HIG-22-001

HIG-22-001

[cern]CMS Collaboration

# A portrait of the Higgs boson by the CMS experiment ten years after the
discovery

###### Abstract

In July 2012, the ATLAS and CMS Collaborations at the CERN Large Hadron
Collider announced the observation of a Higgs boson at a mass of around 125.
Ten years later, and with the data corresponding to the production of 30 times
larger number of Higgs bosons, we have learnt much more about the properties
of the Higgs boson. The CMS experiment has observed the Higgs boson in
numerous fermionic and bosonic decay channels, established its spin-parity
quantum numbers, determined its mass and measured its production cross
sections in various modes. Here the CMS Collaboration reports the most up-to-
date combination of results on the properties of the Higgs boson, including
the most stringent limit on the cross section for the production of a pair of
Higgs bosons, on the basis of data from proton-proton collisions at a centre-
of-mass energy of 13. Within the uncertainties, all these observations are
compatible with the predictions of the standard model of elementary particle
physics. Much evidence points to the fact that the standard model is a low-
energy approximation of a more comprehensive theory. Several of the standard
model issues originate in the sector of Higgs boson physics. An order of
magnitude larger number of Higgs bosons, expected to be examined over the next
fifteen years, will help deepen our understanding of this crucial sector.

The established theory of elementary particle physics, commonly referred to as
the standard model (SM), provides a complete description of the
electromagnetic (EM), weak, and strong interactions of matter particles, which
are spin-1/2 fermions, through three different sets of mediators, which are
spin-1 bosons. (In quantum mechanics, spin is an intrinsic form of angular
momentum carried by elementary particles.) These vector bosons are the
massless photons (gluons) for the EM (strong) interaction, and the heavy and
bosons for the weak interaction. The SM has been very successful in providing
accurate predictions for essentially all particle physics experiments carried
out so far. In 2012, the final missing particle of the SM, the Higgs boson,
was observed by the ATLAS [1] and CMS [2, 3] Collaborations at CERN.

The Higgs boson is a prediction of a mechanism that took place in the early
universe, less than a picosecond after the Big Bang, which led to the EM and
the weak interactions becoming distinct in their actions. In the SM, this
mechanism, labelled as the Brout–Englert–Higgs (BEH) mechanism, introduces a
complex scalar (spin-0) field that permeates the entire universe. Its quantum
manifestation is known as the SM Higgs boson. Scalar fields are described only
by a number at every point in space that is invariant under Lorentz
transformations. An analogy can be drawn of a map of an area where temperature
is shown at various positions mimicking a scalar field. The same map, where
instead the wind speed and direction are shown, would correspond to a vector
field.

##  0.1 The long road to the Higgs boson

The BEH mechanism was first proposed in 1964 in the works of Brout and Englert
[4], Higgs [5, 6], and Guralnik, Hagen, and Kibble [7]. Further details of the
mechanism were presented in 1966 by Higgs [8] and in 1967 by Kibble [9]. In
1967, Weinberg [10] and Salam [11], extending the 1961 work of Glashow [12],
proposed the use of the BEH mechanism for a theory of the unification of the
EM and weak interactions, labelled as the electroweak (EW) interaction. The
key element in this work was the conjecture that nature possesses an EW
symmetry, mathematically described by the Lagrangian of the theory, which is
spontaneously broken, granting mass to the and bosons. An additional feature
of this model is that it provides a mechanism for granting masses to fermions
as well, through the so-called Yukawa interactions [10, 13]. Thus, the
elementary particles interacting with the BEH field acquire mass. The impact
is far reaching: for example, electrons become massive, allowing atoms to
form, and endowing our universe with the observed complexity.

Salam and Weinberg had further conjectured that the model they put forward
might be renormalizable (that is, give finite answers). In 1971, ’t Hooft and
Veltman [14, 15] showed how indeed this theory could be renormalized. This
development put the Glashow–Salam–Weinberg model on a firm basis deserving
serious experimental scrutiny.

After the and bosons were discovered by the UA1 and UA2 experiments at CERN in
1983 [16, 17, 18, 19], the search for the Higgs boson became a central thrust
in particle physics and an important motivation for the CERN Large Hadron
Collider (LHC) [20], and the ATLAS and CMS experiments.

Finding the Higgs boson has been demanding. This is a consequence of its large
mass, which puts it beyond the reach of previous electron-positron colliders,
such as LEP [21] at CERN, and low cross section modes coupled with
unfavourable decay channels in the range of mass in which it was eventually
found, which made it challenging to observe at previous hadron colliders, such
as the Tevatron [22] at Fermilab. In the SM, the Higgs boson is an elementary
scalar particle, a type that had never been observed before. Fundamental
scalar particles are subject to quantum corrections that can be as large as
the scale of the physics beyond the SM (BSM). As this scale can be many orders
of magnitude larger than the EW scale, which is $\sim 100$ , the measured mass
of the Higgs boson is puzzlingly small. How to resolve this puzzle is part of
the motivation for future work and accelerators.

The BEH mechanism does not predict the mass of the Higgs boson, but once the
mass is fixed, all its other properties are precisely defined. The Higgs
boson, once produced, decays directly to the heaviest allowed elementary
particles. However, decays to massless particles can also occur through
quantum loops. At the LHC, the production of Higgs bosons is dominated by
gluon-gluon fusion ($\Pg\Pg\PH$) proceeding via a virtual top quark loop. The
mass of a real particle is defined as $m^{2}=E^{2}-p^{2}$, where $E$ is the
energy and $p$ is the momentum vector of the particle. For a virtual particle
this equation is not valid and thus a virtual particle does not have a defined
value of the mass. A virtual particle is denoted by an asterisk, $\PW^{*}$
denoting a virtual boson. Henceforth the distinction between real and virtual
particles will be dropped, unless mentioned otherwise. At a mass of around
125the Higgs boson decays dominantly into a $\PQb$ quark and its antiquark.
Henceforth, the distinction between a particle and its antiparticle will be
dropped.

From the accurate observation and measurement of the products of the Higgs
boson decays and of those associated with its production, experiments are able
to infer its properties, including the strength of its self-interaction
($\lambda$) [23] and, potentially, decays into beyond-the-SM (BSM) particles.

This paper presents the combination of results from single Higgs boson
production and decay, and its pair production, using data sets corresponding
to an integrated luminosity ($\mathcal{L}$) up to 138 [24], collected by CMS
in 2016–2018. An integrated luminosity of 1corresponds to $\approx$100
trillion proton-proton collisions at a centre-of-mass energy of 13.

In addition, a few projections are made for an assumed data sample
corresponding to $\mathcal{L}=3000\fbinv$, recorded at $\sqrt{s}=14~{}\TeV$,
expected to be accumulated by the end of the next decade during the high-
luminosity operation of the LHC accelerator (HL-LHC).

##  0.2 The CMS experiment and data sets

The CMS apparatus [25], illustrated in Extended Data Fig. .9.1, is a
multipurpose, nearly hermetic detector, designed to trigger on [26, 27] and
identify electrons (), muons (), photons (), and (charged and neutral) hadrons
[28, 29, 30]. A trigger is a filter that selects interesting events, where
event refers to the result of the selected interaction in a beam crossing, as
observed in the detector. A global event reconstruction algorithm [31]
combines the information provided by the all-silicon inner tracker, crystal
electromagnetic calorimeter, and brass and scintillator hadron calorimeters,
operating inside a 3.8T superconducting solenoid, with data from gas-
ionization muon detectors embedded in the solenoid flux-return yoke, to build
electrons, muons, tau () leptons, photons, hadronic jets, missing transverse
momentum (), and other physics objects [32, 33, 34]. Collimated streams of
particles arising from the fragmentation of quarks or gluons are called jets.
These jets are identified, and their energies measured, by specialized
reconstruction algorithms [31, 33]. The missing transverse momentum vector is
measured with respect to the incoming proton beams, and it is computed as the
negative vector sum of transverse momenta of all particles in an event.

Several improvements have been introduced into the CMS experiment since the
discovery of the Higgs boson in 2012 (cf. Methods section).

By July 2012, CMS had collected $\mathcal{L}=5.1\fbinv$ at a proton-proton
($\Pp\Pp$) collision centre-of-mass energy $\sqrt{s}=7\TeV$ (in 2011) and
$\mathcal{L}=5.3\fbinv$ at 8(in the first half of 2012), with which the Higgs
boson was discovered. By the end of 2012 (Run 1), CMS had collected data
corresponding to $\mathcal{L}=19.7\fbinv$ at $8\TeV$ [35].

In LHC Run 2 (2015–2018), the accelerator delivered collisions at
$\sqrt{s}=13\TeV$. At this larger energy the cross section for Higgs boson
production increases by a factor of 2.2–4.0, depending on the production mode
[36, 37, 38, 39]. Physics analyses presented here are based on 2016–2018 data,
corresponding to an $\mathcal{L}$ of up to 138(the additional $\sim$2recorded
in 2015 are not used in this combination). This enabled not only a reduction
of statistical, but also of systematic uncertainties, as well as a more
precise calibration of the calorimeters and alignment of the tracking
detectors. During Run 2, approximately 8 million Higgs bosons have been
produced. Many more final states could be studied, since it was possible to
separate the events by production mode and decay channel, as well as by
kinematic properties; and differential distributions could be measured.
Furthermore, improved analysis methods were deployed.

To enable comparison with the more precise experimental results, theoretical
calculations have been carried out with commensurate improvements in accuracy
[36, 37, 38, 39], involving higher orders in perturbation theory.

The statistical procedure was developed in preparation for the
search/discovery of the Higgs boson and hasn’t changed much since then. It is
based on building a combined likelihood from the various input channels (cf.
Methods Section .8.5). Parameter estimation and limit setting are performed
using a profile likelihood technique with asymptotic approximation [40],
taking into account the full correlation of the systematic uncertainties
between individual channels and the years of data taking. The different
channels included in the combination correlate nuisance parameters related to
the same underlying effect, such as the uncertainty in the theoretical
prediction or the energy scale uncertainty of the final-state objects. The
inclusive signal strength ($\mu$) combination has a total of
$\mathcal{O}(10^{4})$ nuisance parameters. The references to the individual
analyses presented in the next section each contain more details of the
statistical procedure employed for combining the several categories used,
created according to various criteria, such as signal-to-background ratios,
mass resolutions, and multiplicities of physics objects.

Figure 1:  Feynman diagrams for the leading Higgs boson interactions
Higgs boson production in (a) gluon-gluon fusion ($\Pg\Pg\PH$), (b) vector
boson fusion (VBF), (c) associated production with a or () boson ($\PV\PH$),
(d) associated production with a top or bottom quark pair ($\PQt\PQt\PH$ or
$\PQb\PQb\PH$), (e, f) associated production with a single top quark
($\PQt\PH$); with Higgs boson decays into (g) heavy vector boson pairs, (h)
fermion-antifermion pairs, and (i, j) photon pairs or $\PZ\PGg$; Higgs boson
pair production: (k, l) via gluon-gluon fusion, and (m, n, o) via vector boson
fusion. The different Higgs boson interactions are labelled with the coupling
modifiers $\kappa$, and highlighted in different colours for Higgs-fermion
interactions (red), Higgs-gauge-boson interactions (blue), and multiple Higgs
boson interactions (green). The distinction between a particle and its
antiparticle is dropped.

##  0.3 Portrait of the Higgs boson

The portrait of the Higgs boson is defined by its production modes, via cross
sections, and its decay channels, via branching fractions. For the value of
mass measured by CMS $m_{\PH}=125.38\pm 0.14\GeV$ [41], these are given in
Extended Data Table .9 [39].

###  0.3.1 Production

The rate of production of Higgs bosons is given by the product of the
instantaneous luminosity, measured in units of $\percms$, and the cross
section, measured in units of cm2. For $m_{\PH}=125.38\GeV$, the total cross
section for the production of the SM Higgs boson at $\sqrt{s}=13\TeV$ is
$55.4\pm 2.6\unit{pb}$ [39]. (A cross section of $1\unit{pb}$ (picobarn)
corresponds to an area of $10^{-36}\,\text{cm}^{2}$.) This results in the
production of one Higgs boson every second at an instantaneous luminosity of
$2\times 10^{34}\percms$. The dominant production mode in the SM is
$\Pg\Pg\PH$, where a pair of gluons, one from each of the incident protons,
fuses, predominantly via a virtual top quark quantum loop. This is depicted in
Fig. 1a and represents 87% of the total cross section. The next most important
production mode is vector boson fusion (VBF) depicted in Fig. 1b, where a
quark from each of the protons radiates a virtual vector boson ($\PW$ or
$\PZ$), which then fuse together to make a Higgs boson. Other processes, with
smaller cross sections, are: production in association with a vector boson or
Higgsstrahlung ($\PV\PH$) depicted in Fig. 1c, and production in association
with top ($\PQt\PH$, $\PQt\PQt\PH$) or bottom ($\PQb\PQb\PH$) quarks, depicted
in Figs. 1d–f. The $\PQb\PQb\PH$ mode has not been studied in the context of
the SM Higgs boson because of limited sensitivity.

Events are categorized according to the signatures particular to each
production mechanism. For example, they are categorized as VBF produced if
there are two high transverse momentum ($\pt$) jets, or as $\PV\PH$ produced
if there are additional charged leptons ($\ell$) and/or , or $\PQt\PQt\PH$,
$\PQt\PH$ produced if there are jets identified as coming from quarks, or
otherwise $\Pg\Pg\PH$ produced. (The top quark predominantly decays into a
boson and a quark jet.)

###  0.3.2 Decays

In the SM, particle masses arise from spontaneous breaking of the gauge
symmetry, through gauge couplings to the Higgs field in the case of vector
bosons, and Yukawa couplings in the case of fermions. The SM Higgs boson
couples to vector bosons, with an amplitude proportional to the gauge boson
mass squared $m^{2}_{\PV}$, and to fermions with an amplitude proportional to
the fermion mass $m_{\mathrm{f}}$. Hence, the coupling is stronger for the 3rd
generation of quarks and leptons than for those in the 2nd generation. The
observation of many Higgs boson decays to SM particles and the measurement of
their branching fractions are a crucial test of the validity of the theory.
Any sizeable deviation from the predictions could indicate the presence of BSM
physics.

The Higgs boson, once produced, rapidly decays into a pair of fermions or a
pair of bosons. In the SM its lifetime is $\tau_{\PH}\approx 1.6\times
10^{-22}\unit{s}$, and its inverse, the natural width, is
$\Gamma=\hslash/\tau_{\PH}=4.14\pm 0.02\MeV$ [39], where $\hslash$ is the
reduced Planck’s constant. The natural width is the sum of all the partial
widths, and the ratios of the partial widths to the total width are called
branching fractions and represent the probabilities for that decay channel to
occur. The Higgs boson does not couple directly to massless particles (the
gluon or the photon), but can do so via quantum loops (Figs. 1a, 1i, and 1j).

By design, the event selections do not overlap among analyses targeting
different final states. Where the final states are similar, the overlap has
been checked and found to be negligible.

Detailed information on the analyses included in the new combination along
with improvements, and the online and offline criteria used to select events
for the analyses can be found in the Methods Section, in Extended Data Tables
.9 and .9, and in the associated references. Online reconstruction is
performed in real time as data are being collected. Offline reconstruction is
performed later on stored data. The background-subtracted distributions of the
invariant mass of final-state particles in the individual decay channels are
shown in Extended Data Figs. .9.3 and .9.4. The channels that are used in this
combination are listed below.

Bosonic decay channels: $\PH\to\PGg\PGg$ (Figs. 1i, 1j) [42]; $\PH\to\PZ\PZ\to
4\ell$ (Fig. 1g) [43]; $\PH\to\PW\PW\to\ell\PGn\ell\PGn$ (Fig. 1g) [44];
$\PH\to\PZ\PGg$ (Figs. 1i, 1j) [45].

Fermionic decay channels: $\PH\to\PGt\PGt$, 3rd generation fermion, (Fig. 1h)
[46]; $\PH\to\PQb\PQb$, 3rd generation fermion, (Fig. 1h) [47, 48, 49, 50,
51]; $\PH\to\PGm\PGm$, 2nd generation fermion, (Fig. 1h) [52].

$\PQt\PQt\PH$/$\PQt\PH$ with multileptons (Fig. 1d and Figs. 1e, 1f) [53].

Higgs boson decays beyond the SM [35].

##  0.4 Higgs boson pair production

The measurement of the pair production of Higgs bosons can probe its self-
interaction $\lambda$. The pair production modes are shown in Figs. 1k–o.

In the gluon-gluon fusion mode, there are two leading contributions: in the
first (Fig. 1l), two Higgs bosons emerge from a top/bottom quark loop; in the
second (Fig. 1k), a single virtual Higgs boson, $\PH^{*}$, emerges from the
top/bottom quark loop and then decays to two Higgs bosons
($\Pg\Pg\to\PH^{*}\to\PH\PH$). Explicit establishment of the latter
contribution, a direct manifestation of the Higgs boson’s self-interaction,
would elucidate the strikingly unusual potential of the BEH field.

In the VBF mode, there are three subprocesses that can lead to production of a
pair of Higgs bosons:

  * •

via a virtual Higgs boson (Fig. 1m);

  * •

via a four-point interaction: $\PV\PV\to\PH\PH$ (Fig. 1n); and

  * •

via the exchange of a vector boson (Fig. 1o).

The scattering amplitudes of the processes giving rise to Higgs boson pair
production via gluon-gluon fusion (Figs. 1k, 1l) are similar in magnitude, but
have opposite signs and interfere destructively. This makes the overall Higgs
boson pair production rate small, rendering its experimental observation
challenging. The SM Higgs boson pair production cross section is calculated
for $m_{H}=125\GeV$ to be $32.76^{+1.95}_{-6.83}\unit{fb}$ [54, 55, 56], three
orders of magnitude smaller than the single Higgs boson cross section.

The search for Higgs boson pair production is performed by combining Higgs
bosons candidates reconstructed from different final states [57, 58, 59, 60,
61, 62]. All final states analyzed are defined to be mutually exclusive so
that they could be combined as statistically independent observations.

##  0.5 Measurement of the properties of the Higgs boson

At the time of the Higgs boson discovery [2, 3], the combination of CMS data
gave an observed (obs.) statistical significance of 5.0 standard deviations
(s.d.) with an expected (exp.) significance of 5.8 s.d. Individually, the most
sensitive channels, $\PH\to\PGg\PGg$ and $\PH\to\PZ\PZ\to 4\ell$, yielded 4.1
s.d. obs. (2.8 s.d. exp.), and 3.2 s.d. obs. (3.8 s.d. exp.) respectively.

Using all the Run 1 data, it was possible to observe separately the bosonic
decay channels with significances of 6.5 s.d. for $\PH\to\PZ\PZ\to 4\ell$, 5.6
s.d. for $\PH\to\PGg\PGg$, 4.7 s.d. for $\PH\to\PW\PW$, and 3.8 s.d. for the
fermionic decay channel $\PH\to\PGt\PGt$ [35]. Earlier, first results of the
Higgs boson decay into fermions were presented in Ref. [63], reaching a
significance of 3.8 s.d. by combining the $\PH\to\PGt\PGt$ and
$\PH\to\PQb\PQb$ decay modes. The mass was measured to a precision of
$\approx$0.2% [35]. Using the angular distributions of the leptons in the
bosonic decay channels, the spin ($J$) and parity ($P$, a parity
transformation that effectively turns a phenomenon into its mirror image) were
also found to be compatible with the SM prediction ($J^{P}=0^{+}$) with a
large number of alternative spin-parity hypotheses ruled out at $>$99.9%
confidence level () [64, 65]. The total cross section, combining all of the
different decay channels, was measured to be in agreement with the SM, with an
uncertainty of 14% [35]. Each of the VBF, $\PV\PH$, and $\PQt\PQt\PH$
production modes was measured at a level of 3 s.d. [35].

With Run 2 data, CMS has observed the Higgs boson decaying into a pair of tau
leptons with a significance of 5.9 s.d. [66], a pair of bottom quarks with a
significance of 5.6 s.d. [48], and the $\PQt\PQt\PH$ production mode at 5.2
s.d. [67]. The Higgs boson has also been seen in its decays into muons with a
significance of 3 s.d. [52]. The mass of the Higgs boson has been measured to
be $125.38\pm 0.14$using the decay channels $\PH\to\PGg\PGg$ and
$\PH\to\PZ\PZ\to 4\ell$ [41]. The natural width of the Higgs boson has been
extracted and is found to be $\Gamma_{\PH}=3.2^{+2.4}_{-1.7}\MeV$ by using
off-mass-shell and on-mass-shell Higgs boson production [68]. On-mass-shell
refers to a particle with its physical mass, while off-mass-shell refers to a
virtual particle.

Figure 2:  The agreement with the SM predictions for production modes and
decay channels.
Signal strength parameters extracted for (left) various production modes
$\mu_{i}$, assuming $\mathcal{B}^{f}=(\mathcal{B}^{f})_{\text{SM}}$, and
(right) decay channels $\mu^{f}$, assuming
$\sigma_{i}=(\sigma_{i})_{\text{SM}}$. The thick (thin) black lines indicate
the 1 (2) s.d. confidence intervals, with the systematic and statistical
components of the 1 s.d. interval indicated by the red and blue bands,
respectively. The vertical dashed line at unity represents the values of
$\mu_{i}$ and $\mu^{f}$ in the SM. The covariance matrices of the fitted
signal strength parameters are shown in Extended Data Fig. .9.5. The $p$-value
with respect to the SM prediction are 3.1% and 30.1% for the left and right
plot, respectively. The $p$-value corresponds to the probability that a result
deviates as much, or more, from the SM prediction as the observed one.

###  0.5.1  The $\mu$-framework for signal strengths.

The agreement between the observed signal yields and the SM expectations can
be quantified by fitting the data with a model that introduces signal strength
parameters. These are generically labelled $\mu$, and scale the observed
yields with respect to those predicted by the SM, without altering the shape
of the distributions. The specific meaning of $\mu$ varies depending on the
analysis. For given initial (i) and final (f) states, $i\to\PH\to f$, the
signal strengths for individual production channels, $\mu_{i}$, and decay
modes, $\mu^{f}$, are defined as $\mu_{i}=\sigma_{i}/(\sigma_{i})_{\text{SM}}$
and $\mu^{f}=\mathcal{B}^{f}/(\mathcal{B}^{f})_{\text{SM}}$, where $\sigma$ is
the production cross section and $\mathcal{B}$ is the branching fraction.
Perfect agreement with SM expectations would yield all $\mu$ equal to one.

A first test of compatibility is performed by fitting all data from production
modes and decay channels with a common signal strength parameter, $\mu$. At
the time of discovery, the common $\mu$ was found to be $0.87\pm 0.23$. The
new combination of all Run 2 data yields $\mu=1.002\pm 0.057$, in excellent
agreement with the SM expectation. The uncertainties in the new measurement
correspond to an improvement by a factor of 4.5 in precision compared to what
was achieved at the time of discovery. At present, the theoretical
uncertainties in the signal prediction, the experimental statistical, and the
systematic uncertainties separately contribute at a similar level, and they
are $0.036$, $0.029$, and $0.033$, respectively.

Relaxing the assumption of a common signal strength parameter, and introducing
different $\mu_{i}$ and $\mu^{f}$, our measurements are shown in Fig. 2. The
production modes $\Pg\Pg\PH$, VBF, $\PW\PH$, $\PZ\PH$, and $\PQt\PQt\PH$ are
all observed with a significance of 5 s.d. or larger.

###  0.5.2  The $\kappa$-framework for coupling modifiers.

Beyond-the-SM physics is expected to affect the production modes and decay
channels in a correlated way if they are governed by similar interactions. Any
modification in the interaction between the Higgs boson and, the $\PW$ bosons
and top quarks not only would affect the $\PH\to\PW\PW$ (Fig. 1g) or
$\PH\to\PGg\PGg$ (Fig. 1i and 1j) decay rates, but also the production cross
section for the $\Pg\Pg\PH$ (Fig. 1a), $\PW\PH$ (Fig. 1c), and VBF (Fig. 1b)
modes. To probe such deviations from the predictions of the SM, the
$\kappa$-framework [38] is used. The quantities, such as $\sigma_{i}$,
$\Gamma^{f}$, and $\Gamma_{\PH}$, computed from the corresponding SM
predictions, are scaled by $\kappa_{i}^{2}$, as indicated by the vertex labels
in Fig. 1. As an example, for the decay $\PH\to\PGg\PGg$ proceeding via the
loop processes of Fig. 1i or 1j, the branching fraction is proportional to
$\kappa_{\PGg}^{2}$ or $(1.26\kappa_{\PW}-0.26\kappa_{\PQt})^{2}$. In the SM
all $\kappa$ values are equal to one.

A first such fit to Higgs boson couplings introduces two parameters,
$\kappa_{\mathrm{V}}$ and $\kappa_{\mathrm{f}}$, scaling the Higgs boson
couplings to massive gauge bosons and to fermions, respectively. With the
limited data set available at the time of discovery, such a fit provided first
indications for the existence of both kinds of couplings. The sensitivity with
present data is much improved, and both coupling modifiers are measured to be
in agreement, within an uncertainty of 10%, with the predictions from the SM,
as shown in Fig. 3 (left).

Figure 3:  A portrait of the Higgs boson couplings to fermions and vector
bosons.
(left) Constraints on the Higgs boson coupling modifiers to fermions
($\kappa_{\mathrm{f}}$) and heavy gauge bosons ($\kappa_{\mathrm{V}}$), in
different data sets: discovery (red), the full LHC Run 1 (blue), and the data
presented here (black). The SM prediction corresponds to
$\kappa_{\mathrm{V}}=\kappa_{\mathrm{f}}=1$ (diamond marker). (right) The
measured coupling modifiers of the Higgs boson to fermions and heavy gauge
bosons, as functions of fermion or gauge boson mass, where $\upsilon$ is the
vacuum expectation value of the BEH field (cf. Methods section .8.7). For
gauge bosons, the square root of the coupling modifier is plotted, to keep a
linear proportionality to the mass, as predicted in the SM. The $p$-value with
respect to the SM prediction for the right plot is 37.5%.

A second fit is performed to extract the coupling modifiers $\kappa$ for the
heavy gauge bosons ($\kappa_{\PW}$, $\kappa_{\PZ}$) and the fermions probed in
the present analyses ($\kappa_{\PQt}$, $\kappa_{\PQb}$, $\kappa_{\PGt}$,
$\kappa_{\PGm}$). Predictions for processes that in the SM occur via loops of
intermediate virtual particles, Higgs boson production via $\Pg\Pg\PH$, or
Higgs boson decay to a pair of gluons, photons, or $\PZ\PGg$, are computed in
terms of the $\kappa_{i}$ above. The result is shown in Fig. 3 (right), as a
function of the mass of the probed particles. The remarkable agreement with
the predictions of the BEH mechanism over three orders of magnitude of mass is
a powerful test of the validity of the underlying physics. Statistical and
systematic uncertainties contribute at the same level to all measurements,
except for $\kappa_{\PGm}$, which still is dominated by the statistical
uncertainty.

In extensions of the SM with new particles, the loop-induced processes may
receive additional contributions. A more general fit for deviations in the
Higgs boson couplings can then be defined by introducing additional modifiers
for the effective coupling of the Higgs boson to gluons ($\kappa_{\Pg}$),
photons ($\kappa_{\PGg}$), and $\PZ\PGg$ ($\kappa_{\PZ\PGg}$). Results for
this fit are shown in Fig. 4 (left). Coupling modifiers are probed at a level
of uncertainty of 10%, except for $\kappa_{\PQb}$ and $\kappa_{\PGm}$
($\approx$20%), and $\kappa_{\PZ\PGg}$ ($\approx$40%), and all measured values
are compatible with the SM expectations, to within 1.5 s.d. These measurements
correspond to an increase in precision by a factor of $\approx$5 compared to
what was possible with the discovery data set. Figure 4 (right) and Extended
Data Fig. .9.8 (left) illustrate the evolution of several $\kappa$
measurements and their uncertainties using the data set:

  * •

at the time of discovery (July 2012) [2, 3],

  * •

for the full Run 1 (end of 2012) [35],

  * •

for results presented in this paper, and

  * •

expected to be accumulated by the end of the HL-LHC running [69],
corresponding to $\mathcal{L}=3000\fbinv$. The statistical uncertainties have
been scaled by $1/\sqrt{\mathcal{L}}$, the experimental systematic ones by
$1/\sqrt{\mathcal{L}}$ where possible, or fixed at values suggested in Ref.
[69], whereas the theoretical uncertainties have been halved.

A sizeable improvement is expected after HL-LHC operation. The
$\PH\to\PGm\PGm$ measurements were not available for the first two data sets
due to the lack of sensitivity. The evolution of several signal strength
measurements $\mu$ are shown in Extended Data Fig. .9.7.

Figure 4:  Coupling modifiers measurements and their evolution in time.
(left) Coupling modifiers resulting from the fit. The $p$-value with respect
to the SM prediction is 28%. (right) Observed and projected values resulting
from the fit in the $\kappa$-framework in different data sets: at the time of
the Higgs boson discovery, using the full data from LHC Run 1, in the data set
used in this paper, and the expected 1 s.d. uncertainty at the HL-LHC for
$\mathcal{L}=3000\fbinv$. The $\PH\to\PGm\PGm$ and $\kappa_{\PQt}$
measurements were not available for earlier data sets due to the lack of
sensitivity.

If new particles exist with masses smaller than $m_{\PH}$, other decay
channels may be open. Examples of such decays could be into new neutral long-
lived particles or into dark matter particles, neither leaving a trace in the
CMS detector. We refer to these as invisible Higgs boson decays, which could
be inferred from the presence of large in the direction of the Higgs boson
momentum. The events are selected based on other particles accompanying the
Higgs boson. Dedicated searches for such decays [70, 71, 72] yielded
$\mathcal{B}_{\text{Inv.}}<0.16$ at 95% , where $\mathcal{B}_{\text{Inv.}}$ is
the branching fraction to invisible decays.

##  0.6 Results from the search for Higgs boson pair production

The cross section for Higgs boson pair production in the SM is extremely
small, thus escaping detection at the LHC so far. The results of the search
are therefore expressed as an upper limit on the production cross section.
Figure 5 (left) shows the expected and observed limits on Higgs boson pair
production, expressed as ratios with respect to the SM expectation, in
searches using the different final states and their combination. With the
current data set, and combining data from all currently studied modes and
channels, the Higgs boson pair production cross section is found to be less
than $3.4$ times the SM expectation at 95% . Figure 5 (right) shows the
evolution of the limits from the three most sensitive modes and the overall
combination for: the first comprehensive set of measurements using early LHC
Run 2 data ($35.9\fbinv$) [73], the present measurements using the full LHC
Run 2 data ($138\fbinv$), and the projections for the HL-LHC ($3000\fbinv$)
[69]. The HL-LHC projections are also expressed as limits, assuming that there
is no Higgs boson pair production. The fact that the combined limit is
expected to be below unity shows that the sensitivity is sufficient to
establish the existence of the SM $\PH\PH$ production.

Figure 5:  Limits on the production of Higgs boson pairs and their time
evolution.
(left) The expected and observed limits on the ratio of experimentally
estimated production cross section and the expectation from the SM
($\sigma_{\text{Theory}}$) in searches using different final states and their
combination. The search modes are ordered, from upper to lower, by their
expected sensitivities from the least to the most sensitive. The overall
combination of all searches is shown by the lowest entry. (right) Expected and
observed limits on $\PH\PH$ production in different data sets: early LHC Run 2
data ($35.9\fbinv$), present results using full LHC Run 2 data ($138\fbinv$),
and projections for the HL-LHC ($3000\fbinv$).

Figure 6 presents the expected and observed experimental limits on the
$\PH\PH$ production cross section as functions of the Higgs boson self-
interaction coupling modifier $\kappa_{\lambda}$ and the quartic
$\PV\PV\PH\PH$ coupling modifier $\kappa_{\mathrm{2V}}$. Cross section values
above the solid black lines are experimentally excluded at 95% . The red lines
show the predicted cross sections as functions of $\kappa_{\lambda}$ or
$\kappa_{\mathrm{2V}}$, which exhibit a characteristic dip in the vicinity of
the SM values ($\kappa=1$) due to the destructive interference of the
contributing production amplitudes, as highlighted in Section 0.4. The
experimental limits on the Higgs boson pair production cross section (black
lines) also show a strong dependence on the assumed values of $\kappa$. This
is because the interference between different subprocesses, besides changing
the expected cross sections, also changes the differential kinematic
properties of the two Higgs bosons, which in turn affects strongly the
efficiency for detecting signal events. With the current data set we can
ascertain at 95% that the Higgs boson self-interaction coupling modifier
$\kappa_{\lambda}$ is in the range $-1.24$ to $6.49$, while the quartic
$\kappa_{\mathrm{2V}}$ coupling modifier is in the range $0.67$ to $1.38$.
Figure 6 (right) shows that $\kappa_{\mathrm{2V}}=0$ is excluded, with a
significance of $6.6$ s.d., establishing the existence of the quartic coupling
$\PV\PV\PH\PH$ depicted in Fig. 1n.

Figure 6:  Limits on the Higgs boson self-interaction and quartic coupling.
Combined expected and observed 95% upper limits on the $\PH\PH$ production
cross section for different values of $\kappa_{\lambda}$ (left) and
$\kappa_{\mathrm{2V}}$ (right), assuming the SM values for the modifiers of
Higgs boson couplings to top quarks and vector bosons. The green and yellow
bands represent, respectively, the 1 and 2 s.d. extensions beyond the expected
limit; the red solid line (band) shows the theoretical prediction for the
$\PH\PH$ production cross section (its 1 s.d. uncertainty). The areas to the
left and to the right of the hatched regions are excluded at 95% .

##  0.7 Current knowledge and future prospects

The discovery of the Higgs boson in 2012 completed the particle content of the
standard model (SM) of elementary particle physics, a theory that explains
visible matter and its interactions in exquisite detail. The completion of the
SM spanned 60 years of theoretical and experimental work. In the ten years
following the discovery, great progress has been made in painting a clearer
portrait of the Higgs boson.

In this paper, the CMS Collaboration reports the most up-to-date combination
of results on the properties of the Higgs boson, based on data corresponding
to an $\mathcal{L}$ of up to 138, recorded at 13. Many of its properties have
been determined with accuracies better than 10%. All measurements made so far
are found to be consistent with the expectations of the SM. In particular, the
overall signal strength parameter has been measured to be $\mu=1.002\pm
0.057$. It has been shown that the Higgs boson directly couples to bottom
quarks, tau leptons, and muons, which had not been observed at the time of the
discovery, and also proven that it is indeed a scalar particle. The CMS
experiment is approaching the sensitivity necessary to probe Higgs boson
couplings to charm quarks [74]. The observed (expected) 95% value for
$\kappa_{\PQc}$ is found to be $1.1<\abs{\kappa_{\PQc}}<5.5$
($\abs{\kappa_{\PQc}}<3.40$), the most stringent result to date. Moreover, the
recent progress in searches for the pair production of Higgs bosons has
allowed the setting of tight constraints on the Higgs boson self-interaction
strength, and the setting of limits on the Higgs boson pair production cross
section not much above twice the expected SM value.

Much evidence points to the fact that the SM is a low-energy approximation of
a more comprehensive theory. In connection with the mechanism of spontaneous
symmetry breaking, several puzzles appear: the so-called naturalness, a
technical issue related to the fact that the Higgs boson mass is close to the
electroweak scale; in relation with cosmology, the metastability of the vacuum
state of the SM and the conjectured period of inflation in the early universe;
the dynamics of electroweak phase transition and its connection to the matter-
antimatter asymmetry of our universe. These issues motivate attempts at
obtaining a deeper understanding of the physics of the Higgs boson. The
impressive progress made over the last decade is foreseen to continue into the
next one. The current data set is expected to be doubled in size by the middle
of this decade, enabling the establishment of rare decays channels such as
$\PH\to\PGm\PGm$ and $\PH\to\PZ\PGg$. Operation with the high-luminosity LHC
is expected during the next decade and should yield ten times more data then
originally foreseen. This should allow the ATLAS and CMS experiments to
establish the SM Higgs boson pair production with a significance of 4 s.d., as
well as the Higgs boson coupling to charm quarks, and to search for any exotic
decays. Improvements in experimental techniques and theoretical calculations
are also anticipated to continue.

The CMS experiment is entering the era of precision Higgs physics that will
shed light on the physics beyond the SM.

###### 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
Stavros Niarchos Foundation (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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##  .8 Methods

###  .8.1 Large Hadron Collider project and the Higgs boson

The primary goals of the LHC and its two general-purpose experiments, ATLAS
and CMS, are to:

  * •

elucidate the mechanism of EW symmetry breaking and find the associated
particle, which in the SM of particle physics is the Higgs boson [4, 5, 6],
and,

  * •

search for BSM physics.

The necessity to study the wide range of processes in Fig. 1 largely drove the
design of the ATLAS and CMS experiments. The production cross sections and the
decay branching fractions for a SM Higgs boson with a mass of 125.38are shown
in Extended Table .9.

The LHC [20] is designed to accelerate protons to an energy up to $7\TeV$ by
powerful electric fields generated in superconducting radio frequency cavities
and guided around their circular orbits by strong ($8.3\unit{T}$)
superconducting dipole magnets in tubes under very high vacuum. The
counterrotating LHC beams are organized in $\approx$2800 bunches comprising
${>}10^{11}$ protons per bunch, separated by $25\unit{ns}$, leading to a bunch
crossing rate of $\approx$32MHz. The two proton beams are brought into
collision at the center of the four LHC experiments. In Run 2, $\Pp\Pp$
interaction rates of 2GHz were reached. Multiple pairs of protons interact in
each bunch crossing, the average number ranging from 21 in 2012 to 32 in 2018.
These are superposed on the triggered interaction and are labelled pileup.

###  .8.2 The CMS experiment

#### Design criteria and the SM Higgs boson

In the early 1990s, during the design phase of the Compact Muon Solenoid (CMS)
experiment, considerable emphasis was placed on the identification and
measurement of high-energy electrons, photons, and muons, as these particles
were expected to play an important role in the search for the SM Higgs boson
and in the search for BSM physics.

As the rate of production of energetic muons at high-luminosity hadron
colliders is very large, the online selection of events using muons is a
particularly formidable task. The muon momentum has to be measured in real
time and a momentum threshold placed to limit the rate. This requires a high
bending power (high magnetic field) and an adequately precise and robust
measurement of the trajectory of muons. This consideration determined the
starting point of the design of CMS, and by implication the choice, size, and
the power of the analyzing magnet. The next design priority was driven by the
search for the Higgs boson via its decay $\PH\to\PGg\PGg$, requiring an
excellent EM calorimeter (ECAL). The muon system and the ECAL were to be
complemented by a precision inner tracking system, immersed in a high magnetic
field, giving good momentum resolution and a hadron calorimeter (HCAL) that
provided an almost full calorimetric coverage (for the search for the Higgs
boson if its mass turned out to be larger than 500).

#### The CMS detector

The longitudinal cut-away view of the CMS detector is shown in Extended Data
Fig. .9.1. The CMS detector comprises four principal layers: the inner
tracker, the ECAL, the HCAL, and the muon system. The various types of
detecting elements and their channel counts are also indicated. Physics
objects (electrons, photons, muons, quark or gluon jets, etc.) are identified
by different combinations of the patterns of energy deposits and/or traces in
these four layers.

The defining choice and the central element of the CMS detector is the long
(13m), large inner diameter ($\approx$6m), state-of-the-art high-field
($3.8\unit{T}$) superconducting solenoid, generating the magnetic field both
for the inner tracker and the muon system. The large size of the solenoid
allows the inner tracker and almost all the calorimetry to be installed inside
the solenoid.

##### Inner tracking

Particles emerge from the interaction region into the inner tracker, housed in
a cylindrical volume with a length of 5.8mand a diameter of 2.5m. The
particles first encounter the pixel detector, configured in three (four)
cylindrical layers of silicon sensors in the barrel region, and two (three)
disks in the endcap region before (after) 2017. The pixel detector is
surrounded by 10 concentric layers of silicon sensors in the barrel region,
with 10long or 20long silicon microstrips, and 12 vertical planes in each
endcap region. Points are measured with an accuracy of ${\approx}15\mum$ in
the bending plane. The geometric coverage extends down to angles of
$9^{\circ}$ from the beamline.

##### Electromagnetic and hadron calorimeters

The ECAL employs dense lead tungstate scintillating crystals. Each crystal has
a length of ${\approx}23\cm$ that is sufficient to contain the full energy of
high-energy electron and photon showers. The amount of generated or collected
light is proportional to the energy of the incident particle. The fine
transverse size of the crystals means that the energy of an EM shower is
distributed over a cluster of crystals ranging from 9 ($3{\times}3$) to 25
($5{\times}5$) crystals. The geometric coverage of the ECAL goes down to about
$6^{\circ}$ from the beamline.

The HCAL, comprising $\approx$7000 channels, is a sandwich of $\approx$5thick
brass absorber plates and $\approx$4thick scintillator plates. The charged
particles in the shower, generated in the absorber plates, traverse the
scintillator plates and produce light that is collected and guided by fibres
to the photodetectors. The geometric coverage of the HCAL goes down to about
$6^{\circ}$ from the beamline. This coverage is augmented by the very forward
calorimeter, comprising an iron absorber with quartz fibres embedded in a
matrix arrangement. The relativistic charged particles in the showers traverse
the fibres and generate Cherenkov light, a part of which is guided by the
fibres to the photodetectors. This calorimeter extends the calorimetric
coverage down to an angle of ${\approx}0.75^{\circ}$ from the beamline. The
thickness of hadron calorimetry is sufficient to absorb almost all of the
energy of high energy hadrons.

##### Muon system

Muons (and neutrinos) are the only particles that normally reach the muon
system. All other particles deposit almost all of their energies in the
calorimeters, and hence are said to have been absorbed. In addition to the
measurements inside the inner tracker, the momentum of muons is measured a
second time in gas-ionization chambers. These chambers are organized in four
stations that measure several points, to a precision of $\approx$150, and
generate track segments whose direction is measured online with an angular
precision of ${\approx}5\unit{mrad}$. An independent set of gas-ionization
chambers, provide a signal timing resolution of ${\approx}3\unit{ns}$ aiding
the triggering process. The instrumented geometric coverage of the muon system
goes down to an angle of $10^{\circ}$ from the beamline.

##### Event selection

As the resources needed to record data for later use from all $\approx$32
million beam crossings per second would be prohibitively costly, specific
filters (known as triggers) are used to select the most interesting ones. An
online two-tiered trigger system [26, 27] is deployed, with the first tier
(Level-1) being hardware-based and the second one (high-level or HLT) being
software-based. The Level-1 uses custom hardware that processes coarse
information from the calorimeters or the muon chambers to select around 100
thousand crossings of interest per second, corresponding to a reduction of a
factor of $\approx$400\. Crossings of interest are selected if the energy
deposits in the calorimeters or the momentum of muons, are above predefined
thresholds. Upon the issuance of a Level-1 trigger, and after a fixed latency
of just under 4, all data from the triggered crossing are off-loaded from the
pipeline memories in the $\approx$100 million on-detector electronics
channels. These data, after suitable treatment in electronics housed in the
underground services cavern, are sent up 100mto the surface as fragments on
$\approx$1000 optical fibres and fed into a commercial telecommunication
switch. The switch takes the individual fragments, puts them together, builds
the event, and feeds the event into the next available CPU core, in a computer
farm of some 50 000 CPU cores. There, in real time, full-event physics-grade
software algorithms, optimized for fast processing, reconstruct physics
objects and select for permanent storage some 1000 events or crossings per
second, based on topological and kinematic information (see Extended Table
.9).

##### Event reconstruction

The CMS experiment generates a large amount of collision and simulated data.
To handle, store, and analyze all these data required the development of the
worldwide LHC distributed computing grid (wLCG), providing universal access to
data for all CMS Collaboration members.

The data from the stored events are transferred to the Tier-0 centre housed on
CERN’s main site, where a first processing stage is performed. The result of
this stage is then distributed to seven other major centres worldwide,
labelled Tier-1 centres, for offline analysis. The Tier-1s are designed to
carry out tasks of further reconstruction of the collision data with improved
calibration and alignment of the various CMS subdetectors, while the
generation and reconstruction of Monte Carlo event samples is carried out both
at the Tier-1 centres and smaller university-based locations, labelled Tier-2
centres.

The particle-flow (PF) algorithm [31] reconstructs and identifies each
individual particle in an event, with an optimized combination of information
from the various elements of the CMS detector. The energy of photons is
obtained from the measurements in the ECAL. The energy of electrons is
determined from a combination of the electron momentum at the primary
interaction vertex as determined by the tracker, and the energy in the
corresponding cluster of crystals, including the energy sum of all
bremsstrahlung photons spatially compatible with originating from the electron
track. The momentum of muons is derived from the curvature of the
corresponding track. The energy of charged hadrons is determined from a
combination of their momentum measured in the tracker, and the matching ECAL
and HCAL energy deposits. The energy of neutral hadrons is obtained from the
corresponding corrected ECAL and HCAL energies.

Hadronic jets, arising from quarks or gluons, are created from all the
particles reconstructed by the PF algorithm within a cone of half-angle of
${\approx}25^{\circ}$, centred on the axis determined by the vectorial sum of
the momenta of all particles in the jet.

##### Improvements of the CMS detector

Several improvements have been introduced into the CMS experiment since the
discovery of the Higgs boson in 2012. These included:

  * •

The replacement, in late 2016, of the silicon pixel detector, with a new one
comprising four concentric layers in the barrel region, at radii of 29, 68,
109, and 160, and six endcap disks placed at $\pm 34$, $\pm 41$, and $\pm
51\mm$ from the interaction point, along the beamline. The new configuration
leads to an improvement in the reconstruction of the secondary vertices and in
the quality of tagging of $\PQb$ quarks. The sensitivity of $\PH\to\PQb\PQb$
analysis is found to be improved by a factor of 2.

  * •

The replacement of photodetectors in HCAL (hybrid photodiodes replaced by
silicon photomultipliers) and implementation of more precise timing, allowing
a reduction of accidental or instrumental backgrounds, stray or out-of-time
particles.

  * •

The installation in 2013 and 2014 of chambers in the fourth endcap muon
station that were left out for Run 1.

  * •

The upgrade of the Level-1 trigger hardware prior to LHC Run 2 to improve the
selection of physics events of interest. The trigger rate from background
processes is reduced and the trigger efficiency improved for a wide variety of
physics signals. In the muon system, new trigger processor boards deploy
powerful commercial field-programmable gate arrays (FPGAs). A time-multiplexed
architecture was introduced that enabled data from all the calorimetry in each
crossing to be pushed into a single FPGA of the type used in the muon trigger
system. The FPGAs allow sophisticated and innovative algorithms to be
implemented and evolved as conditions change.

  * •

In the data acquisition system a new switch was installed and the CPU power of
the computer farm increased. The whole fabric of the distributed computing
systems was upgraded to allow more events to be stored (at least 1000 events/s
instead of the initially foreseen 100 events/s).

###  .8.3 Offline event analysis

The principal physics objects are required to have transverse momenta or
energies above a set threshold. The thresholds are lowered for the second, or
any further, objects. Typical values of these thresholds are listed in
Extended Table .9.

Lepton and photons resulting from the decays of Higgs bosons are expected to
be unaccompanied by other particles; they are said to be isolated. Isolation
criteria are imposed by requiring no additional energetic particles within a
cone of ${\approx}20^{\circ}$ opening angle around the object’s direction.
Particles, other than from decays of and quarks or $\tau$ leptons, are
expected to emerge directly from the primary interaction vertex, defined as
the vertex corresponding to the $\Pp\Pp$ collision identified by the online
selection.

Increased use of regression and classification algorithms implemented using
machine learning (ML) methods, such as deep neural networks (DNNs) and boosted
decision trees (BDTs), led to a simultaneous increase in purity and in
efficiencies of identification and reconstruction of physics objects
(electrons, muons, photons, quarks, tau leptons, jets, and ), and improvements
in the calibration of related kinematic observables.

All analyses make extensive use of Monte Carlo simulation of the signal and
background processes. The CMS detector is precisely described in software code
that is used to generate Monte Carlo event samples. Multiple interactions are
included, that match the distribution of the number of pileup interactions
observed in data. All the simulated event samples are then processed through
the same chain of software programs and procedures as are collision data.
Simulated samples are used to evaluate or determine geometric acceptances,
energy/momentum/mass resolutions, as well as for online and offline particle
identification and reconstruction efficiencies, and for training for the many
BDT algorithms and DNNs.

###  .8.4 Higgs boson decay channels: notes

Distributions of the invariant mass of final-state particles in the individual
decay channels are shown in Extended Data Figs. .9.3 and .9.4.

#### Bosonic decay channels

##### $\PH\to\PGg\PGg$

The signal is extracted by measuring the narrow signal peak over a smoothly
falling background distribution [42]. Despite its small branching fraction
(0.23%), this mode is a sensitive one due to the excellent precision in the
measurement of the energies of photons. The diphoton invariant mass resolution
is $\sigma_{m_{\PGg\PGg}}/m_{\PH}\approx 1\%$. All the principal production
modes can be studied ($\Pg\Pg\PH$, VBF, $\PV\PH$, $\PQt\PQt\PH$, and
$\PQt\PH$). The background largely consists of an irreducible one from quantum
chromodynamics (QCD) production of two photons. There is also a reducible
background where one or more of the reconstructed photon candidates originate
from misidentification of jet fragments, that is dominated by QCD Compton
scattering from quarks.

##### $\PH\to\PZ\PZ\to 4\ell$

The study of this decay channel uses the distinctive decay of the $\PZ$ bosons
to charged leptons ($\ell$) leading to a final state with 4$\Pe$, or 4$\PGm$,
or 2$\Pe$2$\PGm$ [43]. The signal appears as a narrow peak on top of a smooth
and small background. The momentum (energy) measurement of muons (electrons)
is precise enough to give an invariant mass resolution with
$\sigma_{m_{4\ell}}/m_{\PH}\approx 1\%$. The background comprises an
irreducible part arising from the nonresonant production of two $\PZ$ bosons
or $\PZ\PGg^{*}$, and a reducible part from the production of $\PZ$+jets and
top pair events, where the jets originate from heavy quarks, and thus could
contain charged leptons, or are misidentified as charged leptons. The event
yield for this process is tiny due to the small branching fractions of
$\PH\to\PZ\PZ$ (2.71%) and subsequent $\PZ\to\ell\ell$ (3.37% per lepton type)
decays. To enhance the signal over background and to categorize events,
discriminants exploiting the production and decay kinematics expected for the
signal and background events based on a matrix element likelihood approach are
used together with the invariant mass of the particle.

Extended Data Fig. .9.2 (upper) shows a display of a candidate
$\PH\to\PZ\PZ\to\Pe\Pe\PGm\PGm$ event produced in $\Pp\Pp$ collisions at a
centre-of-mass energy $\sqrt{s}=13\TeV$ and recorded in the CMS detector.

##### $\PH\to\PW\PW\to\ell\PGn\ell\PGn$

Two high-$\ell$ and large characterize this final state [44] and benefit from
the $\PH\to\PW\PW$ decay having one of the largest branching fractions
($\sim$22%). Due to the presence of two neutrinos, the computation of the
$\PW\PW$ invariant mass is not possible. However, an associated variable, the
transverse mass, , can be computed from the $\ptvec$ of the charged leptons
and the $\ptvecmiss$. The square of transverse mass for a collection of
particles $[P_{i}]$ is defined as
$\mT^{2}([P_{i}])=(\sum\abs{\vec{p}_{\mathrm{T},i}})^{2}-\abs{\sum\vec{p}_{\mathrm{T},i}}^{2}$.
The dominant background arises from irreducible nonresonant $\PW\PW$
production and is estimated from data. The channel has a good sensitivity to
the $\Pg\Pg\PH$ and VBF production processes. In the analysis, $3\ell$ and
$4\ell$ categories are also included, sensitive to production of the Higgs
boson in association with a leptonically decaying vector boson. The analysis
does not target the $\PQt\PQt\PH$ and $\PQt\PH$ production modes, which are
covered by a dedicated analysis discussed in Section .8.4.

##### $\PH\to\PZ\PGg$

The signal is sought as a peak over a smoothly falling background distribution
[45]. This analysis targets decays of the boson into 2$\Pe$ or 2$\PGm$. To
increase the sensitivity to the signal, the events are divided into different
categories based on the production mode. Multivariate analysis (MVA)
techniques are used to further categorize regions with high and low signal-to-
background ratios. The dominant background arises from Drell–Yan dilepton
production in association with an initial-state photon.

#### Fermionic decay channels

##### $\PH\to\PGt\PGt$

Four different ditau final states are studied [46]: $\Pe\PGm$, $\Pe\tauh$,
$\PGm\tauh$, and $\tauh\tauh$, where $\tauh$ refers to a hadronically decaying
tau lepton. The analysis of this decay channel targets the $\Pg\Pg\PH$, VBF,
and $\PV\PH$ production modes. The identification of $\tauh$ candidates uses
DNN discriminants to reject quark and gluon jets misidentified as $\tauh$. In
order to separate the $\PH\to\PGt\PGt$ signal events from the sizeable
contribution of irreducible $\PZ\to\PGt\PGt$ events, the likelihood estimate
of the reconstructed mass of the $\PGt\PGt$ system is used. This analysis does
not target $\PQt\PQt\PH$ production, which is covered by the dedicated
analysis discussed in Section .8.4.

##### $\PH\to\PQb\PQb$

The $\PH\to\PQb\PQb$ decay channel has by far the largest branching fraction
of all the decay channels considered, with around 60% of Higgs bosons decaying
in this way. The background from QCD production of pairs of jets is very
large, hence final states with special characteristics have been chosen to
enhance the signal-to-background ratio [47, 48, 49, 50, 51].

To select jets most likely to originate from $\PQb$ quarks, a DNN algorithm is
used [75, 76]. It provides a continuous discriminant score, which combines
information typical of $\PQb$ quark jets, such as the presence of tracks
displaced from the primary vertex, identified secondary vertices, and the
presence of low-leptons in the jet. The threshold on the discriminant score is
set such that the misidentification rate for light ($\PQu$, $\PQd$, $\PQs$)
quarks or gluons is low. For example, setting this misidentification rate at
0.1% gives a 50% efficiency for $\PQb$ quark jet identification when applied
to jets in top quark-antiquark events.

The $\PV\PH$ production mode uses the presence of one or more leptons from the
decay of the vector boson, or large . In the signal-sensitive region, DNNs are
used to separate the signal from the background dominated by QCD multijet
production.

The $\PQt\PQt\PH$ and $\PQt\PH$ production modes are included in the
combination and MVA techniques are used to separate the signal from the large
multijet backgrounds. This analysis uses the 2016 data set.

Lastly, an inclusive analysis is included that targets Higgs bosons produced
with large [51]. In this kinematic region the signal to background ratio is
larger. The two $\PQb$ jets from decays of highly Lorentz-boosted Higgs bosons
are close in space and appear in the detector as a single broad jet with
distinctive internal structure.

Extended Data Fig. .9.2 (lower) shows a display of a candidate
$\PH\to\PQb\PQb$ event produced in $\Pp\Pp$ collisions at a centre-of-mass
energy $\sqrt{s}=13\TeV$ and recorded in the CMS detector.

##### $\PH\to\PGm\PGm$

The signal is searched for as a peak in the dimuon mass distribution, over a
smoothly falling background [52]. The dimuon invariant mass resolution is
$\sigma_{m_{\PGm\PGm}}/m_{\PH}\approx 1\%$. The analysis of this decay channel
targets the $\Pg\Pg\PH$, VBF, $\PV\PH$, and $\PQt\PQt\PH$ production modes,
and is most sensitive in the first two modes. The largest background in this
decay channel comes from Drell–Yan dimuon production in which an off-shell
$\PZ^{*}$ boson decays to a pair of muons. Events are split into production
modes based on their kinematical properties. To improve the sensitivity of the
analysis, MVA techniques are used in each of these different categories.

##### $\PH\to\PQc\PQc$

The analysis of this final state in the $\PV\PH$ production mode (Fig. 1c) has
recently been presented [74] but has not been included in the present
combination. The analysis yields
$\sigma(\PV\PH)\mathcal{B}(\PH\to\PQc\PQc)<0.94\unit{pb}$ at 95% . The
observed 95% interval (expected upper limit) for $\kappa_{\PQc}$ is found to
be $1.1<\abs{\kappa_{\PQc}}<5.5$ ($\abs{\kappa_{\PQc}}<3.4$), the most
stringent to date. A search for $\PZ\to\PQc\PQc$ in $\PV\PZ$ events is used to
validate the analysis strategy and yields a first observation of this decay
channel, at a hadron collider, with a significance of 5.7 s.d.

#### ttH/tH with multileptons

The $\PQt\PQt\PH$ (Fig. 1d) and $\PQt\PH$ (Figs. 1e, 1f) production channels,
which probe the coupling of the Higgs boson to the top quarks, are studied in
the case where the Higgs boson and the top quarks subsequently decay into
final states with several leptons [53], supplementing dedicated studies of the
$\PH\to\PGg\PGg$, $\PH\to\PZ\PZ\to 4\ell$, and $\PH\to\PQb\PQb$ decay modes.

This analysis uses a categorization based on the number of leptons and/or
$\tauh$ candidates to target both the different Higgs boson final states and
$\PQt\PQt$ decay channels. Categories with at least two leptons, or one lepton
and two $\tauh$ candidates, target cases where at least one top quark decays
via a leptonically decaying $\PW$ boson. Categories with one lepton and one
$\tauh$, or with no leptons and two $\tauh$ candidates are used to target
events in which both top quarks decay via hadronically decaying $\PW$ bosons.
This analysis is sensitive to the $\PH\to\PW\PW$, $\PH\to\PGt\PGt$, and
$\PH\to\PZ\PZ$ decay channels. Several MVA techniques are employed to better
separate the $\PQt\PQt\PH$ and $\PQt\PH$ production modes.

#### Higgs boson decays beyond the SM

In addition to the invisible Higgs boson decays discussed in Section 0.5.2,
other BSM decays are possible, into undetected particles. That is, these
particles may or may not leave a trace in the CMS detector, but we do not have
dedicated searches looking for these signatures. Nevertheless, the presence of
undetected decays can be inferred indirectly from a reduction in the branching
fraction for SM decays (or by an increase in the total Higgs boson width). In
this interpretation, the total width becomes
$\Gamma_{\PH}=\sum\Gamma_{f}(\kappa)/(1-\mathcal{B}_{\text{Inv.}}-\mathcal{B}_{\text{Undet.}})$,
where $\mathcal{B}_{\text{Undet.}}$ is the branching fraction to undected
particles.

To probe invisible or undetected decays of the Higgs boson, another fit can be
performed, including $\mathcal{B}_{\text{Inv.}}$ and
$\text{B}_{\text{Undet.}}$ as additional floating parameters, while imposing
as an upper bound on $\kappa_{\PW}$ and $\kappa_{\PZ}$ their SM values, also
valid in most proposed extensions of the SM [77, 78]. As can be seen from
Extended Data Fig. .9.8 (right), $\mathcal{B}_{\text{Inv.}}$ and
$\mathcal{B}_{\text{Undet.}}$ are found to be consistent with zero. The 95%
upper limit on $\mathcal{B}_{\text{Undet.}}$ is found to be ${<}0.16$, with
only small changes to the other $\kappa_{i}$ fitted values, as shown in
Extended Data Fig. .9.8 (right). The measurement of the width [68] of the
Higgs boson will be used in the future to constrain these quantities without
imposing bounds on $\kappa_{\PW}$ and $\kappa_{\PZ}$.

###  .8.5 Statistical analysis

The statistical framework used to build the combination of all the channels is
based on an established combined likelihood method ([40] and references
therein), and briefly detailed in this section.

Given the enormous number of $\Pp\Pp$ collisions produced at the LHC and the
relatively small probability that one of those collisions will produce a
signal-like event, the observations in data are described by Poisson
probability functions,
$\mathcal{P}(k|\lambda)=\mathrm{e}^{-\lambda}\lambda^{k}/k!$, where $k$ is the
observed number of events, and the parameter $\lambda$ is the expected number
of events in a particular bin or region of one or more of the discriminating
distributions used for each channel entering the combination. The combined
likelihood is obtained from the product of the individual Poisson probability
functions, accounting for the observed data and expected number of events
across all channels.

The parameters $\lambda$ are functions of the model parameters of interest:
${\mu}$, which represent the Higgs boson couplings or signal strengths, and
nuisance parameters $\theta$, which model the effect of systematic
uncertainties on the predicted signal and background contributions. Additional
terms are included in the combined likelihood to represent constraints on the
nuisance parameters due to external measurements, such as energy and momentum
scale calibrations or an integrated luminosity determination. The measurements
reported in this paper are determined using the profile likelihood ratio
$q(\mu)=-2\ln\mathcal{L}(\mu,\hat{\theta}_{\mu})/\mathcal{L}(\hat{\mu},\hat{\theta})$
where $\hat{\mu}$ and $\hat{\theta}$ are the values of the parameters of
interest and nuisance parameters that maximize the likelihood
$\mathcal{L}(\mu,\theta)$, and $\hat{\theta}_{\mu}$ are the values of the
nuisance parameters that maximize the likelihood for a fixed value of $\mu$.
The compatibility between a given set of measurements and their corresponding
SM predictions is reported as a $p$-value, derived from the difference between
$q_{\text{SM}}$ and $q(\hat{\mu})$. Expected intervals are derived from the
Asimov data set, in which the nuisance parameters are set to their maximum
likelihood estimator values.

The modified likelihood ratio test statistic
$\tilde{q}(\mu)=-2\ln[\mathcal{L}(\mu,\hat{\theta}_{\mu})/\mathcal{L}(\hat{\mu},\hat{\theta})]$
with a constraint $0\leq\hat{\mu}\leq\mu$ is used to set 95% CL upper limits
on signal strengths and production cross sections using the “CLs criterion”
[40].

All the reported confidence intervals, confidence regions, and $p$-values are
obtained assuming various asymptotic approximations for the distributions of
the (modified) likelihood ratio test statistic [79]. The validity of the
asymptotic assumptions has been routinely checked in the context of individual
analyses whenever the event yields are small or particular validity conditions
are not met.

###  .8.6 Signal strengths $\mu$: production channels and decay modes

For a Higgs boson produced in mode $i$ and decaying into a final state $f$,
the signal event yields are proportional to $\sigma_{i}\mathcal{B}^{f}$, where
$\sigma_{i}$ is the production cross section and $\mathcal{B}^{f}$ the decay
branching fraction. The branching fraction is in turn given by
$\mathcal{B}^{f}=\Gamma^{f}/\Gamma_{\PH}$, where $\Gamma^{f}$ is the partial
decay width in the final state $f$ and $\Gamma_{\PH}$ the total natural width
of the Higgs boson.

Fits are performed under different assumptions:

  * •

per overall single signal strength, yielding $\mu=1.002\pm 0.057$,

  * •

per production channel signal strengths
($\mu_{i}=\sigma_{i}/\sigma_{i}^{\text{SM}}$ with
$\mathcal{B}^{f}=\mathcal{B}^{f}_{\text{SM}}$), Fig. 2 (left),

  * •

per decay mode signal strengths
($\mu^{f}=\mathcal{B}^{f}/\mathcal{B}^{f}_{\text{SM}}$, with
$\sigma_{i}=\sigma_{i}^{\text{SM}}$), Fig. 2 (right), and

  * •

with a free parameter per individual combination of production modes and decay
channels, as illustrated in Extended Data Fig. .9.6.

The covariance matrices for the fitted signal strengths per production mode
$\mu_{i}$ and per decay channel $\mu^{f}$ are shown in Extended Data Fig.
.9.5.

###  .8.7 Notes on self-interaction strength

The potential energy of the BEH field ($\phi$) is given by
$V(\phi)=\frac{1}{2}m_{\PH}^{2}\phi^{2}+\sqrt{\lambda/2}m_{\PH}\phi^{3}+\frac{1}{4}\lambda\phi^{4}$.
The first term accounts for the mass of the Higgs boson $m_{\PH}$. The second
term represents the Higgs boson self interaction, of strength $\lambda$. In
the SM, $\lambda=m_{\PH}^{2}/(2\upsilon^{2})$ (where the vacuum expectation
value of the BEH field, corresponding to its minimum, is $\upsilon=246\GeV$)
and it can be measured via the study of Higgs boson pair production. The third
term represents the interaction of four Higgs bosons at a point, a process
that is even rarer than its pair production. Knowledge of the exact shape of
the potential $V$ is crucial for understanding the phase transition that
occurred in the early universe and its consequences [80].

The search for Higgs boson pair production is performed by combining Higgs
boson pairs, each with differing decay modes. The decay modes that have been
used are $\PQb\PQb$, $\PGt\PGt$, and $\PW\PW$ [57, 58, 59, 60], benefitting
from the large branching fractions, and $\PGg\PGg$ [61] and $\PZ\PZ\to 4\ell$
[62], benefitting from the presence of narrow mass peaks, thus improving the
signal-to-background ratio. All final states analyzed are defined to be
mutually exclusive so that they could be properly combined as statistically
independent observations.

Measurements of Higgs boson pair production are used to constrain the Higgs
boson self-interaction strength $\lambda$. Several combinations of individual
Higgs boson decay modes are employed in this search. The highest rate for
Higgs boson pair production and decays occurs when both Higgs bosons decay to
$\PQb$ quark pairs, $\PH\PH\to\PQb\PQb\PQb\PQb$, corresponding to $\approx$35%
of all the possible $\PH\PH$ decays in the SM.

The search in the $4\PQb$ decay mode [57, 58] is performed separately under
the assumptions that $m_{\PH^{*}}\gg 2m_{\PH}$ or not. In the case
$m_{\PH^{*}}\gg 2m_{\PH}$, each Higgs boson is energetic (and hence said to be
boosted), such that its decay products, $\PQb$ quark jets, merge and appear as
one broad jet, but with a distinctive internal structure. In the latter case,
all four $\PQb$ quark jets rarely overlap, and hence said to be resolved.

Another group of analyses targets the $\PH\PH$ final states where one $\PH$
decays to $\PQb$ quarks and the other to $\PGt\PGt$ [59], $\PGg\PGg$ [61], or
$\PZ\PZ\to 4\ell$ [62]. Analyses targeting a set of multileptons final states
with are $\PH\PH\to(\PW\PW)(\PW\PW)$, $(\PW\PW)(\PGt\PGt)$, or
$(\PGt\PGt)(\PGt\PGt)$ [60], where hadronic tau lepton decays are also
included.

A fit to Higgs boson pair production data can be used to simultaneously
constrain $\kappa_{\lambda}$ and $\kappa_{\mathrm{2V}}$, as shown in Extended
Data Fig. .9.9 (left).

Measurements of single Higgs boson production and decay can also be used to
constrain $\kappa_{\lambda}$ as quantum corrections to the SM Higgs boson
production modes and decay channels depend on $\kappa_{\lambda}$ [81, 82].
These corrections have been derived [83] for the different production and
decay modes entering the combination, as shown in Extended Data Table .9.

The values of $\kappa_{\lambda}$ extracted from single and pair Higgs boson
production are shown in Extended Data Fig. .9.9 (right).

###  .8.8 Upgrade of the CMS experiment for HL-LHC running

To exploit the full potential of the LHC, the accelerator and its experiments
will be upgraded. The HL-LHC will operate at an instantaneous luminosity of
$5\times 10^{34}\percms$. The intention is to collect ten times more data than
the $300\fbinv$ foreseen in the initial LHC phase. This means that the
integrated radiation levels will be correspondingly larger.

The physics to be studied drives the technical choices for the upgrade. The
physics goals are:

  * •

precise measurements of the properties of the Higgs boson and its self-
coupling, to elucidate further the physics of EW symmetry breaking;

  * •

search for BSM physics; and

  * •

selected precision SM measurements.

The translation of these physics goals into experimental design goals
requires:

  * •

The construction of a new higher-granularity, more radiation-hard silicon
tracker. The design of the new front-end electronics will allow information
from the inner tracker to participate in the Level-1 trigger. The size of the
individual detecting elements will be decreased leading to about ten times
larger number of electronics channels. All components inside the tracker
(silicon sensors, front-end electronics, 10Gb/s data links, etc.) will have to
withstand integrated doses of up to 500Mrad and fluences of $10^{16}$ ($1\MeV$
equivalent neutrons)/$\,\text{cm}^{2}$. The geometric coverage of the inner
tracker will be increased, extending it down an angle of $2^{\circ}$ from the
beamline.

  * •

The replacement of other components affected by radiation. Principally these
are the endcap calorimeters and the ECAL front-end electronics. The endcap
calorimeters will be replaced with a new high-granularity “imaging”
calorimeter with precision timing. It will be based on $600\unit{m}^{2}$ of
silicon sensors with detecting cells of sizes of 0.5 to 1.0$\,\text{cm}^{2}$.
Regions in this calorimeter will reach integrated doses of up to 500Mrad and
fluences of $10^{16}$ ($1\MeV$ equivalent neutrons)/$\mathrm{cm}^{2}$. The new
front-end electronics for the ECAL barrel will allow data from each crystal to
be sent to the calorimeter Level-1 trigger processor, instead of the sum of 25
crystals today, and which will allow better measurement of the timing of the
impact of electrons or photons.

  * •

Higher-bandwidth Level-1 and high-level triggers. Information from the inner
trackers will be used at Level-1. The Level-1 trigger latency will be
increased from 4 to over $12\mus$, requiring corresponding changes in the
front-end electronics, allowing more processing time leading to a purer
selection of events. The output rate from the Level-1 processors will be
increased from 100 to 750kHz and correspondingly the number of events stored
for later analysis will be increased from 1 to 10kHz.

  * •

The introduction of precision timing detectors. A new set of detectors will be
installed in the barrel and endcap regions, covering a region down to an angle
of 9∘ from the beamline. The precision timing of photons (in the barrel
region) and charged tracks will greatly improve the localization of the
correct interaction vertex. At HL-LHC, on the average, some 140 pairs of
protons are expected to interact in each crossing, spread over a time
characterized by $\sigma\approx 200\unit{ps}$. Furthermore, suppression of
energy can be carried out that is not consistent in time with the interaction
of interest.

The upgraded CMS experiment at HL-LHC will be more powerful than the current
one. Uncertainties in many measurements of the properties of the Higgs boson
are expected to approach the percent level, benefitting from the anticipated
larger event samples, reduced experimental systematic uncertainties, and more
accurate theoretical calculations.

###  .8.9 Theoretical references

The theoretical works used in our analyses can be found in the LHC Higgs Cross
Section Working Group reports [36, 37, 38, 39] and in the following Refs. [84,
85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102,
103, 104, 105, 106, 107, 108, 54, 56].

###  .8.10 Data availability

Tabulated results are provided in the HEPData record for this analysis.
Release and preservation of data used by the CMS collaboration as the basis
for publications is guided by the CMS data preservation, re-use and open acess
policy.

###  .8.11 Code availability

The CMS core software is publicly available on GitHub (https://github.com/cms-
sw/cmssw).

###  .8.12 Ethics declarations

Author contributions All authors have contributed to the publication, being
variously involved in the design and the construction of the detectors, in
writing software, calibrating subsystems, operating the detectors and
acquiring data, and finally analysing the processed data. The CMS
Collaboration members discussed and approved the scientific results. The
manuscript was prepared by a subgroup of authors appointed by the
collaboration and subject to an internal collaboration-wide review process.
All authors reviewed and approved the final version of the manuscript.

Competing interests The authors declare no competing interests.

##  .9 Extended data

9.1.Figure:  The CMS detector at the CERN LHC.
Schematic longitudinal cut-away view of the CMS detector, showing the
different layers around the LHC beam axis, with the collision point in the
centre.

The SM Higgs production cross sections and branching fractions.
Theoretical cross sections for each production mode and branching fractions
for the decay channels, at $\sqrt{s}=13$and for $m_{\PH}=125.38$[39].
Production mode Cross section (pb) Decay channel Branching fraction (%)
$\Pg\Pg\PH$ $48.31$ ± 2.44 $\PQb\PQb$ $57.63$ ± 0.70 VBF $3.771$ ± 0.807
$\PW\PW$ $22.00$ ± 0.33 $\PW\PH$ $1.359$ ± 0.028 $\Pg\Pg$ $8.15$ ± 0.42
$\PZ\PH$ $0.877$ ± 0.036 $\PGt\PGt$ $6.21$ ± 0.09 $\PQt\PQt\PH$ $0.503$ ±
0.035 $\PQc\PQc$ $2.86$ ± 0.09 $\PQb\PQb\PH$ $0.482$ ± 0.097 $\PZ\PZ$ $2.71$ ±
0.04 $\PQt\PH$ $0.092$ ± 0.008 $\PGg\PGg$ $0.227$ ± 0.005 $\PZ\PGg$ $0.157$ ±
0.009 $\PQs\PQs$ $0.025$ ± 0.001 $\PGm\PGm$ $0.0216$ ± 0.0004

Summary of the Higgs boson analyses included in this paper.
The analysis and decay channels are indicated in the first two columns, with
the third column containing the production mechanism and kinematic regions
targeted by each analysis. All analyses, apart from $\PQt\PQt\PH$ in the
$\PH\to\PQb\PQb$ final state (2016 data only) and $\PV\PH$ in the
$\PH\to\PQb\PQb$ final state (2016–2017 data), use the full data set collected
in Run 2. The various symbols are as follows: $\ell$ is $\Pe$ or $\PGm$, jet
(j), di-jet mass ($m_{\text{jj}}$), number of jets ($N_{\text{j}}$), same-sign
(SS) of electric charge, hadronic decay of the tau lepton ($\tauh$).  Analysis
Decay tags Production tags Single Higgs boson production $\PH\to\PGg\PGg$ [42]
$\Pg\Pg\PH$, $\pt(\PH)$ $\times$ $N_{\text{j}}$ bins VBF/VH hadronic,
$\pt(\PH\text{jj})$ bins WH leptonic, $\pt(\PV)$ bins ZH leptonic $\PGg\PGg$
$\PQt\PQt\PH$ $\pt(\PH)$ bins, $\PQt\PH$ $\PH\to\PZ\PZ\to 4\ell$ [43]
$\Pg\Pg\PH$, $\pt(\PH)$ $\times$ $N_{\text{j}}$ bins VBF, $m_{\text{jj}}$ bins
V$\PH$ hadronic V$\PH$ leptonic, $\pt(\PV)$ bins 4$\PGm$, $2\Pe 2\PGm$, 4$\Pe$
$\PQt\PQt\PH$ $\PH\to\PW\PW\to\ell\PGn\ell\PGn$ [44] $\Pe\PGm/\Pe\Pe/\PGm\PGm$
$\Pg\Pg\PH$ $\leq$ 2-jets VBF $\PGm\PGm$+jj/$\Pe\Pe$+jj/$\Pe\PGm$+jj V$\PH$
hadronic $3\ell$ $\PW\PH$ leptonic $4\ell$ $\PZ\PH$ leptonic $\PH\to\PZ\PGg$
[45] $\Pg\Pg\PH$ $\PZ\PGg$ VBF $\PH\to\PGt\PGt$ [46] $\Pg\Pg\PH$, $\pt(\PH)$
$\times$ $N_{\text{j}}$ bins V$\PH$ hadronic VBF
$\Pe\PGm,\Pe\tauh,\PGm\tauh,\tauh\tauh$ V$\PH$, high-$\pt(\PV)$
$\PH\to\PQb\PQb$ [47, 48, 49, 50, 51] $\PW(\ell\PGn)\PH(\PQb\PQb)$ $\PW\PH$
leptonic $\PZ(\PGn\PGn)\PH(\PQb\PQb)$, $\PZ(\ell\ell)\PH(\PQb\PQb)$ $\PZ\PH$
leptonic $\PQt\PQt\PH$, $\tt\to$ 0, 1, 2$\ell+\mathrm{jets}$ $\PQb\PQb$
$\Pg\Pg\PH$, high-$\pt(\PH)$ bins $\PH\to\PGm\PGm$ [52] $\Pg\Pg\PH$ $\PGm\PGm$
VBF $\PQt\PQt\PH$ production $2\ell$ SS, $3\ell$, $4\ell$, with
$\PH\to\mathrm{leptons}$ [53] $1\ell+\tauh$, $2\ell$ SS$+1\tauh$,
$3\ell+1\tauh$ $\PQt\PQt\PH$ $\PH\to$ Inv. [71, 72] $\ptmiss$ $\Pg\Pg\PH$ VBF
$\PV\PH$ hadronic $\PZ\PH$ leptonic Higgs boson pair production
$\PH\PH\to\PQb\PQb\PQb\PQb$ [57, 58] $\PH(\PQb\PQb)\PH(\PQb\PQb)$
$\Pg\Pg\PH\PH$, VBF$\PH\PH$ (resolved, boosted) $\PH\PH\to\PQb\PQb\PGt\PGt$
[59] $\PH(\PQb\PQb)\PH(\PGt\PGt)$ $\Pg\Pg\PH\PH$, VBF$\PH\PH$ $\PH\PH\to$
leptons [60] $\PH(\PW\PW)\PH(\PW\PW)$, $\PH(\PW\PW)\PH(\PGt\PGt)$,
$\PH(\PGt\PGt)\PH(\PGt\PGt)$ $\Pg\Pg\PH\PH$, VBF$\PH\PH$
$\PH\PH\to\PQb\PQb\PGg\PGg$ [61] $\PH(\PQb\PQb)\PH(\PGg\PGg)$ $\Pg\Pg\PH\PH$,
VBF$\PH\PH$ $\PH\PH\to\PQb\PQb\PZ\PZ$ [62] $\PH(\PQb\PQb)\PH(\PZ\PZ)$
$\Pg\Pg\PH\PH$

Summary of the event selections.
Some of the typical selection criteria used in the trigger (online selection)
and in offline analysis for some of the final states and for leading (1) and
subleading (2) particles. The is a measure of the imbalance in energy in the
plane transverse to the colliding proton beams.  Analysis Physics objects
Trigger selections threshold [] Kinematic requirements [] $\PH\to\PGg\PGg$
$\PGg$ $\pt^{\PGg}(1/2)>30/18$ $\pt^{\PGg}>35/25$ $\PH\to\PZ\PZ\to 4\ell$
$\PGm$, $\Pe$ $\pt^{\PGm}(1/2)>23/8$ $\pt^{\PGm}>5$ $\pt^{\Pe}(1/2)>17/8$
$\pt^{\Pe}>7$ $\PH\to\PW\PW\to\ell\PGn\ell\PGn$ $\PGm$, $\Pe$,
$\pt^{\PGm}(1/2)>23/12$ $\pt^{\PGm}(1/2)>25/13$ $\pt^{\Pe}(1/2)>23/12$
$\pt^{\Pe}(1/2)>25/13$ $>20$ $\PH\to\PZ\PGg$ $\PGm$, $\Pe$, $\PGg$
$\pt^{\PGm}(1/2)>17/8$ $\pt^{\PGm}(1/2)>20/10$ $\pt^{\Pe}(1/2)>23/12$
$\pt^{\Pe}(1/2)>25/15$ $\pt^{\PGg}>15$ $\PH\to\PGt\PGt$ $\PGm$, $\Pe$, $\tauh$
$\pt^{\PGm}>20$ $\pt^{\PGm}>20$ $\pt^{\Pe}>24$ $\pt^{\Pe}>25$ $\pt^{\tauh}>35$
$\pt^{\tauh}>40$ $\PH\to\PQb\PQb$ $\PGm$, $\Pe$, , jet $\pt^{\PGm}>22$
$\pt^{\PGm}>25$ $\pt^{\Pe}>32$ $\pt^{\Pe}>30$ $\ptmiss>120$ $\ptmiss>170$
$E_{\text{j}}>330$ $E_{\text{j}}>450$ $\PH\to\PGm\PGm$ $\PGm$ $\pt^{\PGm}>24$
$\pt^{\PGm}(1/2)>26/20$

9.2.Figure:  Higgs boson candidate events.
(upper) An event display of a candidate $\PH\to\PZ\PZ\to\Pe\Pe\PGm\PGm$.
(lower) An event display of an $\PH\to\PQb\PQb$ candidate produced in
association with a boson decaying into an electron-positron pair, in $\Pp\Pp$
collisions at $\sqrt{s}=13\TeV$ recorded by CMS. The charged-particle tracks,
as reconstructed in the inner tracker, are shown in yellow; the electrons are
shown in green, the energy deposited by the electrons in the ECAL is shown as
large green towers, the size of which is proportional of the amount of energy
deposited; the blue towers are indicative of the energy deposits in the HCAL,
while the red boxes are the muon chambers crossed by the muons (red tracks);
the yellow cones represent the reconstructed jets. (lower, inset) The zoom
into the collision region shows the displaced secondary vertices (in red) of
the two quarks decaying away from the primary vertex (in yellow). One of the
bottom hadrons decays into a charm hadron that moves away from the secondary
vertex before decaying ($\PQb\to\PQc\to\PX$; vertex in cyan).

9.3.Figure:  Higgs boson mass peak in diboson decay channels.
(upper left) The background-subtracted diphoton invariant mass distribution
targeting the study of the decay channel $\PH\to\PGg\PGg$. (upper right) The
invariant mass distribution of four charged leptons targeting the study of the
decay channel $\PH\to\PZ\PZ\to 4\ell$. (lower left) The background-subtracted
transverse mass distribution targeting the study of the decay channel
$\PH\to\PW\PW$. (lower right) The background-subtracted $\ell\ell\PGg$
invariant mass distribution targeting the study of the decay channel
$\PH\to\PZ\PGg$. The SM prediction for the signal (red line) is scaled by the
value of $\mu$, as estimated in the dedicated analysis for that channel, and
computed for $m_{\PH}=125.38\GeV$. The grey band around zero shows the 1 s.d.
uncertainty in the background subtraction.

9.4.Figure:  Higgs boson mass peak in difermion decay channels.
The background-subtracted diparticle invariant mass distribution targeting the
study of the decay channel (left) $\PH\to\PGt\PGt$, (center) $\PH\to\PQb\PQb$,
(right) $\PH\to\PGm\PGm$. The SM prediction for the signal (red line) is
scaled by the value of $\mu$, as estimated in the dedicated analysis for that
channel, and computed for $m_{\PH}=125.38\GeV$. The grey band around zero
shows the 1 s.d. uncertainty in the background subtraction.

9.5.Figure:  Correlations between the measurements of different couplings.
Covariance matrices for the fits of the signal strength parameters per
production mode $\mu_{i}$ (left) and per decay mode $\mu^{f}$ (right). The
values of the correlation coefficients, $\rho$, are indicated both in text and
in the color scale. 9.6.Figure:  The agreement with the SM predictions in
Higgs boson production and decay.
Signal strength parameters per individual production mode and decay channel
$\mu_{i}^{f}$, and combined per production mode $\mu_{i}$ and decay channel
$\mu^{f}$. In this fit, $\PQt\PQt\PH$ and $\PQt\PH$ are considered together
and the $\mu_{i}$ results are slightly different from those of Fig. 2 (left).
The dashed vertical lines at 1 represent the SM value. Light grey shading
indicates that $\mu$ is contained to be positive. Dark grey shading indicates
the absence of measurement. The $p$-value with respect to the SM prediction is
5.8%. 9.7.Figure:  Time evolution of the signal strength measurements and
their precision.
Comparison of the signal strength parameter $\mu$ fit results in different
data sets; in each panel, from left to right: at the time of the Higgs boson
discovery, using the full data from LHC Run 1, in the data set analyzed for
this paper, and the expected 1 s.d. uncertainty for HL-LHC for
$\mathcal{L}=3000\fbinv$. The $\PH\to\PGm\PGm$ measurements were not available
for the earlier data sets due to the lack of sensitivity.

9.8.Figure:  Time evolution of the coupling measurements and their precision.
(left) Comparison of the expected 1 s.d. uncertainties in the
$\kappa$-framework fit including coupling modifiers for both tree-level and
loop-induced Higgs boson interactions, in different data sets: at the time of
the Higgs boson discovery, using the full data from LHC Run 1, in the data set
used in this paper, and the expected 1 s.d. uncertainty for HL-LHC for
$\mathcal{L}=3000\fbinv$. (right) Results of a fit to the coupling modifiers
$\kappa$ allowing both invisible and the undetected decay modes, with the SM
value used as an upper bound on both $\kappa_{\PW}$ and $\kappa_{\PZ}$. The
thick (thin) black lines indicate the 1 (2) s.d. confidence intervals, with
the systematic and statistical components of the 1 s.d. interval indicated by
the red and blue bands, respectively. The $p$-value with respect to the SM
prediction is 33%.

9.9.Figure:  Constraints on Higgs boson self-interaction and quartic coupling.
(left) Constraints on $\kappa_{\lambda}$ and $\kappa_{\mathrm{2V}}$ from the
production of Higgs boson pairs. (right) Constraint on the Higgs boson self-
coupling modifier $\kappa_{\lambda}$ from single and pair production of Higgs
boson(s).

##  .10 The CMS Collaboration

Yerevan Physics Institute, Yerevan, Armenia A. Tumasyan

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. Jeitler10000-0002-5141-9560, 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. Schieck10000-0002-1058-8093, R. Schöfbeck0000-0002-2332-8784, D.
Schwarz0000-0002-3821-7331, S. Templ0000-0003-3137-5692, W.
Waltenberger0000-0002-6215-7228, C.-E. Wulz10000-0001-9226-5812

Universiteit Antwerpen, Antwerpen, Belgium M.R. Darwish20000-0003-2894-2377,
T. Janssen0000-0002-3998-4081, T. Kello3, 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. Pétré, 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.
Chinellato4, E.M. Da Costa0000-0002-5016-6434, G.G. Da
Silveira50000-0003-3514-7056, D. De Jesus Damiao0000-0002-3769-1680, V. Dos
Santos Sousa0000-0002-4681-9340, S. Fonseca De Souza0000-0001-7830-0837, J.
Martins60000-0002-2120-2782, C. Mora Herrera0000-0003-3915-3170, K. Mota
Amarilo0000-0003-1707-3348, L. Mundim0000-0001-9964-7805, H.
Nogima0000-0001-7705-1066, A. Santoro, S.M. Silva Do
Amaral0000-0002-0209-9687, A. Sznajder0000-0001-6998-1108, M.
Thiel0000-0001-7139-7963, F. Torres Da Silva De Araujo70000-0002-4785-3057, A.
Vilela Pereira0000-0003-3177-4626

Universidade Estadual Paulista, Universidade Federal do ABC, São Paulo, Brazil
C.A. Bernardes50000-0001-5790-9563, L. Calligaris0000-0002-9951-9448, E.M.
Gregores0000-0003-0205-1672, P.G. Mercadante0000-0001-8333-4302, S.F.
Novaes0000-0003-0471-8549, Sandra S. Padula0000-0003-3071-0559, T.R. Fernandez
Perez Tomei0000-0002-1809-5226

Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of
Sciences, Sofia, Bulgaria A. Aleksandrov, 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. Javaid8, M.
Mittal0000-0002-6833-8521, L. Yuan0000-0002-6719-5397

Department of Physics, Tsinghua University, Beijing, China M.
Ahmad0000-0001-9933-995X, G. Bauer9, Z. Hu0000-0001-8209-4343, S.
Lezki0000-0002-6909-774X, K. Yi9,10

Institute of High Energy Physics, Beijing, China G.M.
Chen80000-0002-2629-5420, H.S. Chen80000-0001-8672-8227, M.
Chen80000-0003-0489-9669, F. Iemmi0000-0001-5911-4051, C.H. Jiang, A.
Kapoor0000-0002-1844-1504, H. Liao0000-0002-0124-6999, Z.-A.
Liu110000-0002-2896-1386, V. Milosevic0000-0002-1173-0696, F.
Monti0000-0001-5846-3655, R. Sharma0000-0003-1181-1426, J.
Tao0000-0003-2006-3490, J. Thomas-Wilsker0000-0003-1293-4153, J.
Wang0000-0002-3103-1083, H. Zhang0000-0001-8843-5209, J.
Zhao0000-0001-8365-7726

State Key Laboratory of Nuclear Physics and Technology, Peking University,
Beijing, China A. Agapitos0000-0002-8953-1232, Y. An0000-0003-1299-1879, Y.
Ban0000-0002-1912-0374, C. Chen, A. Levin0000-0001-9565-4186, 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.
Gao30000-0001-7205-2318, 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.
Starodumov120000-0001-9570-9255, T. Susa0000-0001-7430-2552

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

Charles University, Prague, Czech Republic M. Finger Jr.120000-0003-3155-2484,
M. Finger120000-0002-7828-9970, A. Kveton0000-0001-8197-1914

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

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

Academy of Scientific Research and Technology of the Arab Republic of Egypt,
Egyptian Network of High Energy Physics, Cairo, Egypt A.A.
Abdelalim13,140000-0002-2056-7894, E. Salama15,160000-0002-9282-9806

Center for High Energy Physics (CHEP-FU), Fayoum University, El-Fayoum, Egypt
M.A. Mahmoud0000-0001-8692-5458, Y. Mohammed0000-0001-8399-3017

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, O.
Davignon0000-0001-8710-992X, B. Diab0000-0002-6669-1698, G.
Falmagne0000-0002-6762-3937, B.A. Fontana Santos Alves0000-0001-9752-0624, S.
Ghosh0009-0006-5692-5688, R. Granier de Cassagnac0000-0002-1275-7292, A.
Hakimi0009-0008-2093-8131, B. Harikrishnan0000-0003-0174-4020, J.
Motta0000-0003-0985-913X, M. Nguyen0000-0001-7305-7102, C.
Ochando0000-0002-3836-1173, 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. Andrea, D. Apparu, D. Bloch0000-0002-4535-5273,
G. Bourgatte, J.-M. Brom0000-0003-0249-3622, E.C. Chabert0000-0003-2797-7690,
C. Collard0000-0002-5230-8387, D. Darej, 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. Boudoul, C.
Camen, 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, K. Shchablo, 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 I. Lomidze0009-0002-3901-2765,
T. Toriashvili200000-0003-1655-6874, Z. Tsamalaidze120000-0001-5377-3558

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. Redjeb, 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.
Dziwok, G. Flügge0000-0003-3681-9272, W. Haj Ahmad210000-0003-1491-0446, O.
Hlushchenko, T. Kress0000-0002-2702-8201, A. Nowack0000-0002-3522-5926, O.
Pooth0000-0001-6445-6160, A. Stahl220000-0002-8369-7506, T.
Ziemons0000-0003-1697-2130, A. Zotz0000-0002-1320-1712

Deutsches Elektronen-Synchrotron, Hamburg, Germany H. Aarup Petersen, M.
Aldaya Martin0000-0003-1533-0945, P. Asmuss, S. Baxter, M.
Bayatmakou0009-0002-9905-0667, O. Behnke, A. Bermúdez
Martínez0000-0001-8822-4727, S. Bhattacharya0000-0002-3197-0048, A.A. Bin
Anuar0000-0002-2988-9830, F. Blekman230000-0002-7366-7098, K.
Borras240000-0003-1111-249X, D. Brunner0000-0001-9518-0435, A.
Campbell0000-0003-4439-5748, A. Cardini0000-0003-1803-0999, C. Cheng, F.
Colombina, S. Consuegra Rodríguez0000-0002-1383-1837, G. Correia
Silva0000-0001-6232-3591, M. De Silva0000-0002-5804-6226, L.
Didukh0000-0003-4900-5227, G. Eckerlin, D. Eckstein, L.I. Estevez
Banos0000-0001-6195-3102, O. Filatov0000-0001-9850-6170, E.
Gallo230000-0001-7200-5175, 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.
Jafari250000-0001-7327-1870, N.Z. Jomhari0000-0001-9127-7408, B.
Kaech0000-0002-1194-2306, M. Kasemann0000-0002-0429-2448, H.
Kaveh0000-0002-3273-5859, C. Kleinwort0000-0002-9017-9504, R.
Kogler0000-0002-5336-4399, M. Komm0000-0002-7669-4294, D.
Krücker0000-0003-1610-8844, W. Lange, D. Leyva Pernia, K.
Lipka0000-0002-8427-3748, W. Lohmann260000-0002-8705-0857, 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, A.
Kasem240000-0002-6753-7254, M. Mormile0000-0003-0456-7250, A.
Mussgiller0000-0002-8331-8166, A. Nürnberg0000-0002-7876-3134, Y. Otarid, D.
Pérez Adán0000-0003-3416-0726, A. Raspereza, B. Ribeiro
Lopes0000-0003-0823-447X, J. Rübenach, A. Saggio0000-0002-7385-3317, A.
Saibel0000-0002-9932-7622, M. Savitskyi0000-0002-9952-9267, M.
Scham27,240000-0001-9494-2151, V. Scheurer, S. Schnake24, P.
Schütze0000-0003-4802-6990, C. Schwanenberger230000-0001-6699-6662, M.
Shchedrolosiev, R.E. Sosa Ricardo0000-0002-2240-6699, D. Stafford, N.
Tonon${}^{\textrm{\textdagger}}$0000-0003-4301-2688, M. Van De