. Mundim0000-0001-9964-7805, H.
Nogima0000-0001-7705-1066, A. Santoro, S.M. Silva Do
Amaral0000-0002-0209-9687, A. Sznajder0000-0001-6998-1108, M.
Thiel0000-0001-7139-7963, F. Torres Da Silva De Araujo80000-0002-4785-3057, A.
Vilela Pereira0000-0003-3177-4626

Universidade Estadual Paulista, Universidade Federal do ABC, São Paulo, Brazil
C.A. Bernardes60000-0001-5790-9563, L. Calligaris0000-0002-9951-9448, E.M.
Gregores0000-0003-0205-1672, D. S. Lemos0000-0003-1982-8978, P.G.
Mercadante0000-0001-8333-4302, S.F. Novaes0000-0003-0471-8549, Sandra S.
Padula0000-0003-3071-0559, T.R. Fernandez Perez Tomei0000-0002-1809-5226

Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of
Sciences, Sofia, Bulgaria A. Aleksandrov0000-0001-6934-2541, G.
Antchev0000-0003-3210-5037, R. Hadjiiska0000-0003-1824-1737, P.
Iaydjiev0000-0001-6330-0607, M. Misheva0000-0003-4854-5301, M. Rodozov, M.
Shopova0000-0001-6664-2493, G. Sultanov0000-0002-8030-3866

University of Sofia, Sofia, Bulgaria A. Dimitrov0000-0003-2899-701X, T.
Ivanov0000-0003-0489-9191, L. Litov0000-0002-8511-6883, B.
Pavlov0000-0003-3635-0646, P. Petkov0000-0002-0420-9480, A. Petrov

Beihang University, Beijing, China T. Cheng0000-0003-2954-9315, T. Javaid9, M.
Mittal0000-0002-6833-8521, L. Yuan0000-0002-6719-5397

Department of Physics, Tsinghua University, Beijing, China M.
Ahmad0000-0001-9933-995X, G. Bauer, C. Dozen100000-0002-4301-634X, Z.
Hu0000-0001-8209-4343, Y. Wang, K. Yi11,12

Institute of High Energy Physics, Beijing, China E. Chapon0000-0001-6968-9828,
G.M. Chen90000-0002-2629-5420, H.S. Chen90000-0001-8672-8227, M.
Chen0000-0003-0489-9669, F. Iemmi0000-0001-5911-4051, A.
Kapoor0000-0002-1844-1504, H. Liao0000-0002-0124-6999, Z.-A.
Liu130000-0002-2896-1386, V. Milosevic0000-0002-1173-0696, F.
Monti0000-0001-5846-3655, R. Sharma0000-0003-1181-1426, J.
Tao0000-0003-2006-3490, J. Thomas-Wilsker0000-0003-1293-4153, J.
Wang0000-0002-3103-1083, H. Zhang0000-0001-8843-5209, J.
Zhao0000-0001-8365-7726

State Key Laboratory of Nuclear Physics and Technology, Peking University,
Beijing, China A. Agapitos0000-0002-8953-1232, Y. An0000-0003-1299-1879, Y.
Ban0000-0002-1912-0374, C. Chen, A. Levin0000-0001-9565-4186, Q.
Li0000-0002-8290-0517, X. Lyu, Y. Mao, S.J. Qian0000-0002-0630-481X, D.
Wang0000-0002-9013-1199, J. Xiao0000-0002-7860-3958, H. Yang

Sun Yat-Sen University, Guangzhou, China M. Lu0000-0002-6999-3931, Z.
You0000-0001-8324-3291

Institute of Modern Physics and Key Laboratory of Nuclear Physics and Ion-beam
Application (MOE) - Fudan University, Shanghai, China X.
Gao40000-0001-7205-2318, D. Leggat, H. Okawa0000-0002-2548-6567, Y.
Zhang0000-0002-4554-2554

Zhejiang University, Hangzhou, Zhejiang, China Z. Lin0000-0003-1812-3474, M.
Xiao0000-0001-9628-9336

Universidad de Los Andes, Bogota, Colombia C. Avila0000-0002-5610-2693, A.
Cabrera0000-0002-0486-6296, C. Florez0000-0002-3222-0249, J.
Fraga0000-0002-5137-8543

Universidad de Antioquia, Medellin, Colombia J. Mejia
Guisao0000-0002-1153-816X, F. Ramirez0000-0002-7178-0484, J.D. Ruiz
Alvarez0000-0002-3306-0363

University of Split, Faculty of Electrical Engineering, Mechanical Engineering
and Naval Architecture, Split, Croatia D. Giljanovic0009-0005-6792-6881, N.
Godinovic0000-0002-4674-9450, D. Lelas0000-0002-8269-5760, I.
Puljak0000-0001-7387-3812

University of Split, Faculty of Science, Split, Croatia Z. Antunovic, M.
Kovac0000-0002-2391-4599, T. Sculac0000-0002-9578-4105

Institute Rudjer Boskovic, Zagreb, Croatia V. Brigljevic0000-0001-5847-0062,
D. Ferencek0000-0001-9116-1202, D. Majumder0000-0002-7578-0027, M.
Roguljic0000-0001-5311-3007, A. Starodumov140000-0001-9570-9255, T.
Susa0000-0001-7430-2552

University of Cyprus, Nicosia, Cyprus A. Attikis0000-0002-4443-3794, K.
Christoforou0000-0003-2205-1100, G. Kole0000-0002-3285-1497, M.
Kolosova0000-0002-5838-2158, S. Konstantinou0000-0003-0408-7636, J.
Mousa0000-0002-2978-2718, C. Nicolaou, F. Ptochos0000-0002-3432-3452, P.A.
Razis0000-0002-4855-0162, H. Rykaczewski, H. Saka0000-0001-7616-2573

Charles University, Prague, Czech Republic M. Finger Jr.140000-0003-3155-2484,
M. Finger140000-0002-7828-9970, A. Kveton0000-0001-8197-1914

Escuela Politecnica Nacional, Quito, Ecuador E. Ayala0000-0002-0363-9198

Universidad San Francisco de Quito, Quito, Ecuador E. Carrera
Jarrin0000-0002-0857-8507

Academy of Scientific Research and Technology of the Arab Republic of Egypt,
Egyptian Network of High Energy Physics, Cairo, Egypt H.
Abdalla150000-0002-4177-7209, Y. Assran16,17

Center for High Energy Physics (CHEP-FU), Fayoum University, El-Fayoum, Egypt
A. Lotfy0000-0003-4681-0079, M.A. Mahmoud0000-0001-8692-5458

National Institute of Chemical Physics and Biophysics, Tallinn, Estonia S.
Bhowmik0000-0003-1260-973X, R.K. Dewanjee0000-0001-6645-6244, K.
Ehataht0000-0002-2387-4777, M. Kadastik, S. Nandan0000-0002-9380-8919, C.
Nielsen0000-0002-3532-8132, J. Pata0000-0002-5191-5759, M.
Raidal0000-0001-7040-9491, L. Tani0000-0002-6552-7255, C.
Veelken0000-0002-3364-916X

Department of Physics, University of Helsinki, Helsinki, Finland P.
Eerola0000-0002-3244-0591, H. Kirschenmann0000-0001-7369-2536, K.
Osterberg0000-0003-4807-0414, M. Voutilainen0000-0002-5200-6477

Helsinki Institute of Physics, Helsinki, Finland S.
Bharthuar0000-0001-5871-9622, E. Brücken0000-0001-6066-8756, F.
Garcia0000-0002-4023-7964, J. Havukainen0000-0003-2898-6900, M.S.
Kim0000-0003-0392-8691, R. Kinnunen, T. Lampén0000-0002-8398-4249, K. Lassila-
Perini0000-0002-5502-1795, S. Lehti0000-0003-1370-5598, T.
Lindén0009-0002-4847-8882, M. Lotti, L. Martikainen0000-0003-1609-3515, M.
Myllymäki0000-0003-0510-3810, J. Ott0000-0001-9337-5722, M.m.
Rantanen0000-0002-6764-0016, H. Siikonen0000-0003-2039-5874, E.
Tuominen0000-0002-7073-7767, J. Tuominiemi0000-0003-0386-8633

Lappeenranta-Lahti University of Technology, Lappeenranta, Finland P.
Luukka0000-0003-2340-4641, H. Petrow0000-0002-1133-5485, T. Tuuva

IRFU, CEA, Université Paris-Saclay, Gif-sur-Yvette, France C.
Amendola0000-0002-4359-836X, M. Besancon0000-0003-3278-3671, F.
Couderc0000-0003-2040-4099, M. Dejardin0009-0008-2784-615X, D. Denegri, J.L.
Faure, F. Ferri0000-0002-9860-101X, S. Ganjour0000-0003-3090-9744, P.
Gras0000-0002-3932-5967, G. Hamel de Monchenault0000-0002-3872-3592, P.
Jarry0000-0002-1343-8189, B. Lenzi0000-0002-1024-4004, V.
Lohezic0009-0008-7976-851X, J. Malcles0000-0002-5388-5565, J. Rander, A.
Rosowsky0000-0001-7803-6650, M.Ö. Sahin0000-0001-6402-4050, A. Savoy-
Navarro180000-0002-9481-5168, P. Simkina0000-0002-9813-372X, M.
Titov0000-0002-1119-6614, G.B. Yu0000-0001-7435-2963

Laboratoire Leprince-Ringuet, CNRS/IN2P3, Ecole Polytechnique, Institut
Polytechnique de Paris, Palaiseau, France S. Ahuja0000-0003-4368-9285, C.
Baldenegro Barrera0000-0002-6033-8885, F. Beaudette0000-0002-1194-8556, M.
Bonanomi0000-0003-3629-6264, A. Buchot Perraguin0000-0002-8597-647X, P.
Busson0000-0001-6027-4511, A. Cappati0000-0003-4386-0564, C.
Charlot0000-0002-4087-8155, O. Davignon0000-0001-8710-992X, B.
Diab0000-0002-6669-1698, G. Falmagne0000-0002-6762-3937, B.A. Fontana Santos
Alves0000-0001-9752-0624, S. Ghosh0009-0006-5692-5688, R. Granier de
Cassagnac0000-0002-1275-7292, A. Hakimi0009-0008-2093-8131, B.
Harikrishnan0000-0003-0174-4020, J. Motta0000-0003-0985-913X, M.
Nguyen0000-0001-7305-7102, C. Ochando0000-0002-3836-1173, P.
Paganini0000-0001-9580-683X, L. Portales0000-0002-9860-9185, J.
Rembser0000-0002-0632-2970, R. Salerno0000-0003-3735-2707, U.
Sarkar0000-0002-9892-4601, J.B. Sauvan0000-0001-5187-3571, Y.
Sirois0000-0001-5381-4807, A. Tarabini0000-0001-7098-5317, A.
Zabi0000-0002-7214-0673, A. Zghiche0000-0002-1178-1450

Université de Strasbourg, CNRS, IPHC UMR 7178, Strasbourg, France J.-L.
Agram190000-0001-7476-0158, J. Andrea, D. Apparu, D. Bloch0000-0002-4535-5273,
G. Bourgatte, J.-M. Brom0000-0003-0249-3622, E.C. Chabert0000-0003-2797-7690,
C. Collard0000-0002-5230-8387, D. Darej, J.-C. Fontaine19, U.
Goerlach0000-0001-8955-1666, C. Grimault, A.-C. Le Bihan0000-0002-8545-0187,
E. Nibigira0000-0001-5821-291X, P. Van Hove0000-0002-2431-3381

Institut de Physique des 2 Infinis de Lyon (IP2I ), Villeurbanne, France S.
Beauceron0000-0002-8036-9267, C. Bernet0000-0002-9923-8734, G.
Boudoul0009-0002-9897-8439, C. Camen, A. Carle, N. Chanon0000-0002-2939-5646,
D. Contardo0000-0001-6768-7466, P. Depasse0000-0001-7556-2743, H. El Mamouni,
J. Fay0000-0001-5790-1780, S. Gascon0000-0002-7204-1624, M.
Gouzevitch0000-0002-5524-880X, B. Ille0000-0002-8679-3878, I.B. Laktineh, M.
Lethuillier0000-0001-6185-2045, L. Mirabito, S. Perries, K. Shchablo, V.
Sordini0000-0003-0885-824X, L. Torterotot0000-0002-5349-9242, M. Vander
Donckt0000-0002-9253-8611, S. Viret

Georgian Technical University, Tbilisi, Georgia D.
Chokheli0000-0001-7535-4186, I. Lomidze0009-0002-3901-2765, Z.
Tsamalaidze140000-0001-5377-3558

RWTH Aachen University, I. Physikalisches Institut, Aachen, Germany V.
Botta0000-0003-1661-9513, L. Feld0000-0001-9813-8646, K.
Klein0000-0002-1546-7880, M. Lipinski0000-0002-6839-0063, D.
Meuser0000-0002-2722-7526, A. Pauls0000-0002-8117-5376, N.
Röwert0000-0002-4745-5470, J. Schulz, M. Teroerde0000-0002-5892-1377

RWTH Aachen University, III. Physikalisches Institut A, Aachen, Germany A.
Dodonova0000-0002-5115-8487, N. Eich0000-0001-9494-4317, D.
Eliseev0000-0001-5844-8156, M. Erdmann0000-0002-1653-1303, P.
Fackeldey0000-0003-4932-7162, B. Fischer0000-0002-3900-3482, T.
Hebbeker0000-0002-9736-266X, K. Hoepfner0000-0002-2008-8148, F.
Ivone0000-0002-2388-5548, M.y. Lee0000-0002-4430-1695, L. Mastrolorenzo, M.
Merschmeyer0000-0003-2081-7141, A. Meyer0000-0001-9598-6623, S.
Mondal0000-0003-0153-7590, S. Mukherjee0000-0001-6341-9982, D.
Noll0000-0002-0176-2360, A. Novak0000-0002-0389-5896, A.
Pozdnyakov0000-0003-3478-9081, Y. Rath, H. Reithler0000-0003-4409-702X, A.
Schmidt0000-0003-2711-8984, S.C. Schuler, A. Sharma0000-0002-5295-1460, L.
Vigilante, S. Wiedenbeck0000-0002-4692-9304, S. Zaleski

RWTH Aachen University, III. Physikalisches Institut B, Aachen, Germany C.
Dziwok0000-0001-9806-0244, G. Flügge0000-0003-3681-9272, W. Haj
Ahmad200000-0003-1491-0446, O. Hlushchenko, T. Kress0000-0002-2702-8201, A.
Nowack0000-0002-3522-5926, O. Pooth0000-0001-6445-6160, D.
Roy0000-0002-8659-7762, A. Stahl210000-0002-8369-7506, T.
Ziemons0000-0003-1697-2130, A. Zotz0000-0002-1320-1712

Deutsches Elektronen-Synchrotron, Hamburg, Germany H. Aarup Petersen, M.
Aldaya Martin0000-0003-1533-0945, P. Asmuss, S. Baxter0009-0008-4191-6716, M.
Bayatmakou0009-0002-9905-0667, O. Behnke, A. Bermúdez
Martínez0000-0001-8822-4727, S. Bhattacharya0000-0002-3197-0048, A.A. Bin
Anuar0000-0002-2988-9830, F. Blekman220000-0002-7366-7098, K.
Borras230000-0003-1111-249X, D. Brunner0000-0001-9518-0435, A.
Campbell0000-0003-4439-5748, A. Cardini0000-0003-1803-0999, C. Cheng, F.
Colombina, S. Consuegra Rodríguez0000-0002-1383-1837, G. Correia
Silva0000-0001-6232-3591, M. De Silva0000-0002-5804-6226, L.
Didukh0000-0003-4900-5227, G. Eckerlin, D. Eckstein, L.I. Estevez
Banos0000-0001-6195-3102, O. Filatov0000-0001-9850-6170, E.
Gallo220000-0001-7200-5175, A. Geiser0000-0003-0355-102X, A.
Giraldi0000-0003-4423-2631, G. Greau, A. Grohsjean0000-0003-0748-8494, V.
Guglielmi0000-0003-3240-7393, M. Guthoff0000-0002-3974-589X, A.
Jafari240000-0001-7327-1870, N.Z. Jomhari0000-0001-9127-7408, B.
Kaech0000-0002-1194-2306, M. Kasemann0000-0002-0429-2448, H.
Kaveh0000-0002-3273-5859, C. Kleinwort0000-0002-9017-9504, R.
Kogler0000-0002-5336-4399, D. Krücker0000-0003-1610-8844, W. Lange, K.
Lipka0000-0002-8427-3748, W. Lohmann250000-0002-8705-0857, R.
Mankel0000-0003-2375-1563, I.-A. Melzer-Pellmann0000-0001-7707-919X, M.
Mendizabal Morentin0000-0002-6506-5177, J. Metwally, A.B.
Meyer0000-0001-8532-2356, M. Meyer0000-0003-2436-8195, A.
Kasem230000-0002-6753-7254, M. Mormile0000-0003-0456-7250, A.
Mussgiller0000-0002-8331-8166, A. Nürnberg0000-0002-7876-3134, Y. Otarid, D.
Pérez Adán0000-0003-3416-0726, D. Pitzl, A. Raspereza, B. Ribeiro
Lopes0000-0003-0823-447X, J. Rübenach, A. Saggio0000-0002-7385-3317, A.
Saibel0000-0002-9932-7622, M. Savitskyi0000-0002-9952-9267, M.
Scham260000-0001-9494-2151, V. Scheurer, S. Schnake0000-0003-3409-6584, P.
Schütze0000-0003-4802-6990, C. Schwanenberger220000-0001-6699-6662, M.
Shchedrolosiev0000-0003-3510-2093, R.E. Sosa Ricardo0000-0002-2240-6699, D.
Stafford, N. Tonon${}^{\textrm{\textdagger}}$0000-0003-4301-2688, M. Van De
Klundert0000-0001-8596-2812, F. Vazzoler0000-0001-8111-9318, R.
Walsh0000-0002-3872-4114, D. Walter0000-0001-8584-9705, Q.
Wang0000-0003-1014-8677, Y. Wen0000-0002-8724-9604, K. Wichmann, L.
Wiens0000-0002-4423-4461, C. Wissing0000-0002-5090-8004, S.
Wuchterl0000-0001-9955-9258, A. Zimermmane Castro Santos

University of Hamburg, Hamburg, Germany R. Aggleton, S.
Albrecht0000-0002-5960-6803, S. Bein0000-0001-9387-7407, L.
Benato0000-0001-5135-7489, P. Connor0000-0003-2500-1061, K. De
Leo0000-0002-8908-409X, M. Eich, K. El Morabit0000-0001-5886-220X, F. Feindt,
A. Fröhlich, C. Garbers0000-0001-5094-2256, E. Garutti0000-0003-0634-5539, M.
Hajheidari, J. Haller0000-0001-9347-7657, A. Hinzmann0000-0002-2633-4696, G.
Kasieczka0000-0003-3457-2755, R. Klanner0000-0002-7004-9227, T.
Kramer0000-0002-7004-0214, V. Kutzner, J. Lange0000-0001-7513-6330, T.
Lange0000-0001-6242-7331, A. Lobanov0000-0002-5376-0877, A.
Malara0000-0001-8645-9282, C. Matthies0000-0001-7379-4540, A.
Mehta0000-0002-0433-4484, L. Moureaux0000-0002-2310-9266, A.
Nigamova0000-0002-8522-8500, K.J. Pena Rodriguez0000-0002-2877-9744, M.
Rieger0000-0003-0797-2606, O. Rieger, P. Schleper0000-0001-5628-6827, M.
Schröder0000-0001-8058-9828, J. Schwandt0000-0002-0052-597X, H.
Stadie0000-0002-0513-8119, G. Steinbrück0000-0002-8355-2761, A. Tews

Karlsruher Institut fuer Technologie, Karlsruhe, Germany J.
Bechtel0000-0001-5245-7318, S. Brommer0000-0001-8988-2035, M. Burkart, E.
Butz0000-0002-2403-5801, R. Caspart0000-0002-5502-9412, T.
Chwalek0000-0002-8009-3723, W. De Boer${}^{\textrm{\textdagger}}$, A.
Dierlamm0000-0001-7804-9902, A. Droll, N. Faltermann0000-0001-6506-3107, M.
Giffels0000-0003-0193-3032, J.O. Gosewisch, A. Gottmann0000-0001-6696-349X, F.
Hartmann210000-0001-8989-8387, C. Heidecker, M. Horzela0000-0002-3190-7962, U.
Husemann0000-0002-6198-8388, P. Keicher, R. Koppenhöfer0000-0002-6256-5715, S.
Maier0000-0001-9828-9778, S. Mitra0000-0002-3060-2278, Th.
Müller0000-0003-4337-0098, M. Neukum, G. Quast0000-0002-4021-4260, K.
Rabbertz0000-0001-7040-9846, J. Rauser, D. Savoiu0000-0001-6794-7475, M.
Schnepf, D. Seith, I. Shvetsov, H.J. Simonis, R. Ulrich0000-0002-2535-402X, J.
van der Linden0000-0002-7174-781X, R.F. Von Cube0000-0002-6237-5209, M.
Wassmer0000-0002-0408-2811, M. Weber0000-0002-3639-2267, S.
Wieland0000-0003-3887-5358, R. Wolf0000-0001-9456-383X, S. Wozniewski, S.
Wunsch

Institute of Nuclear and Particle Physics (INPP), NCSR Demokritos, Aghia
Paraskevi, Greece G. Anagnostou, P. Assiouras0000-0002-5152-9006, G.
Daskalakis0000-0001-6070-7698, A. Kyriakis, A. Stakia0000-0001-6277-7171

National and Kapodistrian University of Athens, Athens, Greece M.
Diamantopoulou, D. Karasavvas, P. Kontaxakis0000-0002-4860-5979, C.K.
Koraka0000-0002-4548-9992, A. Manousakis-Katsikakis0000-0002-0530-1182, A.
Panagiotou, I. Papavergou0000-0002-7992-2686, N. Saoulidou0000-0001-6958-4196,
K. Theofilatos0000-0001-8448-883X, E. Tziaferi0000-0003-4958-0408, K.
Vellidis0000-0001-5680-8357, E. Vourliotis0000-0002-2270-0492

National Technical University of Athens, Athens, Greece G.
Bakas0000-0003-0287-1937, K. Kousouris0000-0002-6360-0869, I.
Papakrivopoulos0000-0002-8440-0487, G. Tsipolitis, A. Zacharopoulou

University of Ioánnina, Ioánnina, Greece K. Adamidis, I. Bestintzanos, I.
Evangelou0000-0002-5903-5481, C. Foudas, P. Gianneios0009-0003-7233-0738, P.
Katsoulis, P. Kokkas0009-0009-3752-6253, N. Manthos0000-0003-3247-8909, I.
Papadopoulos0000-0002-9937-3063, J. Strologas0000-0002-2225-7160

MTA-ELTE Lendület CMS Particle and Nuclear Physics Group, Eötvös Loránd
University, Budapest, Hungary M. Csanád0000-0002-3154-6925, K.
Farkas0000-0003-1740-6974, M.M.A. Gadallah270000-0002-8305-6661, S.
Lökös280000-0002-4447-4836, P. Major0000-0002-5476-0414, K.
Mandal0000-0002-3966-7182, G. Pásztor0000-0003-0707-9762, A.J.
Rádl0000-0001-8810-0388, O. Surányi0000-0002-4684-495X, G.I.
Veres0000-0002-5440-4356

Wigner Research Centre for Physics, Budapest, Hungary M.
Bartók290000-0002-4440-2701, G. Bencze, C. Hajdu0000-0002-7193-800X, D.
Horvath30,310000-0003-0091-477X, F. Sikler0000-0001-9608-3901, V.
Veszpremi0000-0001-9783-0315

Institute of Nuclear Research ATOMKI, Debrecen, Hungary S. Czellar, D.
Fasanella0000-0002-2926-2691, F. Fienga0000-0001-5978-4952, J.
Karancsi290000-0003-0802-7665, J. Molnar, Z. Szillasi, D.
Teyssier0000-0002-5259-7983

Institute of Physics, University of Debrecen, Debrecen, Hungary P. Raics, Z.L.
Trocsanyi320000-0002-2129-1279, B. Ujvari330000-0003-0498-4265

Karoly Robert Campus, MATE Institute of Technology, Gyongyos, Hungary T.
Csorgo340000-0002-9110-9663, F. Nemes340000-0002-1451-6484, T.
Novak0000-0001-6253-4356

Panjab University, Chandigarh, India S. Bansal0000-0003-1992-0336, S.B. Beri,
V. Bhatnagar0000-0002-8392-9610, G. Chaudhary0000-0003-0168-3336, S.
Chauhan0000-0001-6974-4129, N. Dhingra350000-0002-7200-6204, R. Gupta, A.
Kaur0000-0002-1640-9180, A. K. Virdi0000-0002-0866-8932, H.
Kaur0000-0002-8659-7092, M. Kaur0000-0002-3440-2767, P.
Kumari0000-0002-6623-8586, M. Meena0000-0003-4536-3967, K.
Sandeep0000-0002-3220-3668, J.B. Singh360000-0001-9029-2462

University of Delhi, Delhi, India A. Ahmed0000-0002-4500-8853, A.
Bhardwaj0000-0002-7544-3258, B.C. Choudhary0000-0001-5029-1887, M. Gola, S.
Keshri0000-0003-3280-2350, A. Kumar0000-0003-3407-4094, M.
Naimuddin0000-0003-4542-386X, P. Priyanka0000-0002-0933-685X, K.
Ranjan0000-0002-5540-3750, S. Saumya0000-0001-7842-9518, A.
Shah0000-0002-6157-2016

Saha Institute of Nuclear Physics, HBNI, Kolkata, India R.
Bhattacharya0000-0002-7575-8639, S. Bhattacharya0000-0002-8110-4957, D.
Bhowmik, S. Dutta0000-0001-9650-8121, S. Dutta, B.
Gomber370000-0002-4446-0258, M. Maity38, P. Palit0000-0002-1948-029X, P.K.
Rout0000-0001-8149-6180, G. Saha0000-0002-6125-1941, B.
Sahu0000-0002-8073-5140, S. Sarkar, M. Sharan

Indian Institute of Technology Madras, Madras, India P.K.
Behera0000-0002-1527-2266, S.C. Behera0000-0002-0798-2727, P.
Kalbhor0000-0002-5892-3743, J.R. Komaragiri390000-0002-9344-6655, D.
Kumar390000-0002-6636-5331, A. Muhammad, L. Panwar390000-0003-2461-4907, R.
Pradhan0000-0001-7000-6510, P.R. Pujahari0000-0002-0994-7212, A.
Sharma0000-0002-0688-923X, A.K. Sikdar0000-0002-5437-5217, P.C.
Tiwari390000-0002-3667-3843

Bhabha Atomic Research Centre, Mumbai, India K. Naskar400000-0003-0638-4378

Tata Institute of Fundamental Research-A, Mumbai, India T. Aziz, S. Dugad, M.
Kumar0000-0003-0312-057X, G.B. Mohanty0000-0001-6850-7666

Tata Institute of Fundamental Research-B, Mumbai, India S.
Banerjee0000-0002-7953-4683, R. Chudasama0009-0007-8848-6146, M.
Guchait0009-0004-0928-7922, S. Karmakar0000-0001-9715-5663, S.
Kumar0000-0002-2405-915X, G. Majumder0000-0002-3815-5222, K.
Mazumdar0000-0003-3136-1653, S. Mukherjee0000-0003-3122-0594

National Institute of Science Education and Research, An OCC of Homi Bhabha
National Institute, Bhubaneswar, Odisha, India S.
Bahinipati410000-0002-3744-5332, C. Kar0000-0002-6407-6974, P.
Mal0000-0002-0870-8420, T. Mishra0000-0002-2121-3932, V.K. Muraleedharan Nair
Bindhu420000-0003-4671-815X, A. Nayak420000-0002-7716-4981, P.
Saha0000-0002-7013-8094, N. Sur0000-0001-5233-553X, S.K. Swain, D.
Vats420009-0007-8224-4664

Indian Institute of Science Education and Research (IISER), Pune, India A.
Alpana0000-0003-3294-2345, S. Dube0000-0002-5145-3777, B.
Kansal0000-0002-6604-1011, A. Laha0000-0001-9440-7028, S.
Pandey0000-0003-0440-6019, A. Rastogi0000-0003-1245-6710, S.
Sharma0000-0001-6886-0726

Isfahan University of Technology, Isfahan, Iran E. Khazaie0000-0001-9810-7743,
M. Sedghi43, M. Zeinali440000-0001-8367-6257

Institute for Research in Fundamental Sciences (IPM), Tehran, Iran S.
Chenarani450000-0002-1425-076X, S.M. Etesami0000-0001-6501-4137, M.
Khakzad0000-0002-2212-5715, M. Mohammadi Najafabadi0000-0001-6131-5987

University College Dublin, Dublin, Ireland M. Grunewald0000-0002-5754-0388

INFN Sezione di Bari a, Università di Bari b, Politecnico di Bari c, Bari,
Italy M. Abbresciaa,b0000-0001-8727-7544, R. Alya,c,460000-0001-6808-1335, C.
Arutaa,b0000-0001-9524-3264, A. Colaleoa0000-0002-0711-6319, D.
Creanzaa,c0000-0001-6153-3044, N. De Filippisa,c0000-0002-0625-6811, M. De
Palmaa,b0000-0001-8240-1913, A. Di Florioa,b0000-0003-3719-8041, W.
Elmetenaweea,b0000-0001-7069-0252, F. Erricoa,b0000-0001-8199-370X, L.
Fiorea0000-0002-9470-1320, G. Iasellia,c0000-0003-2546-5341, M.
Incea,b0000-0001-6907-0195, S. Lezkia,b0000-0002-6909-774X, G.
Maggia,c0000-0001-5391-7689, M. Maggia0000-0002-8431-3922, I.
Margjekaa,b0000-0002-3198-3025, V. Mastrapasquaa,b0000-0002-9082-5924, S.
Mya,b0000-0002-9938-2680, S. Nuzzoa,b0000-0003-1089-6317, A.
Pellecchiaa,b0000-0003-3279-6114, A. Pompilia,b0000-0003-1291-4005, G.
Pugliesea,c0000-0001-5460-2638, D. Ramosa0000-0002-7165-1017, A.
Ranieria0000-0001-7912-4062, G. Selvaggia,b0000-0003-0093-6741, L.
Silvestrisa0000-0002-8985-4891, F.M. Simonea,b0000-0002-1924-983X, Ü.
Sözbilira0000-0001-6833-3758, R. Vendittia0000-0001-6925-8649, P.
Verwilligena0000-0002-9285-8631

INFN Sezione di Bologna a, Università di Bologna b, Bologna, Italy G.
Abbiendia0000-0003-4499-7562, C. Battilanaa,b0000-0002-3753-3068, D.
Bonacorsia,b0000-0002-0835-9574, L. Borgonovia0000-0001-8679-4443, L.
Brigliadoria, R. Campaninia,b0000-0002-2744-0597, P.
Capiluppia,b0000-0003-4485-1897, A. Castroa,b0000-0003-2527-0456, F.R.
Cavalloa0000-0002-0326-7515, C. Cioccaa0000-0003-0080-6373, M.
Cuffiania,b0000-0003-2510-5039, G.M. Dallavallea0000-0002-8614-0420, T.
Diotalevia,b0000-0003-0780-8785, F. Fabbria0000-0002-8446-9660, A.
Fanfania,b0000-0003-2256-4117, P. Giacomellia0000-0002-6368-7220, L.
Giommia,b0000-0003-3539-4313, C. Grandia0000-0001-5998-3070, L.
Guiduccia,b0000-0002-6013-8293, S. Lo Meoa,470000-0003-3249-9208, L.
Lunertia,b0000-0002-8932-0283, S. Marcellinia0000-0002-1233-8100, G.
Masettia0000-0002-6377-800X, F.L. Navarriaa,b0000-0001-7961-4889, A.
Perrottaa0000-0002-7996-7139, F. Primaveraa,b0000-0001-6253-8656, A.M.
Rossia,b0000-0002-5973-1305, T. Rovellia,b0000-0002-9746-4842, G.P.
Sirolia,b0000-0002-3528-4125

INFN Sezione di Catania a, Università di Catania b, Catania, Italy S.
Albergoa,b,480000-0001-7901-4189, S. Costaa,b,480000-0001-9919-0569, A. Di
Mattiaa0000-0002-9964-015X, R. Potenzaa,b, A.
Tricomia,b,480000-0002-5071-5501, C. Tuvea,b0000-0003-0739-3153

INFN Sezione di Firenze a, Università di Firenze b, Firenze, Italy G.
Barbaglia0000-0002-1738-8676, B. Camaiania,b0000-0002-6396-622X, A.
Cassesea0000-0003-3010-4516, R. Ceccarellia,b0000-0003-3232-9380, V.
Ciullia,b0000-0003-1947-3396, C. Civininia0000-0002-4952-3799, R.
D’Alessandroa,b0000-0001-7997-0306, E. Focardia,b0000-0002-3763-5267, G.
Latinoa,b0000-0002-4098-3502, P. Lenzia,b0000-0002-6927-8807, M.
Lizzoa,b0000-0001-7297-2624, M. Meschinia0000-0002-9161-3990, S.
Paolettia0000-0003-3592-9509, R. Seiditaa,b0000-0002-3533-6191, G.
Sguazzonia0000-0002-0791-3350, L. Viliania0000-0002-1909-6343

INFN Laboratori Nazionali di Frascati, Frascati, Italy L.
Benussi0000-0002-2363-8889, S. Bianco0000-0002-8300-4124, D.
Piccolo0000-0001-5404-543X

INFN Sezione di Genova a, Università di Genova b, Genova, Italy M.
Bozzoa,b0000-0002-1715-0457, F. Ferroa0000-0002-7663-0805, R.
Mulargiaa0000-0003-2437-013X, E. Robuttia0000-0001-9038-4500, S.
Tosia,b0000-0002-7275-9193

INFN Sezione di Milano-Bicocca a, Università di Milano-Bicocca b, Milano,
Italy A. Benagliaa0000-0003-1124-8450, G. Boldrinia0000-0001-5490-605X, F.
Brivioa,b0000-0001-9523-6451, F. Cetorellia,b0000-0002-3061-1553, F. De
Guioa,b0000-0001-5927-8865, M.E. Dinardoa,b0000-0002-8575-7250, P.
Dinia0000-0001-7375-4899, S. Gennaia0000-0001-5269-8517, A.
Ghezzia,b0000-0002-8184-7953, P. Govonia,b0000-0002-0227-1301, L.
Guzzia,b0000-0002-3086-8260, M.T. Lucchinia,b0000-0002-7497-7450, M.
Malbertia0000-0001-6794-8419, S. Malvezzia0000-0002-0218-4910, A.
Massironia0000-0002-0782-0883, D. Menascea0000-0002-9918-1686, L.
Moronia0000-0002-8387-762X, M. Paganonia,b0000-0003-2461-275X, D.
Pedrinia0000-0003-2414-4175, B.S. Pinolinia, S. Ragazzia,b0000-0001-8219-2074,
N. Redaellia0000-0002-0098-2716, T. Tabarelli de Fatisa,b0000-0001-6262-4685,
D. Valsecchia,b,210000-0001-8587-8266, D. Zuoloa,b0000-0003-3072-1020

INFN Sezione di Napoli a, Università di Napoli ’Federico II’ b, Napoli, Italy;
Università della Basilicata c, Potenza, Italy; Università G. Marconi d, Roma,
Italy S. Buontempoa0000-0001-9526-556X, F. Carnevalia,b, N.
Cavalloa,c0000-0003-1327-9058, A. De Iorioa,b0000-0002-9258-1345, F.
Fabozzia,c0000-0001-9821-4151, A.O.M. Iorioa,b0000-0002-3798-1135, L.
Listaa,b,490000-0001-6471-5492, S. Meolaa,d,210000-0002-8233-7277, P.
Paoluccia,210000-0002-8773-4781, B. Rossia0000-0002-0807-8772, C.
Sciaccaa,b0000-0002-8412-4072

INFN Sezione di Padova a, Università di Padova b, Padova, Italy; Università di
Trento c, Trento, Italy P. Azzia0000-0002-3129-828X, N.
Bacchettaa0000-0002-2205-5737, D. Biselloa,b0000-0002-2359-8477, P.
Bortignona0000-0002-5360-1454, A. Bragagnoloa,b0000-0003-3474-2099, R.
Carlina,b0000-0001-7915-1650, P. Checchiaa0000-0002-8312-1531, T.
Dorigoa0000-0002-1659-8727, U. Dossellia0000-0001-8086-2863, F.
Gasparinia,b0000-0002-1315-563X, U. Gasparinia,b0000-0002-7253-2669, G.
Grossoa, L. Layera,50, E. Lusiania0000-0001-8791-7978, M.
Margonia,b0000-0003-1797-4330, F. Marinia0000-0002-2374-6433, A.T.
Meneguzzoa,b0000-0002-5861-8140, J. Pazzinia,b0000-0002-1118-6205, P.
Ronchesea,b0000-0001-7002-2051, R. Rossina,b0000-0003-3466-7500, F.
Simonettoa,b0000-0002-8279-2464, G. Stronga0000-0002-4640-6108, M.
Tosia,b0000-0003-4050-1769, H. Yarara,b, M. Zanettia,b0000-0003-4281-4582, P.
Zottoa,b0000-0003-3953-5996, A. Zucchettaa,b0000-0003-0380-1172, G.
Zumerlea,b0000-0003-3075-2679

INFN Sezione di Pavia a, Università di Pavia b, Pavia, Italy C.
Aimèa,b0000-0003-0449-4717, A. Braghieria0000-0002-9606-5604, S.
Calzaferria,b0000-0002-1162-2505, D. Fiorinaa,b0000-0002-7104-257X, P.
Montagnaa,b0000-0001-9647-9420, S.P. Rattia,b, V. Rea0000-0003-0697-3420, C.
Riccardia,b0000-0003-0165-3962, P. Salvinia0000-0001-9207-7256, I.
Vaia0000-0003-0037-5032, P. Vituloa,b0000-0001-9247-7778

INFN Sezione di Perugia a, Università di Perugia b, Perugia, Italy P.
Asenova,510000-0003-2379-9903, G.M. Bileia0000-0002-4159-9123, D.
Ciangottinia,b0000-0002-0843-4108, L. Fanòa,b0000-0002-9007-629X, M.
Magherinia,b0000-0003-4108-3925, G. Mantovania,b, V.
Mariania,b0000-0001-7108-8116, M. Menichellia0000-0002-9004-735X, F.
Moscatellia,510000-0002-7676-3106, A. Piccinellia,b0000-0003-0386-0527, M.
Presillaa,b0000-0003-2808-7315, A. Rossia,b0000-0002-2031-2955, A.
Santocchiaa,b0000-0002-9770-2249, D. Spigaa0000-0002-2991-6384, T.
Tedeschia,b0000-0002-7125-2905

INFN Sezione di Pisa a, Università di Pisa b, Scuola Normale Superiore di Pisa
c, Pisa, Italy; Università di Siena d, Siena, Italy P.
Azzurria0000-0002-1717-5654, G. Bagliesia0000-0003-4298-1620, V.
Bertacchia,c0000-0001-9971-1176, L. Bianchinia0000-0002-6598-6865, T.
Boccalia0000-0002-9930-9299, E. Bossinia,b0000-0002-2303-2588, D.
Bruschinia0000-0001-7248-2967, R. Castaldia0000-0003-0146-845X, M.A.
Cioccia,b0000-0003-0002-5462, V. D’Amantea,d0000-0002-7342-2592, R.
Dell’Orsoa0000-0003-1414-9343, M.R. Di Domenicoa,d0000-0002-7138-7017, S.
Donatoa0000-0001-7646-4977, A. Giassia0000-0001-9428-2296, F.
Ligabuea,c0000-0002-1549-7107, E. Mancaa,c0000-0001-8946-655X, G.
Mandorlia,c0000-0002-5183-9020, D. Matos Figueiredoa0000-0003-2514-6930, A.
Messineoa,b0000-0001-7551-5613, M. Musicha0000-0001-7938-5684, F.
Pallaa0000-0002-6361-438X, S. Paroliaa,b0000-0002-9566-2490, G. Ramirez-
Sancheza,c0000-0001-7804-5514, A. Rizzia,b0000-0002-4543-2718, G.
Rolandia,c0000-0002-0635-274X, S. Roy Chowdhurya,c0000-0001-5742-5593, A.
Scribanoa0000-0002-4338-6332, N. Shafieia,b0000-0002-8243-371X, P.
Spagnoloa0000-0001-7962-5203, R. Tenchinia0000-0003-2574-4383, G.
Tonellia,b0000-0003-2606-9156, N. Turinia,d0000-0002-9395-5230, A.
Venturia0000-0002-0249-4142, P.G. Verdinia0000-0002-0042-9507

INFN Sezione di Roma a, Sapienza Università di Roma b, Roma, Italy P.
Barriaa0000-0002-3924-7380, M. Campanaa,b0000-0001-5425-723X, F.
Cavallaria0000-0002-1061-3877, D. Del Rea,b0000-0003-0870-5796, E. Di
Marcoa0000-0002-5920-2438, M. Diemoza0000-0002-3810-8530, E.
Longoa,b0000-0001-6238-6787, P. Meridiania0000-0002-8480-2259, G.
Organtinia,b0000-0002-3229-0781, F. Pandolfia0000-0001-8713-3874, R.
Paramattia,b0000-0002-0080-9550, C. Quarantaa,b0000-0002-0042-6891, S.
Rahatloua,b0000-0001-9794-3360, C. Rovellia0000-0003-2173-7530, F.
Santanastasioa,b0000-0003-2505-8359, L. Soffia0000-0003-2532-9876, R.
Tramontanoa,b0000-0001-5979-5299

INFN Sezione di Torino a, Università di Torino b, Torino, Italy; Università
del Piemonte Orientale c, Novara, Italy N. Amapanea,b0000-0001-9449-2509, R.