EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 CERN-EP-2022-030 LHCb-PAPER-2021-048

First measurement of the $Z\rightarrow{\mu^{+}}{\mu^{-}}$ angular coefficients
in the forward region of $pp$ collisions at
$\sqrt{s}=13\text{\,Te\kern-2.07413ptV}$

LHCb collaboration†††Authors are listed at the end of this Letter.

The first study of the angular distribution of $\mu^{+}$ $\mu^{-}$ pairs
produced in the forward rapidity region via the Drell-Yan reaction
$pp\rightarrow\gamma^{*}/Z+X\rightarrow{\ell^{+}}{\ell^{-}}+X$ is presented,
using data collected with the LHCb detector at a center-of-mass energy of 13
TeV, corresponding to an integrated luminosity of $5.1$$\text{\,fb}^{-1}$. The
coefficients of the five leading terms in the angular distribution are
determined as a function of the dimuon transverse momentum and rapidity. The
results are compared to various theoretical predictions of the $Z$-boson
production mechanism and can also be used to probe transverse-momentum-
dependent parton distributions within the proton.

Published in Phys. Rev. Lett. 129 (2022) 091801

© 2024 CERN for the benefit of the LHCb collaboration. CC BY 4.0 licence.

Drell-Yan muon pairs ($\mu^{+}\mu^{-}$) produced near the $Z$-boson mass pole
provide an excellent source of information about electroweak (EW) parameters,
probe the proton structure and test the underlying strong-interaction dynamics
of $Z$-boson production in proton-proton ($pp$) collisions, as described by
quantum chromodynamics (QCD). With a dedicated detector instrumented in the
forward region, the LHCb experiment plays a unique role in the study of
$Z\rightarrow{\mu^{+}}{\mu^{-}}$ processes in the forward rapidity ($y^{Z}$)
region [1], especially for $y^{Z}>3.5$. Therefore, the LHCb experiment is
complementary to the ATLAS and CMS experiments, which are more efficient in
the central region. The distributions of the $Z$-boson transverse momentum,
$p_{\mathrm{T}}$, and the scattering angle, $\phi^{*}_{\eta}$, of the muons
with respect to the proton beam direction in the rest frame of the dimuon
system [2] have already been measured by the LHCb collaboration [3, 4, 5, 1].
Key information is also encoded in the $Z\rightarrow{\mu^{+}}{\mu^{-}}$
angular distribution in the forward region, which has not been fully explored.

In the Drell-Yan neutral-current process, the lepton pair is produced via a
spin–1 gauge boson. The kinematic distribution of the final-state leptons
($\ell^{\pm}$) provides a direct probe of the polarization of the intermediate
gauge boson, which is in turn sensitive to the underlying QCD production
mechanisms. The QCD mechanisms of the process
$pp\rightarrow\gamma^{*}/Z+X\rightarrow{\ell^{+}}{\ell^{-}}+X$, where $X$
represents any other particles, can be expressed using eight frame-dependent
angular coefficients, $A_{i}$ ($i=0,...,7$). The coefficients depend on the
invariant mass, $p_{\mathrm{T}}$ and rapidity of the lepton pair. At Born
level, the angular distribution of the leptons in the boson rest frame is
given by [6, 7]

$\displaystyle\frac{\rm{d}\sigma}{\rm{d}\cos\theta d\phi}$
$\displaystyle\propto(1+\cos^{2}\theta)+\frac{1}{2}A_{0}(1-3\cos^{2}\theta)+A_{1}\sin
2\theta\cos\phi+\frac{1}{2}A_{2}\sin^{2}\theta\cos 2\phi$ (1) $\displaystyle+$
$\displaystyle A_{3}\sin\theta\cos\phi+A_{4}\cos\theta+A_{5}\sin^{2}\theta\sin
2\phi+A_{6}\sin 2\theta\sin\phi+A_{7}\sin\theta\sin\phi,$

where $\theta$ and $\phi$ are the polar and azimuthal angles of the $\mu^{+}$
lepton in the Collins-Soper frame [8]. At leading-order (LO) approximation
within the framework of QCD, all angular coefficients vanish as the dilepton
transverse momentum approaches zero, with the exception of $A_{4}$, which is
nonzero due to parity violation in the weak interaction. At next-to-leading-
order (NLO), $A_{0-3}$ become nonzero, while $A_{5-7}$ have small deviations
from zero only at next-to-next-to-leading-order (NNLO).

The equality $A_{0}=A_{2}$ is known as the Lam-Tung relation [9], which is
valid for both $q\bar{q}$ and $gq$ processes at LO [10]. However, small
violations of the Lam-Tung relation occur in higher-order perturbative QCD
calculations [11, 12], as well as in QCD resummation calculations to all
orders [13]. Therefore, precision measurements of $A_{0}-A_{2}$ can test the
Lam-Tung relation. Nonperturbative effects can lead to violation of the Lam-
Tung relation via a correlation between the transverse spin and transverse
momentum of the initial-state quark or antiquark, represented by the Boer-
Mulders transverse-momentum-dependent (TMD) parton distribution function (PDF)
[14, 15]. Significant violation of the Lam-Tung relation, with large
$\cos{2\phi}$ modulations, has been observed in pion-induced Drell-Yan
measurements [16, 17, 18]. The $\cos 2\phi$ coefficient ($A_{2}$) in Eq. (1)
is proportional to the convolution of two Boer-Mulders functions, of the quark
and the antiquark [15]. Therefore, the angular measurements of the Drell-Yan
process can improve constraints on nonperturbative partonic spin-momentum
correlations within unpolarised protons via phenomenological extractions of
the Boer-Mulders TMD PDF from these data in conjunction with data from other
experiments. The $Z$-boson cross-section measurements at low $p_{T}$
($\lesssim 20\text{\,Ge\kern-1.00006ptV\\!/}c$) by the LHCb collaboration have
already been used to extract the unpolarised TMD PDF [19].

Previously, the CDF collaboration published the first measurement [20] of the
angular coefficients of lepton pairs produced near the $Z$-boson mass pole at
a hadron collider. Measurements of the $W$-boson angular coefficients have
been published by the CDF [21], CMS [22] and ATLAS [23] collaborations. The
CMS collaboration measured $A_{0}$, $A_{1}$, $A_{2}$ and $A_{4}$ with
$Z\rightarrow{\mu^{+}}{\mu^{-}}$ decays [24], while the ATLAS collaboration
reported measurements of the complete set of coefficients [25].

This Letter reports the first measurement of the
$Z\rightarrow{\mu^{+}}{\mu^{-}}$ angular coefficients in the forward rapidity
region ($2<y^{Z}<5$) by the LHCb experiment, using $Z$-boson candidates
selected in the mass region
$50<M_{\mu\mu}<120\text{\,Ge\kern-1.00006ptV\\!/}c^{2}$, where $M_{\mu\mu}$ is
the invariant mass of the $\mu^{+}\mu^{-}$ pair. The parameters $A_{0}$,
$A_{1}$, $A_{2}$ and $A_{3}$ are determined as a function of the $Z$-boson
$p_{\mathrm{T}}$ and $y^{Z}$, with the candidates selected in the mass region
$75<M_{\mu\mu}<105\text{\,Ge\kern-1.00006ptV\\!/}c^{2}$. Events in the low
mass range, $50<M_{\mu\mu}<75\text{\,Ge\kern-1.00006ptV\\!/}c^{2}$, and high
mass range, $105<M_{\mu\mu}<120\text{\,Ge\kern-1.00006ptV\\!/}c^{2}$, are used
to probe the Boer-Mulders function; these regions are dominated by
contributions from virtual photons and their interference with the $Z$-boson
amplitude, with measurements in multiple mass regions adding sensitivity to
the evolution of the TMD PDF with the hard scale. With the higher-order QCD
effects related to the $Z$-boson $p_{\mathrm{T}}$ being integrated out, the
measurements of the angular coefficients as a function of $y^{Z}$ can be used
to test the resummation calculations in the forward region. Due to the
relatively small data sample containing high-$p_{\mathrm{T}}$
($>50\text{\,Ge\kern-1.00006ptV\\!/}c$) $Z\rightarrow{\mu^{+}}{\mu^{-}}$
events, the coefficients $A_{5}$ to $A_{7}$ are fixed to zero. Since this
study focuses on probing the QCD dynamics of the $Z$-boson production, the
$A_{4}$ coefficient, sensitive to the weak mixing angle [26], is not reported.
Nevertheless, in order to investigate its variation across the kinematic
range, the difference with respect to its mean value, $\Delta A_{4}$, is
measured.

The LHCb detector [27, 28] is a single-arm forward spectrometer covering the
pseudorapidity range $2<\eta<5$, designed for the study of particles
containing $b$ or $c$ quarks. A silicon-strip vertex detector [29] surrounding
the $pp$ interaction region allows $c$ and $b$ hadrons to be identified from
their relatively long flight distance. A tracking system [30] provides a
measurement of momentum, $p$, of charged particles, and two imaging Cherenkov
detectors [31] are able to discriminate between different species of charged
hadrons. Photons, electrons and hadrons are identified by a calorimeter system
consisting of scintillating-pad and preshower detectors, an electromagnetic
and a hadronic calorimeter. Muons are identified by a system composed of
alternating layers of iron and multiwire proportional chambers [32]. The
online event selection is performed by a trigger system [33], which consists
of a hardware stage, based on information from the calorimeter and muon
systems [34, 35], followed by a software stage, which applies a full event
reconstruction incorporating near-real-time alignment and calibration of the
detector [36].

Simulated $pp$ collisions are generated using Pythia8 [37] with a specific
LHCb configuration [38]. The interaction of the generated particles with the
detector, and its response, are implemented using the Geant4 toolkit [39] as
described in Ref. [40]. Various theoretical predictions at the Born-level are
compared with the measured results, including analytic resummed calculations,
ResBos [41] and DYTurbo [42], and a fixed-order calculation with matching
algorithms to veto the double counting of quantum electrodynamic (QED) final-
state radiation (FSR) and parton shower, Powheg-BOX [43, 44, 45, 46].
Predictions from the ResBos [41] generator are produced using the PDF known as
CT14HERA2 [47]. The ResBos calculation combines NLO fixed-order perturbative
calculations at high boson $p_{\mathrm{T}}$, with the soft-gluon Collins-
Soper-Sterman resummation formalism [48, 49, 50] at low boson
$p_{\mathrm{T}}$, with consideration of a nonperturbative contribution from
the parton intrinsic transverse momentum, which is an all-orders summation of
large terms from gluon emission. The DYTurbo [42] program is an NNLO generator
for the calculation of the QCD transverse-momentum resummation of Drell–Yan
cross sections up to next-to-next-to-leading logarithmic accuracy combined
with the fixed-order results. DYTurbo includes the full kinematic dependence
of the lepton pair with the corresponding spin correlations and finite-width
effects. Powheg-BOX is an NLO generator and can be interfaced with Pythia8 for
QCD and EW showering, but without the angular damping factors.

Measurements are performed using $5.1$$\text{\,fb}^{-1}$ of data at a center-
of-mass energy of 13 TeV collected by the LHCb detector during the years
2016–2018. For each $Z\rightarrow{\mu^{+}}{\mu^{-}}$ candidate, at least one
of the muons is required to pass hardware and software single-muon trigger
decision stages. All muon candidates are required to have transverse momentum
$p_{\mathrm{T}}^{\mu}>20\text{\,Ge\kern-1.00006ptV\\!/}c$ and be in the range
$2.0<\eta<4.5$. The relative uncertainty in the momentum of the muon track
must be less than $10\%$. To further suppress background sources, muon
candidates are required to pass an isolation requirement which is
parameterised as $z=p_{\mathrm{T}}^{\mu}/p_{\mathrm{T}}^{\mu-\rm{cone}}>0.85$,
where $p_{\mathrm{T}}^{\mu-\rm{cone}}$ is the sum of the muon $p_{\mathrm{T}}$
and that of the tracks within $\delta R<0.5$, and $\delta R$ is
$\sqrt{\delta\eta^{2}+\delta\Phi^{2}}$. The quantities $\delta\eta$ and
$\delta\Phi$ give the separation between the muon and neighbouring tracks in
pseudorapidity $\eta$ and the laboratory azimuthal angle $\Phi$, respectively.
Candidate $Z$-bosons are composed of two muon candidates with opposite charge
that originate from a common primary $pp$ interaction vertex. In total, 818
074 (745 343) $Z\rightarrow{\mu^{+}}{\mu^{-}}$ candidates are selected in the
mass region $50<M_{\mu\mu}<120\text{\,Ge\kern-1.00006ptV\\!/}c^{2}$
($75<M_{\mu\mu}<105\text{\,Ge\kern-1.00006ptV\\!/}c^{2}$). Background
contributions from heavy-flavour processes and misidentified hadrons are
estimated using data control samples [1], while background sources from
$W^{+}W^{-}$, $W^{\pm}Z$, $ZZ$, $Z\rightarrow\tau^{+}\tau^{-}$ and $t\bar{t}$
processes are estimated from simulation. The total background contribution is
determined to be $0.2\%$.

Detector misalignment effects are studied and suppressed using the
$Z\rightarrow{\mu^{+}}{\mu^{-}}$ data events, where the mass peak position of
the selected $Z$-boson candidates is calibrated in different kinematic and
geometric regions to the world average value [51]. To improve the agreement
between data and simulation, selection efficiencies determined from simulation
are corrected to corresponding values measured in the data. The selection
efficiencies include the muon trigger, muon track reconstruction, muon
isolation and identification. These efficiencies are estimated using
$Z\rightarrow{\mu^{+}}{\mu^{-}}$ data and simulation events, with the tag-and-
probe method [1], as functions of muon $\eta$ and $\Phi$. Additionally,
corrections to the momentum scale and resolution are applied to the
simulation.

The angular coefficients are determined in six intervals of the $Z$-boson
$p_{\mathrm{T}}$ and five intervals of $y^{Z}$, by fitting the two decay
angles $\cos\theta$ and $\phi$ of the selected
$Z\rightarrow{\mu^{+}}{\mu^{-}}$ candidates, using an unbinned maximum-
likelihood method in each interval. The probability density function used in
the fit consists of a signal-only function, obtained from Eq. (1), convoluted
with the detector resolution and acceptance effects. The angular coefficients
($A_{0-4}$) are the only free parameters in the fit, while the background
contributions are effectively subtracted from the data sample by including
background events with negative weights derived from simulation and data
control samples. Simulated Pythia8 events are used to study the background
modeling along with the detector resolution and acceptance effects, with FSR
turned on at the generator level, thereby including the Born/Bare corrections
[52]. This way, the measured $A_{i}$ coefficients are corrected to the Born
level. The normalization weights method is used to avoid computing-intensive
numerical integration of the probability density function in the fit. This
method was introduced and used by the BaBar collaboration [53, 54], and has
been extensively used in LHCb heavy-flavour studies [55]. To avoid potential
bias from the input angular coefficients in the simulation, an iterative
method is used. The measured results are found to be stable after four
iterations.

Several sources of systematic uncertainty are considered. Simulation is used
to determine the detector acceptance effects in the fit process. To estimate
the uncertainty from the finite number of simulated events, the bootstrap
method [56] is used. This uncertainty varies from 0.0016 to 0.0402 in
different kinematic regions, and is the dominant systematic uncertainty.
Another significant uncertainty arises from the selection efficiencies. In the
determination of the uncertainty from the efficiency corrections, two
independent sources are considered: an uncertainty from the size of the
control sample and one from the kinematic dependence of the corrections. For
the second uncertainty, the default two-dimensional (muon $\eta$ and $\phi$)
efficiency corrections are replaced with one-dimensional corrections, and
variations of the results are taken as uncertainties. The fit method is
validated with simulation samples. The angular coefficients of the simulation
are changed to values far from the default (increased by a factor of 1.5, or
set to 0). In the validation, the new angular coefficients are compared with
the values from the fit, and differences between them are taken as
uncertainties. The uncertainty from the muon momentum scaling and smearing are
calculated by varying the corrections by their uncertainties, and the changes
in the measured results are taken as the associated systematic uncertainties.
These are found to be negligible.

The systematic uncertainties associated to the background are estimated by
varying the background contribution by $\pm\sigma$, where $\sigma$ includes
the uncertainties from the theoretical predictions of the cross-sections and
the statistical uncertainties from the simulation. The systematic uncertainty
from the FSR is estimated by comparing the measured results using the
simulation sample weighted to the Powheg prediction with different FSR
algorithms of Photos and Pythia8. Differences from different FSR approaches
are taken as uncertainties. The systematic uncertainty from the PDF is
estimated using 58 sub-PDF sets of CT18NNLO [57], with the prescription
recommended by the PDF sets groups [58]. All systematic uncertainties are
considered as uncorrelated, and the total systematic uncertainty is taken as
their sum in quadrature.

The measured angular coefficients $A_{0-3}$ as well as $\Delta A_{4}$ and the
difference $A_{0}-A_{2}$, are presented as a function of the $Z$-boson
$p_{\mathrm{T}}$ in Fig. 1. The measurements are compared with the predictions
of ResBos, DYTurbo, Powheg-BOX+Pythia8, and Pythia8 with LHCb tuning. The
measurement of $A_{0}$ is in good agreement with DYTurbo, ResBos, and Powheg-
BOX predictions, but disfavors the Pythia8 results in the high
$p_{\mathrm{T}}$ region ($>20\text{\,Ge\kern-1.00006ptV\\!/}c$). However, the
Pythia8 calculations show similar increasing trends as the measurements in the
high $p_{\mathrm{T}}$ region. The measurement of $A_{1}$ disagrees with the
Pythia8 result, but is in good agreement with other calculations in all
$p_{\mathrm{T}}$ regions. Within large statistical uncertainties, the
measurements of $A_{2}$ are mostly in reasonable agreement with predictions,
while for $A_{3}$ there is a noticeable underestimation of most predictions up
to 55$\text{\,Ge\kern-1.00006ptV\\!/}c^{2}$. The measured $\Delta A_{4}$ is in
good agreement with theoretical predictions in all $p_{\mathrm{T}}$ regions.
Finally, for the $A_{0}-A_{2}$ measurement, the LHCb results are compatible
with zero only in the highest $p_{\mathrm{T}}$ interval, but there the
uncertainty is relatively large. Also, most predictions are not compatible
with zero in the high-$p_{\mathrm{T}}$ intervals. This violation of the Lam-
Tung relations measured by the LHCb collaboration is consistent with previous
results from the CMS [24] and ATLAS collaborations [25]. The measured
$A_{0}-A_{2}$ results are significantly smaller than the predictions at low
$p_{\mathrm{T}}$ ($<20\text{\,Ge\kern-1.00006ptV\\!/}c$) and slightly smaller
at high $p_{\mathrm{T}}$ ($>80\text{\,Ge\kern-1.00006ptV\\!/}c$), while larger
than the predictions in other $p_{\mathrm{T}}$ regions. A summary of the full
results, including measurements in bins of $y^{Z}$, is provided in the
Supplemental Material [59]. With the exception of $A_{0}$, the measured
angular coefficients do not vary significantly as a function of $y^{Z}$, when
the measurement is performed for the full $p_{\mathrm{T}}$ range. There is
reasonable agreement between the measurements and ResBos calculations for
$A_{1-3}$ and $\Delta A_{4}$, while for $A_{0}$ there is tension between the
measurements and predictions, especially in the highest $y^{Z}$ region. The
$p$-value between measurements and theoretical predictions is calculated to be
0.06. The differences between $A_{0}$ and the ResBos predictions in the
$y^{Z}$ distribution indicate that there is a $y^{Z}$-dependence in the QCD
resummation or additional higher-order effects. More detailed studies on the
predictions as a function of $y^{Z}$ are necessary.

Figure 1: Comparison of the measured angular coefficients with different
predictions, as a function of the $Z$-boson $p_{\mathrm{T}}$, in the rapidity
region of $Z$-boson $y^{Z}>2$ and
$75<M_{\mu\mu}<105\text{\,Ge\kern-1.00006ptV\\!/}c^{2}$. The total uncertainty
(shown in the figure) is dominated by the statistical component. The
theoretical predictions correspond to the same $Z$-boson $p_{\mathrm{T}}$ bins
as data and the $p_{\mathrm{T}}$ shifts of the theoretical markers in all
plots are for visualization purposes only. DYTurbo and ResBos predictions
include the theoretical uncertainties.

The nonperturbative Boer-Mulders TMD PDF can be probed with the measurement of
$A_{2}$ in the lower $p_{\mathrm{T}}$ region. Measurements of $A_{2}$ in the
low, middle and high $M_{\mu\mu}$ regions are shown in Fig. 2, where the
dimuon $p_{\mathrm{T}}$ region is divided into four intervals from
0–20$\text{\,Ge\kern-1.00006ptV\\!/}c$. Despite the limited sample size with
the finer $p_{\mathrm{T}}$ intervals, several observations can be made. In the
low $M_{\mu\mu}$, the measured $A_{2}$ value in the lowest dimuon
$p_{\mathrm{T}}$ region ($p_{\mathrm{T}}<3\text{\,Ge\kern-1.00006ptV\\!/}c$)
deviates significantly from all predictions. It is unclear if nonperturbative
spin-momentum correlations in the proton, described by the Boer-Mulders
distribution, could lead to such variations as no phenomenological
calculations are available. None of the calculations used in the comparison
include this type of nonperturbative effect. In other $p_{\mathrm{T}}$
regions, reasonable agreement between measurements and predictions is seen.

Figure 2: Comparison of the measured angular coefficient $A_{2}$ with
different predictions, as a function of the $Z$-boson $p_{\mathrm{T}}$, in the
rapidity region of $Z$-boson $y^{Z}>2$ and
$50<M_{\mu\mu}<75\text{\,Ge\kern-1.00006ptV\\!/}c^{2}$ (left),
$50<M_{\mu\mu}<75\text{\,Ge\kern-1.00006ptV\\!/}c^{2}$ (middle) and
$105<M_{\mu\mu}<120\text{\,Ge\kern-1.00006ptV\\!/}c^{2}$ (right). The total
uncertainty (shown in the figure) is dominated by the statistical component.
The horizontal positions of the theoretical predictions within the bins are
adjusted to increase visibility. DYTurbo and ResBos predictions include the
theoretical uncertainties.

In summary, the first measurements of the angular coefficients of Drell-Yan
$\mu^{+}\mu^{-}$ pairs in the forward rapidity region of $pp$ collisions are
presented. These quantities provide more information on the $Z$-boson
production compared to other traditional observables. The measurements, which
are given as a function of the $Z$-boson $p_{\mathrm{T}}$ and $y^{Z}$, in both
the $Z$ peak and lower and higher $M_{\mu\mu}$ regions, are compared with
various predictions. Some tension between the measurements and the theoretical
predictions appears in the lower $M_{\mu\mu}$ and low-$p_{\mathrm{T}}$ region,
and in the $y^{Z}$ dependence (See the Supplemental Material [59] for further
details). More studies of the theoretical models are needed to shed light on
the apparent discrepancies. This analysis provides important and unique inputs
for future phenomenological extractions of spin-momentum correlations in the
proton in terms of the Boer-Mulders TMD PDF and its evolution with the hard
scale.

## Acknowledgements

We express our gratitude to our colleagues in the CERN accelerator departments
for the excellent performance of the LHC. We thank the technical and
administrative staff at the LHCb institutes. We acknowledge support from CERN
and from the national agencies: CAPES, CNPq, FAPERJ and FINEP (Brazil); MOST
and NSFC (China); CNRS/IN2P3 (France); BMBF, DFG and MPG (Germany); INFN
(Italy); NWO (Netherlands); MNiSW and NCN (Poland); MEN/IFA (Romania); MSHE
(Russia); MICINN (Spain); SNSF and SER (Switzerland); NASU (Ukraine); STFC
(United Kingdom); DOE NP and NSF (USA). We acknowledge the computing resources
that are provided by CERN, IN2P3 (France), KIT and DESY (Germany), INFN
(Italy), SURF (Netherlands), PIC (Spain), GridPP (United Kingdom), RRCKI and
Yandex LLC (Russia), CSCS (Switzerland), IFIN-HH (Romania), CBPF (Brazil), PL-
GRID (Poland) and NERSC (USA). We are indebted to the communities behind the
multiple open-source software packages on which we depend. Individual groups
or members have received support from ARC and ARDC (Australia); AvH Foundation
(Germany); EPLANET, Marie Skłodowska-Curie Actions and ERC (European Union);
A*MIDEX, ANR, IPhU and Labex P2IO, and Région Auvergne-Rhône-Alpes (France);
Key Research Program of Frontier Sciences of CAS, CAS PIFI, CAS CCEPP,
Fundamental Research Funds for the Central Universities, and Sci. & Tech.
Program of Guangzhou (China); RFBR, RSF and Yandex LLC (Russia); GVA, XuntaGal
and GENCAT (Spain); the Leverhulme Trust, the Royal Society and UKRI (United
Kingdom).

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## Supplemental material

The number of data candidate events in different $Z$-boson $p_{\mathrm{T}}$
and rapidity intervals are summarized in Table 1. Summaries of measured
angular coefficients $A_{i}$ are shown in Table 2 in intervals of $Z$-boson
$p_{\mathrm{T}}$, and in Table 3 and Fig. 3 in intervals of $Z$-boson
rapidity. Summaries of measured angular coefficients and regularised
uncertainties of $A_{2}$ in the $Z$-boson low-$p_{\mathrm{T}}$ region, with
events in different mass regions, are given in Table 4.

Table 1: The number of selected data candidate events in different $Z$ boson
$p_{\mathrm{T}}$ and rapidity intervals in the mass region
$50<M_{\mu\mu}<120\text{\,Ge\kern-1.00006ptV\\!/}c^{2}$.

$p_{\mathrm{T}}$ interval | Yields |  $y^{Z}$ interval | Yields
---|---|---|---
0-10 | 366305 | 2-2.7 | 203272
10-20 | 214341 | 2.7-3 | 171839
20-35 | 130525 | 3-3.25 | 152349
35-55 | 63285 | 3.25-3.6 | 171900
55-80 | 27445 | 3.6-4.5 | 118714
80-100 | 8120 |  |

Table 2: Summary of measured angular coefficients and regularised
uncertainties for $A_{i}$ and $A_{0}-A_{2}$, in intervals of $Z$-boson
$p_{\mathrm{T}}$, in the region of $Z$-boson $y>2$ and
$75<M_{\mu\mu}<105\text{\,Ge\kern-1.00006ptV\\!/}c^{2}$. The total systematic
uncertainty is shown with the breakdown into its underlying components.
Entries marked with ‘-’ indicate that the uncertainty is below 0.0001.

| $p_{\mathrm{T}}(Z)\in[0,10][\text{\,Ge\kern-1.00006ptV}]$ | $p_{\mathrm{T}}(Z)\in[10,20][\text{\,Ge\kern-1.00006ptV}]$
---|---|---
Coefficient | $A_{0}$ | $A_{1}$ | $A_{2}$ | $A_{3}$ | $\Delta A_{4}$ | $A_{0}-A{2}$ | $A_{0}$ | $A_{1}$ | $A_{2}$ | $A_{3}$ | $\Delta A_{4}$ | $A_{0}-A{2}$
Total | -0.0401 | 0.0180 | 0.0019 | 0.0229 | 0.0219 | -0.0418 | 0.0052 | 0.0417 | 0.0506 | 0.0244 | 0.0280 | -0.0452
Stat | 0.0075 | 0.0046 | 0.0062 | 0.0029 | 0.0054 | 0.0097 | 0.0101 | 0.0061 | 0.0083 | 0.0039 | 0.0073 | 0.0130
Syst | 0.0040 | 0.0028 | 0.0036 | 0.0017 | 0.0030 | 0.0053 | 0.0055 | 0.0037 | 0.0045 | 0.0022 | 0.0042 | 0.0071
MC Stat | 0.0039 | 0.0025 | 0.0033 | 0.0016 | 0.0030 | 0.0051 | 0.0054 | 0.0035 | 0.0044 | 0.0022 | 0.0041 | 0.0070
FSR | - | - | - | - | - | - | - | - | - | - | - | -
Eff | - | - | - | - | - | - | - | - | - | - | - | -
Bkg | - | - | - | - | - | - | - | - | - | - | - | -
Smear | - | - | - | - | - | - | - | - | - | - | - | -
PDF | 0.0003 | 0.0003 | 0.0012 | 0.0002 | 0.0001 | 0.0010 | 0.0003 | 0.0004 | 0.0007 | 0.0002 | 0.0006 | 0.0006
Extraction | 0.0008 | 0.0010 | 0.0004 | - | - | 0.0008 | 0.0007 | 0.0013 | 0.0004 | - | 0.0002 | 0.0008
| $p_{\mathrm{T}}(Z)\in[20,35][\text{\,Ge\kern-1.00006ptV}]$ | $p_{\mathrm{T}}(Z)\in[35,55][\text{\,Ge\kern-1.00006ptV}]$
Coefficient | $A_{0}$ | $A_{1}$ | $A_{2}$ | $A_{3}$ | $\Delta A_{4}$ | $A_{0}-A{2}$ | $A_{0}$ | $A_{1}$ | $A_{2}$ | $A_{3}$ | $\Delta A_{4}$ | $A_{0}-A{2}$
Total | 0.1439 | 0.0995 | 0.1152 | 0.0305 | 0.0371 | 0.0288 | 0.3740 | 0.1334 | 0.2653 | 0.0507 | -0.0021 | 0.1084
Stat | 0.0138 | 0.0083 | 0.0110 | 0.0053 | 0.0096 | 0.0176 | 0.0204 | 0.0134 | 0.0166 | 0.0082 | 0.0140 | 0.0263
Syst | 0.0073 | 0.0044 | 0.0061 | 0.0028 | 0.0054 | 0.0095 | 0.0105 | 0.0078 | 0.0090 | 0.0045 | 0.0081 | 0.0138
MC Stat | 0.0071 | 0.0041 | 0.0060 | 0.0027 | 0.0054 | 0.0094 | 0.0104 | 0.0075 | 0.0086 | 0.0044 | 0.0081 | 0.0134
FSR | - | - | - | - | - | - | 0.0003 | 0.0002 | 0.0002 | - | - | 0.0004
Eff | 0.0001 | - | 0.0001 | - | - | 0.0001 | 0.0001 | - | - | - | - | 0.0002
Bkg | - | - | - | - | - | 0.0001 | - | - | - | - | - | -
Smear | - | - | - | - | - | - | - | - | - | - | - | -
PDF | 0.0009 | 0.0009 | 0.0007 | 0.0002 | 0.0003 | 0.0014 | 0.0006 | 0.0004 | 0.0023 | 0.0009 | 0.0003 | 0.0019
Extraction | 0.0010 | 0.0014 | 0.0006 | 0.0001 | 0.0001 | 0.0012 | 0.0016 | 0.0021 | 0.0017 | 0.0005 | 0.0005 | 0.0023
| $p_{\mathrm{T}}(Z)\in[55,80][\text{\,Ge\kern-1.00006ptV}]$ | $p_{\mathrm{T}}(Z)\in[80,100][\text{\,Ge\kern-1.00006ptV}]$
Coefficient | $A_{0}$ | $A_{1}$ | $A_{2}$ | $A_{3}$ | $\Delta A_{4}$ | $A_{0}-A{2}$ | $A_{0}$ | $A_{1}$ | $A_{2}$ | $A_{3}$ | $\Delta A_{4}$ | $A_{0}-A{2}$
Total | 0.5917 | 0.1639 | 0.3671 | 0.0801 | 0.0123 | 0.2247 | 0.7061 | 0.1826 | 0.6676 | 0.0432 | -0.0971 | 0.0371
Stat | 0.0261 | 0.0237 | 0.0275 | 0.0139 | 0.0200 | 0.0379 | 0.0378 | 0.0442 | 0.0572 | 0.0293 | 0.0311 | 0.0686
Syst | 0.0130 | 0.0132 | 0.0163 | 0.0079 | 0.0110 | 0.0209 | 0.0217 | 0.0241 | 0.0351 | 0.0175 | 0.0167 | 0.0413
MC Stat | 0.0121 | 0.0129 | 0.0160 | 0.0079 | 0.0110 | 0.0201 | 0.0206 | 0.0233 | 0.0345 | 0.0174 | 0.0165 | 0.0402
FSR | 0.0006 | 0.0001 | 0.0004 | - | 0.0001 | 0.0008 | 0.0004 | 0.0008 | 0.0005 | 0.0002 | - | 0.0006
Eff | 0.0006 | 0.0002 | 0.0003 | 0.0001 | 0.0002 | 0.0007 | 0.0004 | 0.0004 | 0.0008 | 0.0005 | 0.0002 | 0.0009
Bkg | 0.0002 | 0.0001 | 0.0002 | - | 0.0001 | 0.0003 | 0.0005 | 0.0002 | 0.0008 | 0.0002 | 0.0002 | 0.0009
Smear | - | - | - | - | - | - | - | - | - | - | - | -
PDF | 0.0010 | 0.0017 | 0.0009 | 0.0006 | 0.0008 | 0.0016 | 0.0011 | 0.0024 | 0.0041 | 0.0009 | 0.0015 | 0.0035
Extraction | 0.0045 | 0.0021 | 0.0029 | 0.0008 | 0.0004 | 0.0054 | 0.0067 | 0.0056 | 0.0054 | 0.0010 | 0.0019 | 0.0086

Table 3: Summary of measured angular coefficients and regularised
uncertainties for $A_{i}$ and $A_{0}-A_{2}$, in intervals of $Z$-boson
rapidity, in the region of $Z$-boson
$p_{\mathrm{T}}<100\text{\,Ge\kern-1.00006ptV\\!/}c$ and
$75<M_{\mu\mu}<105\text{\,Ge\kern-1.00006ptV\\!/}c^{2}$. The total systematic
uncertainty is shown with the breakdown into its underlying components.
Entries marked with ‘-’ indicate that the uncertainty is below 0.0001.

| $y^{Z}\in[2,2.7]$ | $y^{Z}\in[2.7,3]$
---|---|---
Coefficient | $A_{0}$ | $A_{1}$ | $A_{2}$ | $A_{3}$ | $\Delta A_{4}$ | $A_{0}-A{2}$ | $A_{0}$ | $A_{1}$ | $A_{2}$ | $A_{3}$ | $\Delta A_{4}$ | $A_{0}-A{2}$
Total | 0.1124 | 0.0354 | 0.0958 | 0.0357 | -0.0321 | 0.0162 | 0.0543 | 0.0659 | 0.0843 | 0.0388 | 0.0026 | -0.0302
Stat | 0.0180 | 0.0085 | 0.0078 | 0.0039 | 0.0103 | 0.0197 | 0.0119 | 0.0067 | 0.0096 | 0.0046 | 0.0077 | 0.0153
Syst | 0.0102 | 0.0046 | 0.0044 | 0.0022 | 0.0062 | 0.0112 | 0.0068 | 0.0038 | 0.0055 | 0.0024 | 0.0041 | 0.0088
MC Stat | 0.0102 | 0.0044 | 0.0043 | 0.0022 | 0.0062 | 0.0111 | 0.0067 | 0.0035 | 0.0054 | 0.0024 | 0.0041 | 0.0086
FSR | 0.0006 | 0.0013 | 0.0004 | 0.0001 | 0.0001 | 0.0007 | 0.0006 | 0.0013 | 0.0005 | 0.0002 | - | 0.0008
Eff | 0.0005 | 0.0002 | 0.0001 | - | - | 0.0005 | 0.0002 | - | - | - | - | 0.0002
Bkg | 0.0003 | - | 0.0001 | - | - | 0.0003 | 0.0001 | - | - | - | - | 0.0001
Smear | - | - | - | - | - | - | - | - | - | - | - | -
PDF | 0.0001 | 0.0003 | 0.0004 | 0.0001 | 0.0004 | 0.0004 | 0.0007 | 0.0010 | 0.0011 | 0.0003 | 0.0004 | 0.0017
Extraction | 0.0011 | 0.0002 | 0.0004 | - | 0.0004 | 0.0012 | 0.0006 | 0.0001 | 0.0003 | 0.0001 | 0.0003 | 0.0007
| $y^{Z}\in[3,3.25]$ | $y^{Z}\in[3.25,3.6]$
Coefficient | $A_{0}$ | $A_{1}$ | $A_{2}$ | $A_{3}$ | $\Delta A_{4}$ | $A_{0}-A{2}$ | $A_{0}$ | $A_{1}$ | $A_{2}$ | $A_{3}$ | $\Delta A_{4}$ | $A_{0}-A{2}$
Total | 0.0708 | 0.0665 | 0.0778 | 0.0144 | 0.0029 | -0.0070 | 0.0443 | 0.0723 | 0.0583 | 0.0341 | 0.0171 | -0.0139
Stat | 0.0107 | 0.0068 | 0.0110 | 0.0051 | 0.0075 | 0.0154 | 0.0102 | 0.0065 | 0.0102 | 0.0047 | 0.0072 | 0.0145
Syst | 0.0058 | 0.0039 | 0.0064 | 0.0028 | 0.0040 | 0.0087 | 0.0053 | 0.0036 | 0.0059 | 0.0026 | 0.0037 | 0.0078
MC Stat | 0.0057 | 0.0036 | 0.0063 | 0.0027 | 0.0040 | 0.0085 | 0.0052 | 0.0031 | 0.0057 | 0.0026 | 0.0037 | 0.0077
FSR | 0.0009 | 0.0015 | 0.0007 | 0.0003 | - | 0.0012 | 0.0007 | 0.0015 | 0.0006 | 0.0002 | - | 0.0010
Eff | 0.0001 | - | 0.0001 | - | - | 0.0002 | 0.0001 | - | - | - | - | 0.0002
Bkg | - | - | 0.0001 | - | - | 0.0002 | - | - | - | - | - | -
Smear | - | - | - | - | - | - | - | - | - | - | - | -
PDF | 0.0005 | 0.0004 | 0.0006 | 0.0006 | 0.0004 | 0.0009 | 0.0006 | 0.0008 | 0.0008 | 0.0004 | 0.0003 | 0.0005
Extraction | 0.0002 | 0.0001 | 0.0007 | - | 0.0002 | 0.0007 | 0.0004 | 0.0001 | 0.0006 | 0.0001 | 0.0002 | 0.0007

Figure 3: Comparison of the measured angular coefficients with ResBos
predictions as a function of the $y^{Z}$ in the
$75<M_{\mu\mu}<105\text{\,Ge\kern-1.00006ptV\\!/}c^{2}$ mass region. The total
uncertainty (shown in the figure) is dominated by the statistical component.
ResBos predictions include the theoretical uncertainties. Table 4: Summary of
measured angular coefficients and regularised uncertainties for $A_{2}$, in
intervals of $Z$-boson $p_{\mathrm{T}}$, in the region of $Z$-boson $y>2$ and
different mass ranges. The total systematic uncertainty is shown with the
breakdown into its underlying components. Entries marked with ‘-’ indicate
that the uncertainty is below 0.0001.

| $p_{\mathrm{T}}(Z)\in[0,3][\text{\,Ge\kern-1.00006ptV}]$
---|---
| $M_{\mu\mu}\in[55,75]\ \rm{GeV/c^{2}}$ | $M_{\mu\mu}\in[75,105]\ \rm{GeV/c^{2}}$ | $M_{\mu\mu}\in[105,120]\ \rm{GeV/c^{2}}$
Coefficient | $A_{2}$ | $A_{2}$ | $A_{2}$
Total | 0.1931 | 0.0255 | 0.1429
Stat | 0.0399 | 0.0132 | 0.1204
Syst | 0.0235 | 0.0077 | 0.0685
MC Stat | 0.0230 | 0.0075 | 0.0680
FSR | 0.0007 | - | 0.0008
Eff | 0.0012 | 0.0002 | 0.0022
Bkg | 0.0012 | - | 0.0013
Smear | - | - | -
PDF | 0.0028 | 0.0017 | 0.0079
Extraction | 0.0032 | 0.0002 | 0.0017
| $p_{\mathrm{T}}(Z)\in[3,6][\text{\,Ge\kern-1.00006ptV}]$
| $M_{\mu\mu}\in[55,75]\ \rm{GeV/c^{2}}$ | $M_{\mu\mu}\in[75,105]\ \rm{GeV/c^{2}}$ | $M_{\mu\mu}\in[105,120]\ \rm{GeV/c^{2}}$
Coefficient | $A_{2}$ | $A_{2}$ | $A_{2}$
Total | -0.0230 | -0.0122 | -0.0952
Stat | 0.0323 | 0.0102 | 0.0883
Syst | 0.0191 | 0.0062 | 0.0485
MC Stat | 0.0177 | 0.0060 | 0.0483
FSR | 0.0009 | - | 0.0002
Eff | 0.0007 | - | 0.0013
Bkg | 0.0007 | - | 0.0005
Smear | - | - | -
PDF | 0.0062 | 0.0013 | 0.0044
Extraction | 0.0033 | 0.0006 | 0.0028
| $p_{\mathrm{T}}(Z)\in[6,12][\text{\,Ge\kern-1.00006ptV}]$
| $M_{\mu\mu}\in[55,75]\ \rm{GeV/c^{2}}$ | $M_{\mu\mu}\in[75,105]\ \rm{GeV/c^{2}}$ | $M_{\mu\mu}\in[105,120]\ \rm{GeV/c^{2}}$
Coefficient | $A_{2}$ | $A_{2}$ | $A_{2}$
Total | 0.0530 | 0.0335 | 0.0083
Stat | 0.0274 | 0.0083 | 0.0692
Syst | 0.0157 | 0.0048 | 0.0398
MC Stat | 0.0152 | 0.0046 | 0.0390
FSR | 0.0002 | - | 0.0012
Eff | 0.0006 | - | 0.0017
Bkg | 0.0002 | - | 0.0019
Smear | - | - | -
PDF | 0.0019 | 0.0011 | 0.0072
Extraction | 0.0029 | 0.0005 | 0.0019
| $p_{\mathrm{T}}(Z)\in[12,20][\text{\,Ge\kern-1.00006ptV}]$
| $M_{\mu\mu}\in[55,75]\ \rm{GeV/c^{2}}$ | $M_{\mu\mu}\in[75,105]\ \rm{GeV/c^{2}}$ | $M_{\mu\mu}\in[105,120]\ \rm{GeV/c^{2}}$
Coefficient | $A_{2}$ | $A_{2}$ | $A_{2}$
Total | 0.1278 | 0.0583 | 0.1018
Stat | 0.0291 | 0.0097 | 0.0760
Syst | 0.0167 | 0.0052 | 0.0449
MC Stat | 0.0164 | 0.0049 | 0.0422
FSR | 0.0006 | 0.0002 | 0.0013
Eff | 0.0009 | - | 0.0014
Bkg | 0.0007 | 0.0001 | 0.0005
Smear | - | - | -
PDF | 0.0028 | 0.0010 | 0.0151
Extraction | 0.0013 | 0.0012 | 0.0028

LHCb collaboration

R. Aaij32, A.S.W. Abdelmotteleb56, C. Abellán Beteta50, F. Abudinén56, T.
Ackernley60, B. Adeva46, M. Adinolfi54, H. Afsharnia9, C. Agapopoulou13, C.A.
Aidala86, S. Aiola25, Z. Ajaltouni9, S. Akar65, J. Albrecht15, F. Alessio48,
M. Alexander59, A. Alfonso Albero45, Z. Aliouche62, G. Alkhazov38, P. Alvarez
Cartelle55, S. Amato2, J.L. Amey54, Y. Amhis11,48, L. An48, L. Anderlini22, M.
Andersson50, A. Andreianov38, M. Andreotti21, D. Andreou68, D. Ao6, F.
Archilli17, A. Artamonov44, M. Artuso68, E. Aslanides10, M. Atzeni50, B.
Audurier12, S. Bachmann17, M. Bachmayer49, J.J. Back56, P. Baladron
Rodriguez46, V. Balagura12, W. Baldini21, J. Baptista de Souza Leite1, M.
Barbetti22,h, R.J. Barlow62, S. Barsuk11, W. Barter61, M. Bartolini55, F.
Baryshnikov82, J.M. Basels14, G. Bassi29, B. Batsukh4, A. Battig15, A. Bay49,
A. Beck56, M. Becker15, F. Bedeschi29, I. Bediaga1, A. Beiter68, V. Belavin42,
S. Belin46, V. Bellee50, K. Belous44, I. Belov40, I. Belyaev41, G.
Bencivenni23, E. Ben-Haim13, A. Berezhnoy40, R. Bernet50, D. Berninghoff17,
H.C. Bernstein68, C. Bertella62, A. Bertolin28, C. Betancourt50, F. Betti48,
Ia. Bezshyiko50, S. Bhasin54, J. Bhom35, L. Bian73, M.S. Bieker15, N.V.
Biesuz21, S. Bifani53, P. Billoir13, A. Biolchini32, M. Birch61, F.C.R.
Bishop55, A. Bitadze62, A. Bizzeti22,l, M.P. Blago55, T. Blake56, F. Blanc49,
S. Blusk68, D. Bobulska59, J.A. Boelhauve15, O. Boente Garcia46, T.
Boettcher65, A. Boldyrev81, A. Bondar43, N. Bondar38,48, S. Borghi62, M.
Borsato17, J.T. Borsuk35, S.A. Bouchiba49, T.J.V. Bowcock60,48, A. Boyer48, C.
Bozzi21, M.J. Bradley61, S. Braun66, A. Brea Rodriguez46, J. Brodzicka35, A.
Brossa Gonzalo56, D. Brundu27, A. Buonaura50, L. Buonincontri28, A.T. Burke62,
C. Burr48, A. Bursche72, A. Butkevich39, J.S. Butter32, J. Buytaert48, W.
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1Centro Brasileiro de Pesquisas Físicas (CBPF), Rio de Janeiro, Brazil
2Universidade Federal do Rio de Janeiro (UFRJ), Rio de Janeiro, Brazil
3Center for High Energy Physics, Tsinghua University, Beijing, China
4Institute Of High Energy Physics (IHEP), Beijing, China
5School of Physics State Key Laboratory of Nuclear Physics and Technology,
Peking University, Beijing, China
6University of Chinese Academy of Sciences, Beijing, China
7Institute of Particle Physics, Central China Normal University, Wuhan, Hubei,
China
8Univ. Savoie Mont Blanc, CNRS, IN2P3-LAPP, Annecy, France
9Université Clermont Auvergne, CNRS/IN2P3, LPC, Clermont-Ferrand, France
10Aix Marseille Univ, CNRS/IN2P3, CPPM, Marseille, France
11Université Paris-Saclay, CNRS/IN2P3, IJCLab, Orsay, France
12Laboratoire Leprince-Ringuet, CNRS/IN2P3, Ecole Polytechnique, Institut
Polytechnique de Paris, Palaiseau, France
13LPNHE, Sorbonne Université, Paris Diderot Sorbonne Paris Cité, CNRS/IN2P3,
Paris, France
14I. Physikalisches Institut, RWTH Aachen University, Aachen, Germany
15Fakultät Physik, Technische Universität Dortmund, Dortmund, Germany
16Max-Planck-Institut für Kernphysik (MPIK), Heidelberg, Germany
17Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg,
Germany
18School of Physics, University College Dublin, Dublin, Ireland
19INFN Sezione di Bari, Bari, Italy
20INFN Sezione di Bologna, Bologna, Italy
21INFN Sezione di Ferrara, Ferrara, Italy
22INFN Sezione di Firenze, Firenze, Italy
23INFN Laboratori Nazionali di Frascati, Frascati, Italy
24INFN Sezione di Genova, Genova, Italy
25INFN Sezione di Milano, Milano, Italy
26INFN Sezione di Milano-Bicocca, Milano, Italy
27INFN Sezione di Cagliari, Monserrato, Italy
28Universita degli Studi di Padova, Universita e INFN, Padova, Padova, Italy
29INFN Sezione di Pisa, Pisa, Italy
30INFN Sezione di Roma La Sapienza, Roma, Italy
31INFN Sezione di Roma Tor Vergata, Roma, Italy
32Nikhef National Institute for Subatomic Physics, Amsterdam, Netherlands
33Nikhef National Institute for Subatomic Physics and VU University Amsterdam,
Amsterdam, Netherlands
34AGH - University of Science and Technology, Faculty of Physics and Applied
Computer Science, Kraków, Poland
35Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of
Sciences, Kraków, Poland
36National Center for Nuclear Research (NCBJ), Warsaw, Poland
37Horia Hulubei National Institute of Physics and Nuclear Engineering,
Bucharest-Magurele, Romania
38Petersburg Nuclear Physics Institute NRC Kurchatov Institute (PNPI NRC KI),
Gatchina, Russia
39Institute for Nuclear Research of the Russian Academy of Sciences (INR RAS),
Moscow, Russia
40Institute of Nuclear Physics, Moscow State University (SINP MSU), Moscow,
Russia
41Institute of Theoretical and Experimental Physics NRC Kurchatov Institute
(ITEP NRC KI), Moscow, Russia
42Yandex School of Data Analysis, Moscow, Russia
43Budker Institute of Nuclear Physics (SB RAS), Novosibirsk, Russia
44Institute for High Energy Physics NRC Kurchatov Institute (IHEP NRC KI),
Protvino, Russia, Protvino, Russia
45ICCUB, Universitat de Barcelona, Barcelona, Spain
46Instituto Galego de Física de Altas Enerxías (IGFAE), Universidade de
Santiago de Compostela, Santiago de Compostela, Spain
47Instituto de Fisica Corpuscular, Centro Mixto Universidad de Valencia -
CSIC, Valencia, Spain
48European Organization for Nuclear Research (CERN), Geneva, Switzerland
49Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL),
Lausanne, Switzerland
50Physik-Institut, Universität Zürich, Zürich, Switzerland
51NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine
52Institute for Nuclear Research of the National Academy of Sciences (KINR),
Kyiv, Ukraine
53University of Birmingham, Birmingham, United Kingdom
54H.H. Wills Physics Laboratory, University of Bristol, Bristol, United
Kingdom
55Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom
56Department of Physics, University of Warwick, Coventry, United Kingdom
57STFC Rutherford Appleton Laboratory, Didcot, United Kingdom
58School of Physics and Astronomy, University of Edinburgh, Edinburgh, United
Kingdom
59School of Physics and Astronomy, University of Glasgow, Glasgow, United
Kingdom
60Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom
61Imperial College London, London, United Kingdom
62Department of Physics and Astronomy, University of Manchester, Manchester,
United Kingdom
63Department of Physics, University of Oxford, Oxford, United Kingdom
64Massachusetts Institute of Technology, Cambridge, MA, United States
65University of Cincinnati, Cincinnati, OH, United States
66University of Maryland, College Park, MD, United States
67Los Alamos National Laboratory (LANL), Los Alamos, United States
68Syracuse University, Syracuse, NY, United States
69School of Physics and Astronomy, Monash University, Melbourne, Australia,
associated to 56
70Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), Rio de
Janeiro, Brazil, associated to 2
71Physics and Micro Electronic College, Hunan University, Changsha City,
China, associated to 7
72Guangdong Provincial Key Laboratory of Nuclear Science, Guangdong-Hong Kong
Joint Laboratory of Quantum Matter, Institute of Quantum Matter, South China
Normal University, Guangzhou, China, associated to 3
73School of Physics and Technology, Wuhan University, Wuhan, China, associated
to 3
74Departamento de Fisica , Universidad Nacional de Colombia, Bogota, Colombia,
associated to 13
75Universität Bonn - Helmholtz-Institut für Strahlen und Kernphysik, Bonn,
Germany, associated to 17
76Eotvos Lorand University, Budapest, Hungary, associated to 48
77INFN Sezione di Perugia, Perugia, Italy, associated to 21
78Van Swinderen Institute, University of Groningen, Groningen, Netherlands,
associated to 32
79Universiteit Maastricht, Maastricht, Netherlands, associated to 32
80National Research Centre Kurchatov Institute, Moscow, Russia, associated to
41
81National Research University Higher School of Economics, Moscow, Russia,
associated to 42
82National University of Science and Technology “MISIS”, Moscow, Russia,
associated to 41
83National Research Tomsk Polytechnic University, Tomsk, Russia, associated to
41
84DS4DS, La Salle, Universitat Ramon Llull, Barcelona, Spain, associated to 45
85Department of Physics and Astronomy, Uppsala University, Uppsala, Sweden,
associated to 59
86University of Michigan, Ann Arbor, United States, associated to 68

aUniversidade Federal do Triângulo Mineiro (UFTM), Uberaba-MG, Brazil
bHangzhou Institute for Advanced Study, UCAS, Hangzhou, China
cExcellence Cluster ORIGINS, Munich, Germany
dUniversità di Bari, Bari, Italy
eUniversità di Bologna, Bologna, Italy
fUniversità di Cagliari, Cagliari, Italy
gUniversità di Ferrara, Ferrara, Italy
hUniversità di Firenze, Firenze, Italy
iUniversità di Genova, Genova, Italy
jUniversità degli Studi di Milano, Milano, Italy
kUniversità di Milano Bicocca, Milano, Italy
lUniversità di Modena e Reggio Emilia, Modena, Italy
mUniversità di Padova, Padova, Italy
nScuola Normale Superiore, Pisa, Italy
oUniversità di Pisa, Pisa, Italy
pUniversità della Basilicata, Potenza, Italy
qUniversità di Roma Tor Vergata, Roma, Italy
rUniversità di Urbino, Urbino, Italy
sMSU - Iligan Institute of Technology (MSU-IIT), Iligan, Philippines
tP.N. Lebedev Physical Institute, Russian Academy of Science (LPI RAS),
Moscow, Russia
uNovosibirsk State University, Novosibirsk, Russia
†Deceased