HIG-21-006

HIG-21-006

# Search for $CP$ violation in $\PQt\PAQt\PH$ and $\PQt\PH$ production in
multilepton channels in proton-proton collisions at $\sqrt{s}=13\TeV$

###### Abstract

The charge-parity ($CP$) structure of the Yukawa interaction between the Higgs
() boson and the top quark is measured in a data sample enriched in the
$\PQt\PAQt\PH$ and $\PQt\PH$ associated production, using 138of data collected
in proton-proton collisions at $\sqrt{s}=13\TeV$ by the CMS experiment at the
CERN LHC. The study targets events where the boson decays via $\PH\to\PW\PW$
or $\PH\to\PGt\PGt$ and the top quarks decay via $\PQt\to\PW\PQb$: the bosons
decay either leptonically or hadronically, and final states characterized by
the presence of at least two leptons are studied. Machine learning techniques
are applied to these final states to enhance the separation of $CP$-even from
$CP$-odd scenarios. Two-dimensional confidence regions are set on
$\kappa_{\PQt}$ and $\widetilde{\kappa}_{\PQt}$, which are respectively
defined as the $CP$-even and $CP$-odd top-Higgs Yukawa coupling modifiers. No
significant fractional $CP$-odd contributions, parameterized by the quantity
$\abs{f_{CP}^{\PH\PQt\PQt}}$ are observed; the parameter is determined to be
$\abs{f_{CP}^{\PH\PQt\PQt}}=0.59$ with an interval of $(0.24,0.81)$ at 68%
confidence level. The results are combined with previous results covering the
$\PH\to\PZ\PZ$ and $\PH\to\PGg\PGg$ decay modes, yielding two- and one-
dimensional confidence regions on $\kappa_{\PQt}$ and
$\widetilde{\kappa}_{\PQt}$, while $\abs{f_{CP}^{\PH\PQt\PQt}}$ is determined
to be $\abs{f_{CP}^{\PH\PQt\PQt}}=0.28$ with an interval of
$\abs{f_{CP}^{\PH\PQt\PQt}}<0.55$ at 68% confidence level, in agreement with
the standard model $CP$-even prediction of $\abs{f_{CP}^{\PH\PQt\PQt}}=0$.

##  0.1 Introduction

The observation of a spin-0 boson by the ATLAS and CMS Collaborations in 2012
[1, 2, 3] opened a new field of exploration in the realm of particle physics:
the properties of the newly observed boson must be measured in detail to
ascertain if it is compatible with the Higgs () boson predicted by the
standard model (SM). Results from the LHC Run 1 and 2 indicate that the
coupling of the boson to other particles is SM-like [4, 5, 6, 7]. The SM
Yukawa couplings $y_{\textrm{f}}^{\mathrm{SM}}$ of the boson to fermions are
proportional to the fermion mass $m_{\textrm{f}}$, namely
$y_{\textrm{f}}^{\mathrm{SM}}=\sqrt{2}m_{\textrm{f}}/v$, where $v\approx
246\GeV$ denotes the vacuum expectation value of the Higgs field. The top
quark, with a mass of $m_{\PQt}=172.44\pm 0.48\GeV$ [8], is by far the
heaviest fermion known to date: its Yukawa coupling $y_{\PQt}$ is expected to
be of order one. The large $m_{\PQt}$ may indicate that it plays a special
role in the mechanism of electroweak symmetry breaking [9, 10, 11]; deviations
of $y_{\PQt}$ from the SM prediction would unambiguously indicate the presence
of new physics beyond the SM, and thus the determination of $y_{\PQt}$ is of
special interest in the study of the boson.

The associated production of a boson with top quark pairs ($\PQt\PAQt\PH$) has
previously been studied by the ATLAS and CMS Collaborations with up to 24.8of
data recorded at $\sqrt{s}=7$ and 8during the LHC Run 1 [12, 13, 14, 15, 16]
and with up to 138at $\sqrt{s}=13\TeV$ during the Run 2 [17, 18, 19, 20, 21,
22, 23, 24, 25, 26]. The combined analysis of data recorded at $\sqrt{s}=7$,
8, and 13allowed for the observation of $\PQt\PAQt\PH$ production with
significances of 5.2 and 6.3 standard deviations by the CMS and ATLAS
Collaborations, respectively [27, 28]. The production of bosons in association
with a single top quark has been studied by the ATLAS and CMS Collaborations
with data recorded during the LHC Run 1 [29] and Run 2 [30, 24]. These
analyses covered the boson decay modes to bottom quark-antiquark pairs, photon
pairs, pairs of $\Pgt$ leptons, and combinations of quarks and leptons
originating from the decay of intermediate on- or off-shell and bosons.

The SM boson is even under charge-parity ($CP$) inversion; an experimental
observation compatible with the presence of a $CP$-odd term in the boson
Lagrangian would be a direct indication of the presence of new physics.
Determining the $CP$ structure of the couplings of the observed boson is
therefore paramount.

The ATLAS and CMS Collaborations have studied the couplings of the boson to
vector gauge bosons and also tested such interactions for $CP$ violation [31,
32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 25, 24, 44, 45]. All the
studies were compatible with a pure $CP$-even boson Lagrangian, excluding pure
$CP$-odd couplings of the boson to any of the gauge bosons. However,
$CP$-violating effects are expected to be theoretically more motivated in
boson to fermion couplings than those to gauge bosons. In the couplings to V
bosons, $CP$-odd contributions enter via nonrenormalizable higher-order
operators that are suppressed by powers of $1/\Lambda^{2}$ [46], where
$\Lambda$ is the scale of the physics beyond the SM in an effective field
theory, or via nonrenormalizable interaction terms [47, 48]. Overall, these
$CP$-odd contributions are expected to only yield a minor contribution to the
coupling.

For the couplings to fermions, a renormalizable $CP$-violating coupling may
instead occur at tree level. The top-Higgs Yukawa coupling is therefore a
suitable coupling for $CP$ studies in proton-proton ($\Pp\Pp$) collisions
[49]. The ATLAS and CMS Collaborations have performed several searches for
$CP$ violation in the coupling of the boson to fermions, finding no deviation
with respect to the SM prediction of a $CP$-even scenario. The coupling of the
boson to tau lepton was studied in [50]. Besides, measurements of the $CP$
structure of the coupling of the boson to the top quark were performed using
$\PQt\PAQt\PH$ and $\PQt\PH$ production modes with different final states ,
two photons [25, 24] or four leptons [44]; the $CP$ measurements in gluon-
gluon fusion production mode can also be interpreted in terms of fermionic
couplings [44, 51, 52].

The Yukawa couplings of the boson to fermions have been determined with a
large uncertainty during the LHC Run 1 [5]. During the LHC Run 2, the ratio of
$y_{\PQt}$ to its SM expectation,
$\kappa_{\PQt}:=y_{\PQt}/y_{\PQt}^{\mathrm{SM}}$, has been determined by the
CMS Collaboration to be within $-0.9<\kappa_{\PQt}<-0.7$ or
$0.7<\kappa_{\PQt}<1.1$, at 95% confidence level () [26] by probing the
production of the boson in association with one or two top quarks, with
subsequent decay to leptonic final states.

The $\PQt\PAQt\PH$ production and the production of a boson in association
with a single top quark ($\PQt\PH$) provide direct access to the magnitude and
sign of $y_{\PQt}$. The SM cross section for $\PQt\PAQt\PH$ production in
$\Pp\Pp$ collisions at $\sqrt{s}=13\TeV$ amounts to 506.5fb [53] for a boson
mass of $m_{\PH}=125.09\GeV$ [54], computed at next-to-leading (NLO) accuracy
in quantum chromodynamics (QCD), along with electroweak corrections computed
at the same order in perturbation theory. The leading-order (LO) Feynman
diagrams for $\PQt\PAQt\PH$ production are shown in Fig. 1. The cross section
for $\PQt\PH$ production is significantly smaller, amounting to 74.3fb [53] in
the dominant $t$ channel ($\PQt\PH\PQq$), computed at NLO accuracy in QCD with
the so-called five-flavour scheme (5FS). The $\PQt\PH$ production also occurs
via two additional channels, with lower cross sections, amounting to 15.2fb
[53] in the tW-associated channel ($\PQt\PH\PW$) and to 2.9fb [53] in the $s$
channel, both computed at NLO accuracy in QCD with the four-flavour scheme
(4FS). The contribution of the $s$ channel amounts to 4% of the contribution
of the $t$ channel, and is neglected in this analysis. The diagrams
corresponding to the $\PQt\PH\PQq$ and $\PQt\PH\PW$ production modes in the
5FS can be found in Fig. 2. The small rates of the $\PQt\PH\PQq$ and
$\PQt\PH\PW$ production processes in the SM are due to the destructive
interference between diagrams where the boson couples to the top quark (left
diagrams of Fig. 2) and the corresponding diagrams where the boson couples to
the boson (right diagrams of Fig. 2). If $y_{\PQt}$ differs from the value
predicted by the SM, the cross section for $\PQt\PH$ production may be
modified significantly. The largest enhancement of the $\PQt\PH$ production
rate is attained when $y_{\PQt}$= -$y_{\PQt}^{\mathrm{SM}}$, referred to as
the inverted top coupling (ITC) scenario. In the ITC scenario, the destructive
interference between diagrams turns into a constructive interference, and the
cross section amounts to 848.0fb [53]. The measurement of the $\PQt\PH$
production rate thus allows not only a model-independent determination of the
$y_{\PQt}$ magnitude, but also a determination of its relative sign with
respect to the $\PW\PW\PH$ coupling, which makes the study of this process
particularly interesting.

Figure 1: Representative Feynman diagrams for the $\PQt\PAQt\PH$ production
processes.

Figure 2: Upper (lower) row: representative Feynman diagrams for the $\PQt\PH$
process in the $t$-channel ($\PQt\PW$-associated) production mode.

In this paper, we report on the measurement of the $CP$ structure of the boson
at tree level by studying the $\PQt\PAQt\PH$ and $\PQt\PH$ processes in final
states with multiple electrons, muons, and hadronically decaying tau leptons
($\tauh$). The signatures used are $2\ell\mkern 1.0mu\mathrm{SS}+0\tauh$,
$2\ell\mkern 1.0mu\mathrm{SS}+1\tauh$, and $3\ell+0\tauh$, which account for
the boson decay modes $\PH\to\PW\PW$ and $\PH\to\Pgt\Pgt$ (called from now on
multilepton decay channel), targeting events in which at least one top quark
decays leptonically and providing the highest sensitivity to possible $CP$
violation effects. The symbol $\ell$ denotes light leptons ($\Pe$, $\Pgm$),
and $\mkern 1.0mu\mathrm{SS}$ means same-sign. The measurement is based on
data recorded by the CMS experiment in $\Pp\Pp$ collisions at
$\sqrt{s}=13\TeV$ during the LHC Run 2, corresponding to an integrated
luminosity of 138. We extend the cross section measurement published by the
CMS Collaboration [26] by interpreting the results in terms of the spin-parity
of the boson. As in previous analyses [25], the separation of the
$\PQt\PAQt\PH$ and $\PQt\PH$ signals from backgrounds is improved with machine
learning techniques, mainly boosted decision trees (BDTs) and artificial deep
neural networks (DNNs) [55, 56]. Machine learning methods are also employed to
improve the separation between $CP$-odd and $CP$-even scenarios, both pure and
mixed, for the $\PQt\PAQt\PH$ and $\PQt\PH$ signals. Tabulated results are
provided in the HEPData record for this analysis [57].

##  0.2 Phenomenology

The Lagrangian for the fermions-Higgs interaction can be written as a
superposition of amplitudes with a $CP$-even and a $CP$-odd phase, where any
deviation from the SM values for the couplings would mean $CP$ violation in
the top-Higgs sector and would be described as a beyond-the-SM (BSM)
phaenomenon. Assuming that the spin-0 boson is a mass eigenstate, the
$\PQt\PAQt\PH$ Lagrangian can be parametererized as follows:

$\mathcal{L}_{\PQt\PAQt\PH}=\frac{m_{\PQt}}{v}\bar{\psi}_{\PQt}(\kappa_{\PQt}+i\gamma_{5}\widetilde{\kappa}_{\PQt})\psi_{\PQt}\PH\,,$
(1)

where $\bar{\psi}_{t}$ and $\psi_{t}$ are Dirac spinors, $v$ is the SM Higgs
field vacuum expectation value, while $\kappa_{\PQt}$ and
$\widetilde{\kappa}_{\PQt}$ are respectively the $CP$-even and $CP$-odd top-
Higgs Yukawa coupling modifiers. The parameter $\kappa_{\PQt}$ is proportional
to $\mathrm{cos}(\alpha)$, while $\widetilde{\kappa}_{\PQt}$ is proportional
to $\mathrm{sin}(\alpha)$, where $\alpha$ is the mixing angle. In the SM,
there is no $CP$ violation and therefore $\alpha$ is either $0^{\circ}$ or
$180^{\circ}$. The choice of $\kappa_{\PQt}$ and $\widetilde{\kappa}_{\PQt}$
affects the coupling and hence the cross section and kinematic properties of
both the $\PQt\PAQt\PH$ and $\PQt\PH$ processes. We use the variation in the
differential cross section of the $\PQt\PAQt\PH$ and $\PQt\PH$ processes
depending on the choice of $\alpha$ derived in Ref. [58]. Based on the choice
of $\alpha$, we can broadly identify the three possible scenarios detailed in
Table 0.2. Kinematic differences between the purely $CP$-even, the purely
$CP$-odd, and the mixed scenario can be exploited to discriminate between them
and throw light on the exact $CP$ scenario that is favoured by Nature. It is
important to note that the cross section of the $\PQt\PAQt\PH$ process is
symmetric around $\alpha=90^{\circ}$ and is therefore not sensitive to the
difference between the SM coupling ($\alpha=0^{\circ}$) and the inverse
coupling ($\alpha=180^{\circ}$).

Possible $CP$ scenarios  Scenario $\alpha$ Purely $CP$-even $0^{\circ}$ or
$180^{\circ}$ Purely $CP$-odd $90^{\circ}$ or $270^{\circ}$ Mixed $\neq
0^{\circ},\neq 90^{\circ},\neq 180^{\circ}$

##  0.3 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. A silicon pixel and
strip tracker, a lead tungstate crystal electromagnetic calorimeter (ECAL),
and a brass and scintillator hadron calorimeter, each composed of a barrel and
two endcap sections, are positioned within the solenoid volume. The silicon
tracker measures charged particles within the pseudorapidity range
$\abs{\eta}<2.5$. The ECAL is a fine-grained hermetic calorimeter with quasi-
projective geometry, and is segmented into the barrel region of
$\abs{\eta}<1.48$ and in two endcaps that extend up to $\abs{\eta}<3.0$. The
hadron calorimeter barrel and endcaps similarly cover the region
$\abs{\eta}<3.0$. Forward calorimeters extend the coverage up to
$\abs{\eta}<5.0$. Muons are measured and identified in the range
$\abs{\eta}<2.4$ by gas-ionization detectors embedded in the steel flux-return
yoke outside the solenoid. A two-level trigger system [59] is used to reduce
the rate of recorded events to a level suitable for data acquisition and
storage. The first level of the CMS trigger system, composed of custom
hardware processors, uses information from the calorimeters and muon detectors
to select the most interesting events with a fixed latency of 4. The high-
level trigger processor farm further decreases the event rate from around
100kHz to about 1kHz. Details of the CMS detector and its performance,
together with a definition of the coordinate system and the kinematic
variables used in the analysis, are reported in Ref. [60].

##  0.4 Data samples and Monte Carlo simulation

The data and simulated samples used in this analysis are those used in the
inclusive measurement of the $\PQt\PAQt\PH$ and $\PQt\PH$ cross sections
performed by the CMS Collaboration [26]. We report here a few highlights for
completeness.

This analysis uses $\Pp\Pp$ collision data recorded at $\sqrt{s}=13\TeV$ at
the LHC during 2016–2018. Data-taking periods during which the CMS detector
was not fully operational are excluded from the analysis. The total integrated
luminosity of the analyzed data set amounts to 138, of which 36.3 [61], 41.5
[62], and 59.8 [63] have been recorded in 2016, 2017, and 2018, respectively.

The SM cross sections for the $\PQt\PAQt\PH$ and $\PQt\PH$ signals and for the
most relevant background processes estimated from simulation are reported in
Table 0.4. The backgrounds arising from nonprompt or misidentified leptons
(collectively labelled nonprompt in the figures of this paper) and from lepton
charge mismeasurement are described in Section 0.5; regardless of the
processes that originated them, they are fully determined from data. All the
other background contributions are determined from simulation.

The 4FS and 5FS [64, 58] are used to simulate the $\PQt\PH\PQq$ and
$\PQt\PH\PW$ processes: we simulate the $\PQt\PH$ production at leading order
(LO), the $\PQt\PH\PQq$ process in the 4FS, and the $\PQt\PH\PW$ process in
the 5FS, so that interference contributions of the latter with $\PQt\PAQt\PH$
production are not present in the simulation. The contribution from
$s$-channel $\PQt\PH$ production is negligible and is not considered in this
analysis.

The $\PQt\PAQt\PH$ and $\PQt\PH$ signals as well as $\ttbar\Pgg$,
$\ttbar\PGg^{*}$, $\PQt\PZ$, $\PQt\PAQt\PW\PW$, $\PW$+jets, Drell–Yan (DY),
$\PW\Pgg$, and $\PZ\Pgg$ backgrounds are simulated at LO using the program
v2.2.2, v2.3.3 or v2.4.2 [65, 66, 67, 68]. Background arising from production
in association with and bosons ($\PQt\PAQt\PW$, $\PQt\PAQt\PZ$), from triboson
($\PW\PW\PW$, $\PW\PW\PZ$, $\PW\PZ\PZ$, $\PZ\PZ\PZ$, and $\PW\PZ\Pgg$)
production, as well as from the production of four top quarks
($\PQt\PAQt\PQt\PAQt$) are generated at NLO accuracy in perturbative quantum
chromodynamics (pQCD) making use of the same program. The modelling of the
$\PQt\PAQt\PW$ process includes additional electroweak corrections simulated
using and proportional to $\alpha_{S}\alpha_{\text{EW}}^{3}$ [69, 70], where
$\alpha_{S}$ ($\alpha_{\text{EW}}$) is the strong (electroweak) coupling
constant. Another sample of $\PQt\PAQt\PH$ events simulated with at NLO is
used in order to compute one of the uncertainties described in Section 0.7.
The NLO program v2.0 [71, 72, 73] is used to simulate the backgrounds arising
from , $\PQt\PW$, and diboson ($\PW^{\pm}\PW^{\mp}$, $\PW\PZ$, and $\PZ\PZ$)
production, from the production of single top quarks, from SM boson production
via gluon fusion ($\Pg\Pg\PH$) and vector boson fusion ($\PQq\PQq\PH$)
processes, and from the production of SM bosons in association with $\PW$ and
bosons ($\PW\PH$, $\PZ\PH$) and with and bosons along with a pair of top
quarks ($\PQt\PAQt\PW\PH$, $\PQt\PAQt\PZ\PH$).

Parton showering, hadronization, the underlying event as well as the decays of
tau leptons, including polarization effects, are modelled using [74] v8.230
with the tune CP5 [75] in 2017 and 2018 Monte Carlo (MC) samples, and v8.205
with the tunes CUETP8M1, CUETP8M2, or CUETP8M2T4 [76, 77] in 2016 MC samples.
The matching of matrix elements to parton showers is done using the MLM scheme
[66] for the LO samples and the FxFx scheme [68] for the NLO samples. The
$m_{\PQt}$ assumed in all samples is 172.5.

The $\PQt\PAQt\PH$ and $\PQt\PH$ samples are produced assuming all couplings
of the boson have the values expected in the ITC scenario. The variation in
kinematic properties of $\PQt\PAQt\PH$ and $\PQt\PH$ signal events is
accounted for by applying weights calculated signal event with v2.3.3,
following the approach suggested in Refs. [78, 79]. This results in both
signal processes to be reweighted by $\kappa_{\PQt}$ and
$\widetilde{\kappa}_{\PQt}$. This is different from the inclusive measurement
in Ref. [26], where such reweighting was not necessary for the $\PQt\PAQt\PH$
signal, because any variation of $y_{\PQt}$ would only affect the inclusive
cross section for $\PQt\PAQt\PH$ production, which increases proportional to
$y_{\PQt}^{2}$, leaving the kinematic properties of $\PQt\PAQt\PH$ signal
events unaltered.

The presence of simultaneous $\Pp\Pp$ collisions in the same or nearby bunch
crossings, referred to as pileup (PU), is modelled by superimposing inelastic
$\Pp\Pp$ interactions, simulated using , to all MC events. Simulated events
are weighed so that the PU distribution of simulated samples matches the one
observed in the data.

All MC events are passed through a detailed simulation of the CMS apparatus,
based on [80, 81], and are processed using the same version of the CMS event
reconstruction software used for the data.

Simulated events are corrected by means of weights or by varying the relevant
quantities to account for residual differences between data and simulation.
These differences arise in: trigger efficiencies; reconstruction and
identification efficiencies for electrons, muons, and $\tauh$; the energy
scale of $\tauh$ and jets; the efficiency in identifying jets originating from
the hadronization of bottom quarks and the corresponding misidentification
rates for light-quark and gluon jets; and the resolution in missing transverse
momentum (). The corrections are typically at the level of a few percent [82,
83, 84, 85, 86]. They are measured using a variety of SM processes, such as DY
($\PZ/\gamma^{*}\to\Pe\Pe$, $\PZ/\gamma^{*}\to\Pgm\Pgm$, and
$\PZ/\gamma^{*}\to\Pgt\Pgt$), , and $\gamma$+jets production.

Standard model cross sections for the $\PQt\PAQt\PH$ and $\PQt\PH$ signals as
well as for the most relevant background processes estimated from simulation.
The cross sections are quoted for $\Pp\Pp$ collisions at $\sqrt{s}=13\TeV$.
Process Cross section [fb] $\PQt\PAQt\PH$ $507$ [53] $\PQt\PH\PQq$ $74.3$ [53]
$\PQt\PH\PW$ $15.2$ [87] $\Pg\Pg\PH$ $4.86\times 10^{4}$ [53] $\PQq\PQq\PH$
$3.78\times 10^{3}$ [53] $\PW\PH$ $1.37\times 10^{3}$ [53] $\PZ\PH$ $884$ [53]
Process Cross section [fb] $\PQt\PAQt\PZ$ $839$ [53] $\PQt\PAQt\PW$ $650$ [53,
69, 70] $\PQt\PAQt\PW\PW$ $6.98$ [65] $\PW\PZ$ $4.50\times 10^{4}$ [88]
$\PZ\PZ$ $1.69\times 10^{4}$ [88]

##  0.5 Event reconstruction and selection

In this Section, we describe the selection criteria that are applied to
objects and events in the analysis. This selection follows closely that of the
$\PQt\PAQt\PH$ inclusive analysis in the multilepton channel, which is
described in full detail in Ref. [26]: only a brief summary is shown here for
completeness.

###  0.5.1 Event reconstruction

Topologies with prompt leptons are one of the main distinctive features for
the signal in this study, where to identify leptons we make use of a dedicated
BDT classifier trained to efficiently select prompt leptons while rejecting
leptons coming from other sources, such as leptons produced in the decay of
heavy-flavour hadrons or due to detector mismeasurements. A less stringent set
of lepton requirements (loose selection) is used to veto additional leptons in
the signal region (SR) and to calculate the misidentification efficiencies
associated to the main lepton selection.

Hadronic tau leptons are reconstructed using the hadron-plus-strips algorithm
[85]. Similarly to the selection of light leptons and with the same purposes,
different levels of identification are used, based on the output of a deep
neural network, as described in Ref. [26, 89].

Hadronic jets are clustered using candidates compatible with the primary
interaction vertex using the anti- algorithm [90] with a distance parameter
$R=0.4$, and with the particles reconstructed by the particle flow algorithm
[91] as inputs. Charged hadrons associated with PU vertices are excluded from
the clustering. The energy of the reconstructed jets is corrected for residual
PU effects using the method described in Refs. [92, 90] and calibrated as a
function of jet transverse momentum and $\eta$ [83].

The primary vertex (PV) is taken to be the vertex corresponding to the hardest
scattering in the event, evaluated using tracking information alone, as
described in Section 9.4.1 of Ref. [93].

To discriminate jets produced by heavy-flavour quarks from those coming from
light-flavour quarks and gluons, we make use of the DeepJet discriminator [94,
95, 84].

The missing transverse momentum vector ($\vec{\pt}^{\text{miss}}$) is defined
as the negative of the vector sum of all particles reconstructed by the PF
algorithm. In this analysis there is a need to discriminate events where the
reconstructed arises from resolution effects. In order to do so, a linear
combination denoted linear discriminant ($\ptmiss LD$) and defined as
$0.6\ptmiss+0.4\mht$ is used, where $\mht$ corresponds to the magnitude of the
vector sum of electrons, muons, , and jets.

###  0.5.2 Event selection and background estimation

The event selection in this analysis is designed to detect the rare
$\PQt\PAQt\PH$ and $\PQt\PH$ signals in multilepton final states despite the
presence of other SM processes with larger cross section also yielding leptons
in the final state. Events are collected by a set of single-, double-, and
triple-lepton triggers that are designed to maximize the efficiency of the
trigger set. The thresholds on the lepton range 12–27 (8–24)for electrons
(muons). We then target events where the boson is produced through the
$\PQt\PAQt\PH$, $\PQt\PH\PQq$ or $\PQt\PH\PW$ process and decays into a pair
of or bosons or tau leptons. The and bosons can subsequently decay either
hadronically or into electrons or muons, while $\PGt$ leptons can decay to
electrons, muons, or hadronically (denoted $\tauh$). To achieve our
objectives, we define three event categories depending on lepton and
multiplicity: $2\ell\mkern 1.0mu\mathrm{SS}+0\tauh$, $2\ell\mkern
1.0mu\mathrm{SS}+1\tauh$, and $3\ell+0\tauh$. These regions correspond to the
most sensitive ones in the inclusive measurement of $\PQt\PAQt\PH$ and
$\PQt\PH$ production in the same final state [26]: they contain enough
$\PQt\PAQt\PH$ events to be sensitive to the signal kinematic properties,
which is a necessary aspect in a search for $CP$ violation. The selection
requirements in these regions are summarized in Table 0.5.2.

Despite the selection mentioned above, the regions are still dominated by
background events. We therefore use multivariate methods, namely artificial
neural networks, to separate the contribution from the various signal and
background species. These discriminators, developed in the context of Ref.
[26], take as an input features related to the event kinematics and provide as
an output three (four) output nodes, in the $2\ell\mkern
1.0mu\mathrm{SS}+1\tauh$ and $3\ell+0\tauh$ ($2\ell\mkern
1.0mu\mathrm{SS}+0\tauh$) categories, that estimate the probability for each
event to correspond to $\PQt\PAQt\PH$, $\PQt\PH\PQq$, or any of the
backgrounds (to $\PQt\PAQt\PH$, $\PQt\PH\PQq$, $\PQt\PAQt\PW$, or any other
background). An extra node is added in the $2\ell\mkern
1.0mu\mathrm{SS}+0\tauh$ category to gain sensitivity to the irreducible
$\PQt\PAQt\PW$ background. Events are classified according to their most
probable node, with an additional categorization in lepton charge and medium
-tagged jet multiplicity in the $2\ell\mkern 1.0mu\mathrm{SS}+0\tauh$ and
$3\ell+0\tauh$. We define as medium -tagged a jet whose value of the DeepJet
discriminator is larger than a medium working point that corresponds to a
misidentification probability of 1% for light-quark and gluon jets.

Kinematic differences between the $\PQt\PAQt\PH$ $CP$-even component and a
potential $\PQt\PAQt\PH$ $CP$-odd component are then exploited by means of an
additional multivariate discriminator. A dedicated gradient-BDT [96, 97] that
we label $\mathrm{BDT}_{CP}$, is trained for each category to distinguish
between these two components, as described in Section 0.6. Other families of
discriminators have been tested, including a likelihood ratio regression based
on the methods proposed by Ref. [98], finding no significant improvements with
respect to the main BDT approach. The details of the $CP$ hypothesis
discrimination are described in detail in Section 0.6.

In order to determine the normalization of the $\PQt\PAQt\PZ$, $\PW\PZ$, and
$\PZ\PZ$ processes, we make use of control regions (CRs) enriched in these
processes. Two CRs are defined, requiring three and four leptons in the final
state. The three-lepton CR is defined by inverting the boson veto present in
the $3\ell+0\tauh$ SR. The selection criteria on jets and -tagged jets are
dropped in this region. Events are then classified according to the number of
jets and -tagged jets, in order to be sensitive to $\PW\PZ$ and $\PQt\PAQt\PZ$
production. A four-lepton CR is defined by events with four leptons, two of
which are taken to form a boson candidate. Events in this region are
classified according to the number of boson candidates and the jet and -tagged
jet multiplicity.

The contribution of signal and background events is estimated based on methods
outlined in Ref. [26]. Backgrounds are classified as either reducible or
irreducible depending on the source of the reconstructed leptons passing the
object selection criteria. A background is considered reducible when one or
more of the reconstructed leptons passing the main object selection criteria
do not correspond to a lepton originated in the prompt decay of a or boson or
a tau lepton decay. The background is considered irreducible otherwise.

We distinguish three sources of reducible background contributions:
misidentified leptons and $\tauh$s (misidentified lepton), conversions of a
photon into an electron-positron pair in the tracker material (conversions),
and mismeasurement of the lepton charge (charge flip). The main contribution
to misidentified lepton background stems from production, reflecting the large
cross section for this background process. The conversions background is
typically caused by $\ttbar\gamma$ events in which one electron or positron
produced in the photon conversion carries most of the energy of the converted
photon, whereas the other electron or positron is of low energy and fails to
get reconstructed. We refer to such photon conversions as asymmetric
conversions. The contribution of this background is heavily suppressed by
requiring electron tracks not to have missing hits in the innermost layers of
the silicon tracker and by vetoing candidates that are matched to a
reconstructed conversion vertex. The flips background is specific to the
$2\ell\mkern 1.0mu\mathrm{SS}+0\tauh$ and $2\ell\mkern
1.0mu\mathrm{SS}+1\tauh$ channels and consists in events where the charge of a
reconstructed lepton is mismeasured.

The mismeasurement of the electron charge typically results from the emission
of a hard bremsstrahlung photon, followed by an asymmetric conversion of this
photon. The reconstructed particle is typically the electron or positron that
carries most of the energy of the converted photon, resulting in an equal
probability for the reconstructed particle to have either the same or opposite
charge compared to the charge of the electron or positron that emitted the
bremsstrahlung photon [99]. The main contribution to the flips background
stems from events in which both top quarks decay semi-leptonically. In case of
the $2\ell\mkern 1.0mu\mathrm{SS}+1\tauh$ channel, a quark or gluon jet is
additionally misidentified as $\tauh$. The probability of mismeasuring the
charge of muons is negligible in this analysis.

The misidentified leptons and flips backgrounds are largely suppressed by the
lepton and selection described in Section 0.5, and are estimated using control
samples in data with techniques based on the misidentification probability
method [20], whereas the conversions background is modelled using the MC
simulation. More details can be found in Ref. [26].

Irreducible backgrounds are estimated using samples of simulated events. We
call rare backgrounds to the aggregate of background processes which typically
yield a minor contribution and include such processes as $\PQt\PZ$ production,
the production of $\mkern 1.0mu\mathrm{SS}$ boson pairs, triboson, and
$\PQt\PAQt\PQt\PAQt$ production. In particular we include under this label all
backgrounds estimated from simulation other than those arising from
$\PQt\PAQt\PW$, $\PQt\PAQt\PZ$, and diboson backgrounds or from SM boson
production via the processes $\Pg\Pg\PH$, $\PQq\PQq\PH$, $\PW\PH$, $\PZ\PH$,
$\PQt\PAQt\PW\PH$, and $\PQt\PAQt\PZ\PH$.

Additional details on the background categorization and estimation are given
in Ref. [26].

Event selections applied in the $2\ell\mkern 1.0mu\mathrm{SS}+0\tauh$,
$2\ell\mkern 1.0mu\mathrm{SS}+1\tauh$, and $3\ell+0\tauh$ categories.

Selection | $2\ell\mkern 1.0mu\mathrm{SS}+0\tauh$ | $2\ell\mkern 1.0mu\mathrm{SS}+1\tauh$ | $3\ell+0\tauh$
---|---|---|---
Trigger | Single- and double-lepton triggers | Single-, double- and triple-lepton triggers
Lepton  |  $\pt>25$ / $15\GeV$ |  $\pt>25$ / $15$ ($\Pe$) or $10\GeV$ ($\Pgm$) |  $\pt>25$ / $15$ / $10\GeV$
Lepton $\eta$ |  $\abs{\eta}<2.5$ ($\Pe$) or $2.4$ ($\Pgm$) |  $\abs{\eta}<2.5$ ($\Pe$) or $2.4$ ($\Pgm$)
$\tauh$ |  | $\pt>20\GeV$ |
$\tauh$ $\eta$ |  | $\abs{\eta}<2.3$ |
Charge requirements | 2 same-sign leptons and |
| charge quality requirements
|  | $\sum\limits_{\ell,\tauh}q=\pm 1$ | $\sum\limits_{\ell}q=\pm 1$
Jet multiplicity∗∗ |  $\geq$3 jets |  $\geq$2 jets
$\PQb$ tagging requirements∗∗ |  $\geq$1 medium -tagged jet or $\geq$2 loose -tagged jets
Light jet and tag∗∗∗ |  $\geq$1 light jets, $\geq$1 medium -tagged jet
Missing transverse momentum | $\ptmiss LD>30\GeV\,^{\mathsection}\,$ | $\ptmiss LD>45\GeV\,^{\ddagger}\,{}^{**}\\}$
Dilepton mass |  $m_{\ell\ell}>12\GeV\,^{*}$, $\abs{m_{\ell\ell}-m_{\PZ}}>10\GeV$

∗ Applied on all pairs of leptons that pass loose selection.
∗∗ If events do not pass these thresholds, ∗∗∗ is required.
‡ If the event contains a same-flavour opposite-sign (SFOS) lepton pair and
$N_{\text{jet}}\leq 3$. If $N_{\text{jet}}\leq 3$ but there is no SFOS lepton
pair, the threshold is 30.
§ Applied only to $\Pe\Pe$ events.

##  0.6 The $CP$ discrimination

In order to separate $CP$-even and $CP$-odd scenarios, we trained three
separate BDT classifiers, one for each of the channels: $2\ell\mkern
1.0mu\mathrm{SS}+0\tauh$, $2\ell\mkern 1.0mu\mathrm{SS}+1\tauh$, and
$3\ell+0\tauh$. All are based on the XGBoost gradient boosting implementation
[100] and 50% of the samples are used to train the BDTs, 40% for testing, and
10% as validation data set during training. The hyperparameters of each
classifier are optimized using a sequential grid search.

Each of the channel-specific BDTs used a different set of input features. The
transverse momentum, $\eta$, and $\phi$ of the final-state particles are used
as input variables in all BDTs. The jet three-vectors are directly used only
in the $3\ell+0\tauh$ category. Other variables, such as the momentum vectors
of the four leading jets, have also been tested in the other final states. We
found that they don’t provide any increase in performance with respect to the
current set, and their removal did not result in any performance loss. Other
kinematic quantities such as the distance in the ($\eta$, $\phi$) plane
between the final-state objects are also used in all three categories.

The invariant mass of the system composed by the leptons in the final state
(including $\PGt$s), the , and an appropriate number of jets (depending on the
final state), proved to be a useful variable to discriminate between $CP$-even
and $CP$-odd states. We call this variable invariant mass of the reconstructed
$\PQt\PAQt\PH$ and is defined as:

$M_{\PQt\PAQt\PH{}}=\|\sum_{i}p^{\text{lep}_{i}}+(\pt^{\text{miss}},\vec{\pt}^{\text{miss}})+\sum_{i\leq
k}p^{\text{jet}_{i}*}\|\;,$ (2)

where $\|\cdot\|$ denotes the norm in the Minkowski space and
$p^{\text{lep}_{i}}$ ($p^{\text{jet}_{i}*}$) are the four-momenta of the
leptons (jets). The number $k$ of jets used to compute the invariant mass of
the system is taken accordingly to the expected number of jets given by the
$\PQt\PAQt\PH$ subsequent decays in the final state corresponding to the
category, , $k=6$ (4) in the final state $2\ell\mkern 1.0mu\mathrm{SS}+0\tauh$
($2\ell\mkern 1.0mu\mathrm{SS}+1\tauh$ and $3\ell+0\tauh$). If more than the
expected number of jets are present in the event, because of initial- or
final-state radiation or because of misreconstructed jets from detector noise
or PU, then the appropriate subset of jets is chosen by highest . This mass
variable is used in all three BDTs.

For the $2\ell\mkern 1.0mu\mathrm{SS}+0\tauh$ final state, the transverse
masses of each lepton and are included in the training. We define the
transverse mass as:

$m_{\mathrm{T}}(l_{i},\ptmiss)=\sqrt{\left(\abs{\vec{p}_{\mathrm{T,l_{i}}}}+\abs{\vec{\pt}^{\text{miss}}}\right)^{2}-\left\abs{\vec{p}_{\mathrm{T,l_{i}}}+\vec{\pt}^{\text{miss}}^{2}}\;,}$
(3)

where $\vec{p}_{\mathrm{T,l_{i}}}$ is the transverse momenta of the
corresponding lepton.

The jet multiplicity, the $\ptmiss$, the $\phi$ component of the $\ptvecmiss$
vector, and the average distance in the ($\eta$, $\phi$) plane between the
jets are also included, to further increase the performance in the
$2\ell\mkern 1.0mu\mathrm{SS}+0\tauh$ and $2\ell\mkern
1.0mu\mathrm{SS}+1\tauh$ categories.

Besides, jets coming from the hadronic decay of the top quark can also be
exploited to enhance the discrimination between the two $CP$ scenarios. A BDT
is computed over a given triplet of jets, allowing to identify the triplets of
jets produced in the hadronic decay of a top quark, as described in Ref. [26].
We use the highest score of all possible jet triplets present in the event as
input variable in the $2\ell\mkern 1.0mu\mathrm{SS}+0\tauh$ and $2\ell\mkern
1.0mu\mathrm{SS}+1\tauh$ categories. For the $2\ell\mkern
1.0mu\mathrm{SS}+1\tauh$, the output of a BDT classifier that identifies jets
from boson decays from the $\PH\to\PW\PW$ decay chain is also used [26].

The number of input features to each BDT classifier varies between 16 to 25.
Table 0.6 summarizes all the input features used for the BDTs. The modelling
of all variables has been checked in three validation regions enriched in
misidentified lepton background, $\PQt\PAQt\PZ$ and $\PW\PZ$, respectively.
Some of the most important variables in the three validation regions are shown
in Figures 3 and 4.

Figure 3:  One of the most important input variables for the $CP$
discriminant, $M_{\PQt\PAQt\PH{}}$, in the three validation regions enriched
from left to right in $\PW\PZ$, $\PQt\PAQt\PZ$ and misidentified lepton
background.

Figure 4:  One of the most important input variables for the $CP$
discriminant, $\Delta\eta_{BB}$, in the three validation regions enriched from
left to right in $\PW\PZ$, $\PQt\PAQt\PZ$ and misidentified lepton background.

Some representative input feature distributions, corresponding to those with
the highest post-training importance score in each final state, are shown in
Figs. 5 and 6 for the $2\ell\mkern 1.0mu\mathrm{SS}+0\tauh$ and $3\ell+0\tauh$
channels, respectively. The variables shown are found to discriminate between
the two CP scenarios, as indicated in references [49] and [101].

Figure 5:  Most important input variables to the XGBoost used for $CP$
discrimination in $2\ell\mkern 1.0mu\mathrm{SS}+0\tauh$ channel, defined in
Table 0.6. The vertical bars represent the statistical uncertainty originating
from the limited amount of simulated events. When not visible, the bars are
smaller than the line width.

Figure 6:  Most important input variables to the XGBoost used for $CP$
discrimination in $3\ell+0\tauh$ channel, defined in Table 0.6. The vertical
bars represent the statistical uncertainty originating from the limited amount
of simulated events. When not visible, the bars are smaller than the line
width.

Input features for the three BDTs. A check mark (✓) indicates the variable is
used in a given final state, whereas a long dash () indicates the variable is
not used in that final state.  Variable description $2\ell\mkern
1.0mu\mathrm{SS}+0\tauh$ $2\ell\mkern 1.0mu\mathrm{SS}+1\tauh$ $3\ell+0\tauh$
$\pt$ of jet 1 ✓ $\pt$ of jet 2 ✓ $\pt$ of lepton 1 ✓ ✓ ✓ $\pt$ of lepton 2 ✓
✓ ✓ $\pt$ of lepton 3 ✓ $\pt$ of $\PGt$ lepton ✓ $\eta$ of lepton 1 ✓ ✓ $\eta$
of lepton 2 ✓ ✓ $\eta$ of $\PGt$ lepton ✓ $\phi$ of lepton 1 ✓ ✓ $\phi$ of
lepton 2 ✓ ✓ $\phi$ of $\PGt$ lepton ✓ $m_{\mathrm{T}}(l_{1},\ptmiss)+\ptmiss$
✓ $m_{\mathrm{T}}(l_{2},\ptmiss)+\ptmiss$ system ✓ $\Delta R$ of lepton 1 to
its closest jet ✓ ✓ ✓ $\Delta R$ of lepton 2 to its closest jet ✓ ✓ ✓
Invariant mass of the reconstructed $\PQt\PAQt\PH$ system
($M_{\PQt\PAQt\PH{}}=\sum_{i}p^{\text{lep}_{i}}+\vec{\pt}^{\text{miss}}+\sum_{i\leq
k}p^{\text{jet}_{i}*}$) ✓ ✓ ✓ $\Delta\eta$ of two jets with highest b score in
the laboratory frame ($\Delta\eta_{BB}$) ✓ ✓ ✓ $\Delta\eta$ of the two leptons
in frame of two most-likely b jets ✓ ✓ $\Delta\eta$ of two jets with highest b
score in the dilepton system frame ✓ ✓ $\Delta\eta$ of two jets with highest b
score in the $\ell_{1}$-$\ell_{2}$ system frame ✓ $\Delta\eta$ of two jets
with highest b score in the $\ell_{1}$-$\ell_{3}$ system frame ✓ $\Delta\phi$
of the two leptons in frame of two most-likely b jets ✓ $\Delta\phi$ of two
jets with highest b score in the dilepton system frame ✓ Average $\Delta R$
among all jets ✓ ✓ Jet multiplicity ✓ ✓ ✓ ✓ Azimuthal angle of  ✓ ✓ Highest
BDT score of jet triplet from  ✓ ✓ Higgs jet tagger ✓ Angle of $\PQt\PAQt$ and
boson in $\PQt\PAQt\PH$-system ✓ Angle between two in -frame ✓ $\Delta
R_{l_{3}-l_{1}}=\sqrt{(\eta_{\ell_{3}}-\eta_{\ell_{1}})^{2}+(\phi_{\ell_{3}}-\phi_{\ell_{1}})^{2}}$
✓ $\Delta
R_{l_{1}-l_{2}}=\sqrt{(\eta_{\ell_{1}}-\eta_{\ell_{2}})^{2}+(\phi_{\ell_{1}}-\phi_{\ell_{2}})^{2}}$
✓ $\Delta
R_{l_{2}-l_{3}}=\sqrt{(\eta_{\ell_{2}}-\eta_{\ell_{3}})^{2}+(\phi_{\ell_{2}}-\phi_{\ell_{3}})^{2}}$
✓ $\eta_{\mathrm{jet1}}-\eta_{\mathrm{jet2}}$ ✓
$\pt^{\mathrm{jet1}}+\pt^{\mathrm{jet2}}+\pt^{\mathrm{jet3}}+\ptmiss$ ✓ Total
number of variables 19 25 16 ∗ k = 6 (4) in the $2\ell\mkern
1.0mu\mathrm{SS}+0\tauh$ ($2\ell\mkern 1.0mu\mathrm{SS}+1\tauh$ and
$3\ell+0\tauh$) final state

##  0.7 Systematic uncertainties

Various imprecisely-known effects may alter the event yield of the
$\PQt\PAQt\PH$ and $\PQt\PH$ signals and of background processes, as well as
the shape of the distributions in the discriminating observables that are used
for the signal extraction. In this section, these effects, usually called
systematic uncertainties, are described and their impact on the yields in the
various final states is discussed.

The systematic uncertainties are modelled as nuisance parameters in a maximum
likelihood (ML) fit to set limits on BSM scenarios with modified Higgs
couplings using the method described in Ref. [102]. The fit is described in
detail in Section 0.8. The nuisance parameters are allowed to modify the event
yield, accounting also for the migration of events among regions and among
different bins in the distributions fitted in each region. Nuisance parameters
accounting for the limited amount of simulated events are treated using the
Barlow-Beeston-lite approach [103].

We consider two categories of nuisance parameters: those that purely affect
the yield in a category (rate uncertainties) are assigned a log-normal
probability density function, whereas those that affect also the shape of the
distributions (shape uncertainties) are modelled via a polynomial
interpolation with a Gaussian constraint and are also allowed to change the
event yields in a category. The correlations between the various experimental
uncertainty sources across the three years of data taking are detailed in the
text and summarized in Table 0.7.2. Theoretical uncertainties are treated as
correlated between the three years of data taking.

###  0.7.1 Experimental uncertainties

The integrated luminosities for the 2016, 2017, and 2018 data-taking years
have 1.2–2.5% individual uncertainties [61, 62, 63], while the overall
uncertainty for the 2016–2018 period is 1.6%. These effects are applied as
rate uncertainties.

Uncertainties in the instantaneous luminosity and in the $\Pp\Pp$ inelastic
cross section may affect the event yield of the $\PQt\PAQt\PH$ and $\PQt\PH$
signals and of backgrounds obtained from the MC simulation, because different
PU conditions may modify the efficiency to pass the event selection criteria.
We vary the product of instantaneous luminosity and $\Pp\Pp$ inelastic cross
section, referred to as the number of PU interactions, by 5% [104], and
propagate the effect to the event yields, obtaining an uncertainty in the
yield smaller than 1%.

For the 2016 and 2017 data-taking periods, additional corrections to the ECAL
measurements are applied to take into account the inefficiency in the trigger
caused by the gradual shift in the timing of the inputs of the ECAL level 1
(L1) trigger in the region at $\abs{\eta}>2.0$ [105]. Correction factors are
computed from data and applied to the acceptance evaluated by simulation. The
uncertainty in these corrections is propagated to the final discriminators and
taken as a shape uncertainty, uncorrelated across data-taking periods.

The efficiencies of triggers based on the presence of two or three electrons
or muons are measured as a function of the lepton multiplicity using samples
of and diboson events that have been recorded using triggers based on . The
uncertainties on the trigger efficiencies result in uncertainties in the range
1–2%, once propagated to the event yields. For the $2\ell\mkern
1.0mu\mathrm{SS}+0\tauh$ and $2\ell\mkern 1.0mu\mathrm{SS}+1\tauh$ categories,
the uncertainty is taken as shape systematics, to account for effects in and
$\eta$ and is correlated across categories. For the $3\ell+0\tauh$ category,
the uncertainty is taken as a flat normalization and treated as uncorrelated
with the other two categories. Trigger uncertainties are treated as
uncorrelated across years for all categories.

Identification and isolation efficiencies for electrons and muons are
estimated as a function of the lepton and $\eta$ in a dedicated way for the
different lepton selections, as detailed in Ref. [26], and their uncertainties
are propagated to the final results. The total uncertainties in the muon and
electron identification and isolation efficiencies are taken as shape
uncertainties and are correlated across years, amounting to less than 2%. The
uncertainty in the $\tauh$ identification efficiency amounts to about 5%: it
is dominated by statistical effects and is therefore treated as uncorrelated
across years, $\pt$ bins, and decay modes.

The energy scales of electrons and muons are known with an uncertainty of less
than 1% and are neglected in the analysis. The uncertainties associated to the
energy scale of $\tauh$ are obtained by varying the corresponding scale factor
by its uncertainties, which are lower than 1.1% [85]. The total uncertainty in
the $\tauh$ energy scale is taken as a shape uncertainty and is treated as
uncorrelated across years.

The uncertainty in the jet energy scale (JES) is measured to an uncertainty of
a few percent and propagated to the event yields as shape uncertainties [83].
The uncertainty in the jet energy resolution (JER) is smaller than the effect
of the uncertainty in the JES. Since this analysis is moderately sensitive to
the JES and JER corrections, eleven independent uncertainty components are
considered, grouped by the detector region. Some of these components are
correlated across the years and some are not, while all of them are treated as
uncorrelated with eachother.

Uncertainties in the tagging efficiencies and mistag rates as function of the
jet $\pt$ and $\eta$ are propagated to the event yields by considering three
sources: the impact of the JES uncertainties, the purity in the control sample
used to derive the data-to-MC correction factors, and the statistics of the
sample used to derive the data-to-MC correction factors [84]. The effect of
the uncertainties in the tagging efficiency and mistag rate is small compared
to the statistical uncertainties. The tagging efficiency uncertainties of
statistical origin are uncorrelated across years, while the experimental ones
are correlated.

Uncertainties in the $\ptmiss$ resolution and response are taken into account
by varying the jet energy scale and resolution within their respective
uncertainties and recomputing and all related observables after each
variation. The resulting total uncertainty is taken as a shape uncertainty and
is treated as correlated across years. An additional uncertainty in is
obtained by varying the momentum of particle flow candidates according to
their resolution.

The procedures used to compute the uncertainties in the misidentified leptons
background estimation are detailed in Ref. [26]. These uncertainties amount to
about 10–20%, depending on the category. An additional uncertainty is added in
the $2\ell\mkern 1.0mu\mathrm{SS}+1\tauh$ region, because not all effects are
well encapsulated by the current systematic uncertainties in the estimated
misidentification probability.

The uncertainty in the normalization of the charge flip background, which is
present in the $2\ell\mkern 1.0mu\mathrm{SS}+0\tauh$ and $2\ell\mkern
1.0mu\mathrm{SS}+1\tauh$ categories, amounts to 30%, coming mainly from
electrons.

The uncertainties associated to the misidentified leptons background
estimation techniques are treated as uncorrelated across the years.

###  0.7.2 Theoretical uncertainties

The signal rates are measured in units of the SM $\PQt\PAQt\PH$ and $\PQt\PH$
production rates: the measurement is therefore affected by uncertainties in
the $\PQt\PAQt\PH$ and $\PQt\PH$ cross sections.

The uncertainty in the SM $\PQt\PAQt\PH$ ($\PQt\PH$) cross section, computed
at NLO accuracy, amounts to ${}^{+6.8\%}_{-10.0\%}$ (${}^{+4.2\%}_{-6.8\%}$),
of which ${}^{+5.8\%}_{-9.3\%}$ (${}^{+4.1\%}_{-6.7\%}$) are due to missing
higher orders and 3.6% arises from uncertainties in the parton distribution
function (PDF) and the strong coupling $\alpha_{s}$ [106].

The uncertainty applied on the normalization of non-SM scenarios is the same
as the SM one. The $\PQt\PAQt\PH$ process is simulated at LO in this analysis.
An uncertainty in the acceptance due to missing higher orders treated as a
shape systematic is considered to cover for discrepancies between NLO and LO
simulation.

The uncertainties in the branching fraction for the boson to decay into
$\PW\PW$ ($\Pgt\Pgt$) are taken into account, amounting to 1.54 (1.65)% [53].

Uncertainties in the acceptance that are due to missing higher orders are
treated as shape systematics, as they affect the shape of the distribution in
the observable used for signal extraction. They are estimated by varying the
renormalization ($\mu_{\textrm{R}}$) and factorization ($\mu_{\textrm{F}}$)
scales between 0.5 and 2 times their default values, with the constraint that
$0.5\leq\mu_{\textrm{F}}/\mu_{\textrm{R}}<2$, as recommended in [107, 108,
109]. The effect of uncertainties in the PDFs on these distributions is
evaluated as recommended in [110].

All uncertainties associated to theoretical calculations are considered
correlated across years.

The extrapolation of the $\PW\PZ$+jets and $\PZ\PZ$+jets background rates from
the 3$\ell$ and 4$\ell$-CRs to the SR depends on the heavy-flavour content of
$\PW\PZ$+jets and $\PZ\PZ$+jets background events. According to the MC
simulation, most of the jets reconstructed in $\PW\PZ$+jets and $\PZ\PZ$+jets
background events arise from the misidentification of light-flavour quark and
gluon jets rather than from charm or bottom quarks. We assign an uncertainty
of 40 (10)% on $\PW\PZ$+jets and $\PZ\PZ$+jets events with at least (less
than) two -tagged jets, to cover the modelling of the heavy-flavour content in
these background events. Besides, in order to account for the differences in
the jet multiplicity distribution between data and simulation in the 3$\ell$
CR described in Section 0.5, we apply a 30% uncertainty on $\PW\PZ$+jets and
$\PZ\PZ$+jets events with more than two jets.

The uncertainty in the background arising from production of top quark pairs
in association with real or virtual photons amounts to 30% [26]. An
uncertainty of 50% is assigned to other rare backgrounds that are modelled
using MC simulation [26]. These choices account for the extrapolation from the
inclusive phase space to the phase space relevant for this analysis, in
particular to events with a high multiplicity of jets and b-tagged jets, as
required to pass the event selection criteria.

We make no assumption on the rates of the irreducible $\PW\PZ$+jets,
$\PZ\PZ$+jets, $\PQt\PAQt\PW$, $\PQt\PAQt\PW\PW$, and $\PQt\PAQt\PZ$
backgrounds: the normalization of these backgrounds is determined
simultaneously in the ML fit used for the signal extraction, described in
Section 0.8. The total normalization for each process is constrained by the
dedicated CRs defined in Section 0.5.

The largest impacts on the measurement of the coupling modifiers are due to:
the statistical uncertainty of observed data; the uncertainties related to the
estimation of the misidentified leptons and flips backgrounds; the
uncertainties on the jet reconstruction; the theoretical uncertainties, which
affect the yield and the distribution of the discriminating observables for
the ttH and tH signals as well as for the main irreducible backgrounds,
arising from $\PQt\PAQt\PW$, $\PQt\PAQt\PW\PW$, and $\PQt\PAQt\PZ$, and
$\PQt\PZ$ production; and the uncertainty applied to cover for modelling
differences between LO and NLO simulation of the signal.

Summary of the uncertainty sources, their type, and their correlations across
the three data-taking periods. Trigger efficiency uncertainty is taken as a
shape or normalization systematic depending on the channel.  Uncertainty
source Type Correlation 2016–2018 Experimental uncertainties Trigger
efficiency Norm. / Shape Uncorrelated Integrated luminosity Norm. Uncorr. /
Corr. tagging efficiency and mistag rate Shape Uncorr. (stat.) / Corr. (exp.)
Pileup reweighting Shape Correlated L1 ECAL trigger inefficiency Shape
Uncorrelated Jet energy scale and resolution Shape Uncorr. / Corr. Energy
scale of $\tauh$ Shape Uncorrelated Identification and isolation efficiency
for $\Pe$ Shape Correlated Identification and isolation efficiency for $\Pgm$
Shape Correlated Identification efficiency for $\tauh$ Shape Uncorrelated
Misidentified lepton background rate Shape Correlated Flip background rate
Norm. Correlated $\ptmiss$ resolution and response Shape Correlated
Theoretical uncertainties $\Pgm_{r}$/$\Pgm_{f}$ scale Shape Correlated PDF
Norm. Correlated $\PQt\PAQt\PH{}$ LO vs. NLO diferences Norm. Correlated
Branching Ratio Norm. Correlated Extrapolation of the $\PW\PZ$+jets and
$\PZ\PZ$+jets Norm. Correlated $\ttbar\gamma$ Normalization Norm. Correlated
Rare background Normalization Norm. Correlated

##  0.8 Signal extraction

We perform a ML fit of the distributions of selected observables in the SRs
defined for the $2\ell\mkern 1.0mu\mathrm{SS}+0\tauh$, $2\ell\mkern
1.0mu\mathrm{SS}+1\tauh$, and $3\ell+0\tauh$ categories as well as the CRs on
the $3\ell$ and $4\ell$ categories. The regions are further separated into
subcategories that target different processes by means of DNN-based
classifiers, as described in Section 0.5. In the $2\ell\mkern
1.0mu\mathrm{SS}+0\tauh$ category, events are further classified depending on
the flavour of the leptons ($\Pe\Pe$/$\Pe\Pgm$/$\Pgm\Pgm$), except in the
$\PQt\PAQt\PH$ node, where no flavour categorization is applied. In the
$3\ell+0\tauh$ category, the $\PQt\PH$ and $\PQt\PAQt\PH$ nodes are separated
according to the number of -tagged jets. In the node corresponding to the
background-dominated region, events are also separated according to the lepton
flavours ($\Pe\Pe\Pe$, $\Pe\Pe\Pgm$, $\Pe\Pgm\Pgm$, and $\Pgm\Pgm\Pgm$).

In the three SRs ($2\ell\mkern 1.0mu\mathrm{SS}+0\tauh$, $3\ell+0\tauh$, and
$2\ell\mkern 1.0mu\mathrm{SS}+1\tauh$), the $\PQt\PAQt\PH$-like categories
described above are further split depending on the score of the $CP$
classifiers described in Section 0.6.

The diagram depicted in Fig. 7 shows the classification described above.

Figure 7:  Diagram showing the categorization strategy used for the signal
extraction, making use of MVA-based algorithms and topological variables. In
addition to the three signal regions (SRs), the ML fit receives input from two
control regions (CRs).

This categorization allowed us to exploit the different kinematic
characteristics of the $\PQt\PAQt\PH$ process depending on the $CP$ scenario.
On the other hand, the dedicated $\PQt\PH$ node in each of the categories
allows us to constrain the normalization of this process which provides
sensitivity to the sign of $\kappa_{\PQt}$.

The discriminating observables optimized for $\PQt\PAQt\PH$ signal in order to
perform the fit are shown in Fig. 8, showing the agreement between data and
our statistical model evaluated at the best-fit point.

Figure 8: Postfit discriminating distributions used as input to the fit.
Events in the $\PQt\PAQt\PH$ node are categorized as described in Section 0.8
for the three categories: $2\ell\mkern 1.0mu\mathrm{SS}+0\tauh$ (top)
$3\ell+0\tauh$ (center) and $2\ell\mkern 1.0mu\mathrm{SS}+1\tauh$ (bottom).
For the $2\ell\mkern 1.0mu\mathrm{SS}+1\tauh$ bl (bt) denotes events with less
than (at least) two -tagged jets. The $\PQt\PAQt\PH$ $CP$-even (red) and
$CP$-odd (pink) contributions are determined from the fit. The contribution
labeled as Nonprompt refers to the backgrounds arising from misidentified
leptons while the label Charge mism. alludes to to the backgrounds arising
from lepton charge mismeasurement.

###  0.8.1 The BSM interpretation

In order to explore BSM scenarios, in particular possible anomalous effects in
the boson couplings to fermions, we use the prescription introduced in Section
0.2 in order to parameterize the amplitude as a function of $\kappa_{\PQt}$
and $\widetilde{\kappa}_{\PQt}$. These parameters modify the coupling and
therefore the kinematics of $\PQt\PH$ and $\PQt\PAQt\PH$ processes and their
normalization. Moreover, $\PQt\PH$ is sensitive to interferences of the
coupling of the top quark to the boson, in this signal extraction procedure we
keep $\kappa_{\text{V}}$ fixed to its SM value. Branching fractions of the
boson are also set to their SM values.

###  0.8.2 Results

Confidence regions at 68 and 95% for the $\kappa_{\PQt}$ and
$\widetilde{\kappa}_{\PQt}$ couplings are obtained using the strategy
explained in this section, applying the asymptotic properties of the
likelihood ratio. Figure 9 (left) shows the expected likelihood scan as a
function of $\kappa_{\PQt}$ and $\widetilde{\kappa}_{\PQt}$. The observed
likelihood scan as a function of $\kappa_{\PQt}$ and
$\widetilde{\kappa}_{\PQt}$ is shown in Fig. 9 (right): the best fit is
compatible with the SM within 68% . The non-zero postfit value of
$\widetilde{\kappa}_{\PQt}$ is driven by a small excess in the most CP-odd
enriched regions of the $2\ell\mkern 1.0mu\mathrm{SS}+0\tauh$ and
$3\ell+0\tauh$ categories.

Figure 9: Likelihood scan as a function of $\kappa_{\PQt}$ and
$\widetilde{\kappa}_{\PQt}$: expected limits (left) and observed limits
(right). The black cross shows the best value for $\kappa_{\PQt}$ and
$\widetilde{\kappa}_{\PQt}$ given by the fit. The black diamond shows the
expected SM values for $\kappa_{\PQt}$ and $\widetilde{\kappa}_{\PQt}$. Both
68 and 95% limits are shown. $\kappa_{\text{V}}$ and boson branching fractions
are kept to their SM values.

One-dimensional confidence intervals at 68 and 95% are also obtained for
$\kappa_{\PQt}$ (fixing $\widetilde{\kappa}_{\PQt}$ to its SM value) and for
$\widetilde{\kappa}_{\PQt}$ (fixing $\kappa_{\PQt}$ to its SM value), as
illustrated in Table 0.8.2.

One-dimensional confidence intervals at 68 and 95% for $\kappa_{\PQt}$ (fixing
$\widetilde{\kappa}_{\PQt}$ to the SM) and $\widetilde{\kappa}_{\PQt}$ (fixing
$\kappa_{\PQt}$ to the SM). The upper part of the table shows the expected
limits while the lower part shows the observed limits.  Parameter 68%  95%
Expected $\kappa_{\PQt}$ (0.87, 1.14) (0.74, 1.27) $\widetilde{\kappa}_{\PQt}$
(-0.71, 0.71) (-1.01, 1.01) Observed $\kappa_{\PQt}$ (0.89, 1.17) (-1.09,
-0.74) or (0.77, 1.3) $\widetilde{\kappa}_{\PQt}$ (0.37, 1.16) or (-1.16,
-0.37) (-1.4, 1.4)

Figure 10: Likelihood scan as a function of $\abs{f_{CP}^{\PH\PQt\PQt}}$ for
multilepton final estates. The solid (dashed) line shows the observed
(expected) scan.

We also parameterize the $\PQt\PAQt\PH$ process with the signal strength
multiplier to the SM $\PQt\PAQt\PH$ cross section, $\mu_{\PQt\PAQt\PH}$, and a
parameter
$\abs{f_{CP}^{\PH\PQt\PQt}}=\frac{\abs{\widetilde{\kappa}_{\PQt}^{2}}}{(\abs{\widetilde{\kappa}_{\PQt}}^{2}+\abs{\kappa_{\PQt}{}}^{2})}$,
where the boson couplings to other particles are constrained to their SM
prediction. $\PQt\PH$ process is scaled with $\abs{f_{CP}^{\PH\PQt\PQt}}$ and
$\mu_{\PQt\PAQt\PH}$ in the fit. This parameterization results in a probe for
a possible fractional $CP$-odd contribution, yielding a best fit value of
$\abs{f_{CP}^{\PH\PQt\PQt}}=0.59$ with an interval of (0.24, 0.81) at 68%
using multilepton final states only. The result is compatible with the SM
$CP$-even scenario at the 95% CL. The pure $CP$-odd scenario is excluded with
more than two standard deviations.

##  0.9 Combined results for $CP$ in ttH events

We combine the results described in Section 0.8 for the multilepton decay
channel with previously published CMS results on the $CP$ parameters in other
$\PQt\PAQt\PH$ decay channels, namely the $\PH\to\PGg\PGg$ [25] and
$\PH\to\PZ\PZ$ ones [44].

Uncertainties that are common between the various channels are taken as fully
correlated. We detail in Section 0.9.1 the treatment for all systematic
uncertainties.

###  0.9.1 Systematic uncertainties for the combination of $CP$ measurements

As outlined in Section 0.7 for the multilepton final state, we model
systematic uncertainties as nuisance parameters in a ML fit to extract the
$\PQt\PAQt\PH$ and $\PQt\PH$ cross section and set limits on BSM scenarios
with modified Higgs couplings. The statistical model is described in detail in
Section 0.8.

The correlations between the various uncertainty sources across the three
years of data taking are detailed in Section 0.7 and summarized in Table
0.7.2.

The correlations between the various uncertainty sources across the different
channels that we combine, as well as the changes in the modelling of some
nuisance parameters to accommodate a full combination, proceed as follows:

  * •

Each of the nuisance parameters describing the uncertainty in the integrated
luminosity is taken as correlated across decay channels;

  * •

The uncertainties caused by PU effects are taken as correlated across decay
channels;

  * •

Uncertainties in the determination of the trigger efficiencies are taken as
uncorrelated across decay channels, because the uncertainties come from
independent measurements;

  * •

Uncertainties in the identification and isolation for electrons and muons are
taken as uncorrelated across the channels. The dominant component in the
multilepton channel is due to the closure of the method, as scale factors are
obtained in a DY sample and we need to extrapolate them to the analysis phase
space. Hence, the main contribution to the lepton uncertainty comes from a
different source in the multilepton channel than in other channels;
uncertainties in the identification and energy scale of $\tauh$s are specific
to the multilepton channel;

  * •

The uncertainties in the JES, JER, and tagging efficiency and mistag rate are
divided into several uncorrelated components. These uncertainties are taken as
correlated across the analyses, except for the JES and JER uncertainties,
where they are split in a different number of components and are therefore
treated as uncorrelated;

  * •

Uncertainties in the $\ptmiss$ resolution and response are taken as correlated
across decay channels;

  * •

Uncertainties in the estimation of the background from misidentified leptons
and in the normalization of the charge-flip background in the multilepton
final state are specific to this channel;

  * •

The theoretical uncertainties in the signal rates, as well as in the rates of
any background that is estimated from simulation in all decay channels, are
taken as correlated across decay channels;

  * •

The uncertainties in the branching fractions for the boson are taken as
uncorrelated per channel and correlated per decay modes of the boson;

  * •

Uncertainties in the acceptance that are due to missing higher orders are
treated for each process determined from simulation as fully correlated across
decay channels;

  * •

Uncertainties in the rate of backgrounds that were determined from analysis-
specific CRs are taken as uncorrelated. This includes the contribution of the
$\PW\PZ$+jets, $\PZ\PZ$+jets, and $\ttbar\gamma$ backgrounds in the
multilepton channel;

  * •

The normalization of the irreducible $\PQt\PAQt\PW$, $\PQt\PAQt\PW\PW$, and
$\PQt\PAQt\PZ$ backgrounds is determined simultaneously in the ML fit used for
the signal extraction, described in Section 0.8.

###  0.9.2 Results for the combination of $CP$ parameters

The combination yields a significant improvement in sensitivity, as shown in
Fig. 11 (left). Confidence regions at 68 and 95% for the $\kappa_{\PQt}$ and
$\widetilde{\kappa}_{\PQt}$ couplings are obtained using the strategy
explained in this section. Figure 12 shows the likelihood scan, as a function
of $\kappa_{\PQt}$ and $\widetilde{\kappa}_{\PQt}$, for the combination of the
multilepton, $\PH\to\PZ\PZ$, and $\PH\to\PGg\PGg$ decay modes.

Figure 11: Likelihood scan as a function of $\abs{f_{CP}^{\PH\PQt\PQt}}$. The
left plot shows the expected likelihood scan for multilepton final states,
$\PH\to\PGg\PGg$, and $\PH\to\PZ\PZ$ final states, and the combination of
multilepton, $\PH\to\PGg\PGg$, and $\PH\to\PZ\PZ$ final states. The right plot
shows the observed likelihood scan for multilepton final states and the
combination of multilepton, $\PH\to\PGg\PGg$, and $\PH\to\PZ\PZ$ final states.
Figure 12: Likelihood scan as a function of $\kappa_{\PQt}$ and
$\widetilde{\kappa}_{\PQt}$. Two-dimensional confidence intervals at 68% are
depicted as shaded areas, for multilepton (red), the combination of
$\PH\to\PGg\PGg$ and $\PH\to\PZ\PZ$ (blue), and the combination of the three
channels (black). The 95% for the combination is show as a dashed line. The
best fit for each is shown as a cross of the corresponding colour. The plot is
symmetric with respect to the line $\widetilde{\kappa}_{\PQt}$=0, hence there
are two points corresponding to the best fit, here we only show one for
simplicity. The black diamond shows the SM expected value. The nontrivial
correlation between the measurements are the source of the change in the best
fit value and shape of the confidence regions. The coupling
$\kappa_{\text{V}}$ and the boson branching fractions are kept to their SM
values.

One-dimensional confidence intervals at 68 and 95% are also obtained for
$\kappa_{\PQt}$ (fixing $\widetilde{\kappa}_{\PQt}$ to its SM value) and for
$\widetilde{\kappa}_{\PQt}$ (fixing $\kappa_{\PQt}$ to its SM value), as
listed in Table 0.9.2.

One-dimensional confidence intervals at 68 and 95% for $\kappa_{\PQt}$ and
$\widetilde{\kappa}_{\PQt}$.  Parameter 68%  95%  $\kappa_{\PQt}$ (0.96, 1.16)
(0.86, 1.26) $\widetilde{\kappa}_{\PQt}$ (-0.86, 0.85) (-1.07, 1.07)

The likelihood as a function of $\abs{f_{CP}^{\PH\PQt\PQt}}$, while profiling
$\mu_{\PQt\PAQt\PH}$, is shown for the combination of the multilepton,
$\PH\to\PZ\PZ$, and $\PH\to\PGg\PGg$ decay modes in Fig. 11 (right). This
parameterization results in a probe for a possible fractional $CP$-odd
contribution, yielding a best fit value of $\abs{f_{CP}^{\PH\PQt\PQt}}=0.28$
with an interval of $\abs{f_{CP}^{\PH\PQt\PQt}}<0.55$ at 68% . The result is
compatible with the SM $CP$-even scenario within 68% . In addition, the
scenario with $\abs{f_{CP}^{\PH\PQt\PQt}}=1$ is excluded with 3.7 standard
deviations.

##  0.10 Summary

A measurement of the charge–parity ($CP$) structure of the Yukawa coupling
between the Higgs () boson and top quarks at tree level, when the boson is
produced in association with one ($\PQt\PH$) or two ($\PQt\PAQt\PH$) top
quarks, is presented. The measurement is based on data collected in proton-
proton collisions at $\sqrt{s}=13\TeV$ by the CMS experiment at the CERN LHC,
corresponding to an integrated luminosity of 138. The analysis targets events
where the boson decays to leptons and the top quark(s) decay either
leptonically or hadronically. Separation of $CP$-even from $CP$-odd scenarios
is achieved by applying machine learning techniques to final states
characterized by the presence of at least two leptons. Two-dimensional
confidence regions are set on $\kappa_{\PQt}$ and $\widetilde{\kappa}_{\PQt}$
which are respectively the $CP$-even and $CP$-odd top-Higgs Yukawa coupling
modifiers: one-dimensional confidence intervals are also set, constraining
$\kappa_{\PQt}$ to be within $(-1.09,-0.74)$ or $(0.77,1.30)$ and
$\widetilde{\kappa}_{\PQt}$ to be within $(-1.4,1.4)$ at 95% confidence level
(). No significant $CP$-odd contribution is observed, and the corresponding
fraction parameter is determined to be $\abs{f_{CP}^{\PH\PQt\PQt}}=0.59$ with
an interval of $(0.24,0.81)$ at 68% . The results are combined with previously
published analyses covering the $\PH\to\PZ\PZ$ and $\PH\to\PGg\PGg$ decay
modes. Two- and one-dimensional confidence regions are set on $\kappa_{\PQt}$
and $\widetilde{\kappa}_{\PQt}$, constraining $\kappa_{\PQt}$ to be within
$(0.86,1.26)$ and $\widetilde{\kappa}_{\PQt}$ to be within $(-1.07,1.07)$ at
95% . The possibility of a $CP$-odd contribution is also investigated in the
combination, yielding a best fit of $\abs{f_{CP}^{\PH\PQt\PQt}}=0.28$ with an
interval of $\abs{f_{CP}^{\PH\PQt\PQt}}<0.55$ at 68% . The results are
compatible with predictions for the standard model boson.

###### 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 centres and personnel of the Worldwide LHC Computing Grid and other
centres 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 programme 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).

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##  .11 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, P.S.
Hussain0000-0002-4825-5278, 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,
T. Janssen0000-0002-3998-4081, T. Kello4, H. Rejeb Sfar, P. Van
Mechelen0000-0002-8731-9051

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 B.
Clerbaux0000-0001-8547-8211, G. De Lentdecker0000-0001-5124-7693, L.
Favart0000-0003-1645-7454, J. Jaramillo0000-0003-3885-6608, K.
Lee0000-0003-0808-4184, M. Mahdavikhorrami0000-0002-8265-3595, I.
Makarenko0000-0002-8553-4508, A. Malara0000-0001-8645-9282, S.
Paredes0000-0001-8487-9603, L. Pétré0009-0000-7979-5771, 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, 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, E. Coelho0000-0001-6114-9907, 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. Santoro0000-0002-0568-665X, 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, T.R.
Fernandez Perez Tomei0000-0002-1809-5226, E.M. Gregores0000-0003-0205-1672,
P.G. Mercadante0000-0001-8333-4302, S.F. Novaes0000-0003-0471-8549, Sandra S.
Padula0000-0003-3071-0559

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, E.
Shumka0000-0002-0104-2574

Beihang University, Beijing, China T. Cheng0000-0003-2954-9315, T.
Javaid90009-0007-2757-4054, M. Mittal0000-0002-6833-8521, L.
Yuan0000-0002-6719-5397

Department of Physics, Tsinghua University, Beijing, China M.
Ahmad0000-0001-9933-995X, G. Bauer10, Z. Hu0000-0001-8209-4343, S.
Lezki0000-0002-6909-774X, K. Yi10,110000-0002-2459-1824

Institute of High Energy Physics, Beijing, China G.M.
Chen90000-0002-2629-5420, H.S. Chen90000-0001-8672-8227, M.
Chen90000-0003-0489-9669, F. Iemmi0000-0001-5911-4051, C.H. Jiang, A.
Kapoor0000-0002-1844-1504, H. Liao0000-0002-0124-6999, Z.-A.
Liu120000-0002-2896-1386, 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, C. Yuan120000-0001-7438-6848, 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, C.
Li0000-0002-6339-8154, Q. Li0000-0002-8290-0517, X. Lyu, Y. Mao, S.J.
Qian0000-0002-0630-481X, X. Sun0000-0003-4409-4574, D.
Wang0000-0002-9013-1199, J. Xiao0000-0002-7860-3958, H. Yang

Sun Yat-Sen University, Guangzhou, China J. Li, 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, C.
Lu0000-0002-7421-0313, M. Xiao0000-0001-9628-9336

Universidad de Los Andes, Bogota, Colombia C. Avila0000-0002-5610-2693, D.A.
Barbosa Trujillo, 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, M.
Rodriguez0000-0002-9480-213X, 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,
B.K. Chitroda0000-0002-0220-8441, D. Ferencek0000-0001-9116-1202, D.
Majumder0000-0002-7578-0027, M. Roguljic0000-0001-5311-3007, A.
Starodumov130000-0001-9570-9255, 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. Finger0000-0002-7828-9970, M.
Finger Jr.0000-0003-3155-2484, 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.
Abdalla140000-0002-4177-7209, Y. Assran15,16

Center for High Energy Physics (CHEP-FU), Fayoum University, El-Fayoum, Egypt
M. Abdullah Al-Mashad0000-0002-7322-3374, 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, 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-Navarro170000-0002-9481-5168, P.
Simkina0000-0002-9813-372X, M. Titov0000-0002-1119-6614

Laboratoire Leprince-Ringuet, CNRS/IN2P3, Ecole Polytechnique, Institut
Polytechnique de Paris, Palaiseau, France C. Baldenegro
Barrera0000-0002-6033-8885, F. Beaudette0000-0002-1194-8556, A. Buchot
Perraguin0000-0002-8597-647X, P. Busson0000-0001-6027-4511, A.
Cappati0000-0003-4386-0564, C. Charlot0000-0002-4087-8155, F.
Damas0000-0001-6793-4359, 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, G. Liu0000-0001-7002-0937, J.
Motta0000-0003-0985-913X, M. Nguyen0000-0001-7305-7102, C.
Ochando0000-0002-3836-1173, 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, E.
Vernazza0000-0003-4957-2782, A. Zabi0000-0002-7214-0673, A.
Zghiche0000-0002-1178-1450

Université de Strasbourg, CNRS, IPHC UMR 7178, Strasbourg, France J.-L.
Agram180000-0001-7476-0158, J. Andrea0000-0002-8298-7560, D.
Apparu0009-0004-1837-0496, D. Bloch0000-0002-4535-5273, G.
Bourgatte0009-0005-7044-8104, J.-M. Brom0000-0003-0249-3622, E.C.
Chabert0000-0003-2797-7690, C. Collard0000-0002-5230-8387, D. Darej, U.
Goerlach0000-0001-8955-1666, C. Grimault, A.-C. Le Bihan0000-0002-8545-0187,
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, A. Carle, N. Chanon0000-0002-2939-5646, J.
Choi0000-0002-6024-0992, D. Contardo0000-0001-6768-7466, P.
Depasse0000-0001-7556-2743, C. Dozen190000-0002-4301-634X, H. El Mamouni, J.
Fay0000-0001-5790-1780, S. Gascon0000-0002-7204-1624, M.
Gouzevitch0000-0002-5524-880X, G. Grenier0000-0002-1976-5877, B.
Ille0000-0002-8679-3878, I.B. Laktineh, M. Lethuillier0000-0001-6185-2045, L.
Mirabito, S. Perries, V. Sordini0000-0003-0885-824X, L.
Torterotot0000-0002-5349-9242, M. Vander Donckt0000-0002-9253-8611, P.
Verdier0000-0003-3090-2948, S. Viret

Georgian Technical University, Tbilisi, Georgia D.
Chokheli0000-0001-7535-4186, I. Lomidze0009-0002-3901-2765, Z.
Tsamalaidze130000-0001-5377-3558

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, M. Teroerde0000-0002-5892-1377

RWTH Aachen University, III. Physikalisches Institut A, Aachen, Germany S.
Diekmann0009-0004-8867-0881, 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, F. Nowotny, A. Pozdnyakov0000-0003-3478-9081, Y.
Rath, W. Redjeb0000-0001-9794-8292, 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, A.
Stahl210000-0002-8369-7506, T. Ziemons0000-0003-1697-2130, A.
Zotz0000-0002-1320-1712

Deutsches Elektronen-Synchrotron, Hamburg, Germany H. Aarup
Petersen0009-0005-6482-7466, M. Aldaya Martin0000-0003-1533-0945, P. Asmuss,
S. Baxter0009-0008-4191-6716, M. Bayatmakou0009-0002-9905-0667, O.
Behnke0000-0002-4238-0991, 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.
Eckstein0000-0002-7366-6562, 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, A.
Kasem230000-0002-6753-7254, M. Kasemann0000-0002-0429-2448, H.
Kaveh0000-0002-3273-5859, C. Kleinwort0000-0002-9017-9504, R.
Kogler0000-0002-5336-4399, M. Komm0000-0002-7669-4294, D.
Krücker0000-0003-1610-8844, W. Lange, D. Leyva Pernia0009-0009-8755-3698, 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, G. Milella0000-0002-2047-951X, M.
Mormile0000-0003-0456-7250, A. Mussgiller0000-0002-8331-8166, A.
Nürnberg0000-0002-7876-3134, Y. Otarid, D. Pérez Adán0000-0003-3416-0726, A.
Raspereza0000-0003-2167-498X, B. Ribeiro Lopes0000-0003-0823-447X, J.
Rübenach, A. Saggio0000-0002-7385-3317, A. Saibel0000-0002-9932-7622, M.
Savitskyi0000-0002-9952-9267, M. Scham26,230000-0001-9494-2151, V. Scheurer,
S. Schnake230000-0003-3409-6584, 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, A. Ventura
Barroso0000-0003-3233-6636, R. Walsh0000-0002-3872-4114, D.
Walter0000-0001-8584-9705, Q. Wang0000-0003-1014-8677, Y.
Wen0000-0002-8724-9604, K. Wichmann, L. Wiens230000-0002-4423-4461, C.
Wissing0000-0002-5090-8004, S. Wuchterl0000-0001-9955-9258, Y.
Yang0009-0009-3430-0558, A. Zimermmane Castro Santos0000-0001-9302-3102

University of Hamburg, Hamburg, Germany R. Aggleton, A.
Albrecht0000-0001-6004-6180, S. Albrecht0000-0002-5960-6803, M.
Antonello0000-0001-9094-482X, S. Bein0000-0001-9387-7407, L.
Benato0000-0001-5135-7489, M. Bonanomi0000-0003-3629-6264, 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, H.R.
Jabusch0000-0003-2444-1014, G. Kasieczka0000-0003-3457-2755, R.
Klanner0000-0002-7004-9227, W. Korcari0000-0001-8017-5502, T.
Kramer0000-0002-7004-0214, V. Kutzner0000-0003-1985-3807, J.
Lange0000-0001-7513-6330, T. Lange0000-0001-6242-7331, A.
Lobanov0000-0002-5376-0877, C. Matthies0000-0001-7379-4540, A.
Mehta0000-0002-0433-4484, L. Moureaux0000-0002-2310-9266, M. Mrowietz, A.
Nigamova0000-0002-8522-8500, Y. Nissan, A. Paasch0000-0002-2208-5178, 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, M. Wolf0000-0003-3002-2430

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, 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, M.
Horzela0000-0002-3190-7962, U. Husemann0000-0002-6198-8388, P. Keicher, M.
Klute0000-0002-0869-5631, 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. Shvetsov0000-0002-7069-9019, H.J.
Simonis0000-0002-7467-2980, N. Trevisani0000-0002-5223-9342, 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. Wozniewski0000-0001-8563-0412, 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, 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, I.
Zisopoulos0000-0001-5212-4353

National Technical University of Athens, Athens, Greece G.
Bakas0000-0003-0287-1937, T. Chatzistavrou, 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, C.
Kamtsikis, P. Katsoulis, P. Kokkas0009-0009-3752-6253, P.G. Kosmoglou
Kioseoglou0000-0002-7440-4396, 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.
Rádl290000-0001-8810-0388, O. Surányi0000-0002-4684-495X, G.I.
Veres0000-0002-5440-4356

Wigner Research Centre for Physics, Budapest, Hungary M.
Bartók300000-0002-4440-2701, G. Bencze, C. Hajdu0000-0002-7193-800X, D.
Horvath31,320000-0003-0091-477X, F. Sikler0000-0001-9608-3901, V.
Veszpremi0000-0001-9783-0315

Institute of Nuclear Research ATOMKI, Debrecen, Hungary N.
Beni0000-0002-3185-7889, S. Czellar, D. Fasanella0000-0002-2926-2691, J.
Karancsi300000-0003-0802-7665, J. Molnar, Z. Szillasi, D.
Teyssier0000-0002-5259-7983

Institute of Physics, University of Debrecen, Debrecen, Hungary P. Raics, B.
Ujvari330000-0003-0498-4265

Karoly Robert Campus, MATE Institute of Technology, Gyongyos, Hungary T.
Csorgo290000-0002-9110-9663, F. Nemes290000-0002-1451-6484, T.
Novak0000-0001-6253-4356

Panjab University, Chandigarh, India J. Babbar0000-0002-4080-4156, S.
Bansal0000-0003-1992-0336, S.B. Beri, V. Bhatnagar0000-0002-8392-9610, G.
Chaudhary0000-0003-0168-3336, S. Chauhan0000-0001-6974-4129, N.
Dhingra340000-0002-7200-6204, R. Gupta, A. Kaur0000-0002-1640-9180, A.
Kaur0000-0003-3609-4777, H. Kaur0000-0002-8659-7092, M.
Kaur0000-0002-3440-2767, S. Kumar0000-0001-9212-9108, P.
Kumari0000-0002-6623-8586, M. Meena0000-0003-4536-3967, K.
Sandeep0000-0002-3220-3668, T. Sheokand, J.B. Singh350000-0001-9029-2462, A.
Singla0000-0003-2550-139X, A. K. Virdi0000-0002-0866-8932

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 S.
Baradia0000-0001-9860-7262, S. Barman360000-0001-8891-1674, S.
Bhattacharya0000-0002-8110-4957, D. Bhowmik, S. Dutta0000-0001-9650-8121, S.
Dutta, B. Gomber370000-0002-4446-0258, M. Maity36, P.
Palit0000-0002-1948-029X, P.K. Rout0000-0001-8149-6180, G.
Saha0000-0002-6125-1941, B. Sahu0000-0002-8073-5140, S. Sarkar

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. Komaragiri380000-0002-9344-6655, D.
Kumar380000-0002-6636-5331, A. Muhammad0000-0002-7535-7149, L.
Panwar380000-0003-2461-4907, R. Pradhan0000-0001-7000-6510, P.R.
Pujahari0000-0002-0994-7212, A. Sharma0000-0002-0688-923X, A.K.
Sikdar0000-0002-5437-5217, P.C. Tiwari380000-0002-3667-3843, S.
Verma0000-0003-1163-6955

Bhabha Atomic Research Centre, Mumbai, India K. Naskar390000-0003-0638-4378

Tata Institute of Fundamental Research-A, Mumbai, India T. Aziz, I.
Das0000-0002-5437-2067, S. Dugad, M. Kumar0000-0003-0312-057X, G.B.
Mohanty0000-0001-6850-7666, P. Suryadevara

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, A.
Thachayath0000-0001-6545-0350

National Institute of Science Education and Research, An OCC of Homi Bhabha
National Institute, Bhubaneswar, Odisha, India S.
Bahinipati400000-0002-3744-5332, A.K. Das, C. Kar0000-0002-6407-6974, P.
Mal0000-0002-0870-8420, T. Mishra0000-0002-2121-3932, V.K. Muraleedharan Nair
Bindhu410000-0003-4671-815X, A. Nayak410000-0002-7716-4981, P.
Saha0000-0002-7013-8094, N. Sur0000-0001-5233-553X, S.K. Swain, D.
Vats410009-0007-8224-4664

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 H.
Bakhshiansohi42,430000-0001-5741-3357, E. Khazaie430000-0001-9810-7743, 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 Baria, Università di Barib, Politecnico di Baric, Bari, Italy
M. Abbresciaa,b0000-0001-8727-7544, R. Alya,b0000-0001-6808-1335, 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, 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, R.
Radognaa0000-0002-1094-5038, 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, A. Stamerraa0000-0003-1434-1968, R.
Vendittia0000-0001-6925-8649, P. Verwilligena0000-0002-9285-8631, A.
Zazaa,b0000-0002-0969-7284

INFN Sezione di Bolognaa, Università di Bolognab, 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, 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,460000-0003-3249-9208, 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 Cataniaa, Università di Cataniab, Catania, Italy S.
Costaa,b,470000-0001-9919-0569, A. Di Mattiaa0000-0002-9964-015X, R.
Potenzaa,b, A. Tricomia,b,470000-0002-5071-5501, C. Tuvea,b0000-0003-0739-3153

INFN Sezione di Firenzea, Università di Firenzeb, 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, S.
Meola210000-0002-8233-7277, D. Piccolo0000-0001-5404-543X

INFN Sezione di Genovaa, Università di Genovab, 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-Bicoccaa, Università di Milano-Bicoccab, 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. Zuoloa,b0000-0003-3072-1020

INFN Sezione di Napolia, Università di Napoli ’Federico II’b, Napoli, Italy;
Università della Basilicatac, Potenza, Italy; Università G. Marconid, 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,480000-0001-6471-5492, P. Paoluccia,210000-0002-8773-4781, B.
Rossia0000-0002-0807-8772, C. Sciaccaa,b0000-0002-8412-4072

INFN Sezione di Padovaa, Università di Padovab, Padova, Italy; Università di
Trentoc, Trento, Italy N. Bacchettaa,490000-0002-2205-5737, M.
Biasottoa,500000-0003-2834-8335, D. Biselloa,b0000-0002-2359-8477, P.
Bortignona0000-0002-5360-1454, A. Bragagnoloa,b0000-0003-3474-2099, R.
Carlina,b0000-0001-7915-1650, T. Dorigoa0000-0002-1659-8727, S.
Fantinela0000-0002-0079-8708, F. Fanzagoa0000-0003-0336-5729, U.
Gasparinia,b0000-0002-7253-2669, G. Grossoa, L. Layera,51, E.
Lusiania0000-0001-8791-7978, M. Margonia,b0000-0003-1797-4330, 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 Paviaa, Università di Paviab, 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, 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 Perugiaa, Università di Perugiab, Perugia, Italy P.
Asenova,520000-0003-2379-9903, 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,520000-0002-7676-3106, 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