EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 CERN-EP-2016-155 LHCb-PAPER-2016-018 29 September 2016

Observation of $J/\psi\phi$ structures consistent with exotic states from
amplitude analysis of $B^{+}\rightarrow J/\psi\phi K^{+}$ decays

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

The first full amplitude analysis of $B^{+}\rightarrow J/\psi\phi K^{+}$ with
$J/\psi\rightarrow\mu^{+}\mu^{-}$, $\phi\rightarrow K^{+}K^{-}$ decays is
performed with a data sample of 3 fb-1 of $pp$ collision data collected at
$\sqrt{s}=7$ and $8$ TeV with the LHCb detector. The data cannot be described
by a model that contains only excited kaon states decaying into $\phi K^{+}$,
and four $J/\psi\phi$ structures are observed, each with significance over $5$
standard deviations. The quantum numbers of these structures are determined
with significance of at least $4$ standard deviations. The lightest has mass
consistent with, but width much larger than, previous measurements of the
claimed $X(4140)$ state.

Published in Physical Review Letters 118, 022003 (2017).

© CERN on behalf of the LHCb collaboration, license CC-BY-4.0.

There has been a great deal of experimental and theoretical interest in
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\phi$ mass structures in
$B^{+}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\phi K^{+}$
decays111Inclusion of charge-conjugate processes is implied. since the CDF
collaboration presented $3.8\sigma$ evidence for a near-threshold $X(4140)$
mass peak, with width $\Gamma=11.7\mathrm{\,Me\kern-1.00006ptV}$ [1].222Units
with $c=1$ are used. Much larger widths are expected for charmonium states at
this mass because of open flavor decay channels [2], which should also make
the kinematically suppressed
$X\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\phi$ decays
undetectable. Therefore, it has been suggested that the $X(4140)$ peak could
be a molecular state [3, 4, 5, 6, 7, 8, 9], a tetraquark state [10, 11, 12,
13, 14], a hybrid state [15, 16] or a rescattering effect [17, 18]. Subsequent
measurements resulted in the confusing experimental situation summarized in
Table 1. Searches for the narrow $X(4140)$ in
$B^{+}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\phi K^{+}$
decays were negative in the Belle [19, 20] (unpublished), LHCb [21] (0.37
fb-1) and BaBar [22] experiments. The $X(4140)$ structure was, however,
observed by the CMS [23] and D0 [24, 25] collaborations.

Table 1: Previous results related to the
$X(4140)\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\phi$ mass
peak. The number of reconstructed
$B^{+}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\phi K^{+}$
decays ($N_{B}$) is given if applicable. Significances ($\sigma$) correspond
to numbers of standard deviations. Upper limits on the $X(4140)$ fraction of
the total $B^{+}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\phi
K^{+}$ rate are at 90% confidence level. The statistical and systematic errors
are added in quadrature and then used in the weights to calculate the
averages, excluding unpublished results (shown in italics).

Exp. $N_{B}$ Mass [$\mathrm{\,Me\kern-1.00006ptV}$ ] Width
[$\mathrm{\,Me\kern-1.00006ptV}$ ] $\sigma$ Frac. [%] CDF [1] $58$
$4143.0\\!\pm\\!2.9\\!\pm\\!1.2$
$11.7\,^{+\phantom{0}8.3}_{-\phantom{0}5.0}\\!\pm\\!3.7$ $3.8$ Belle [19]
$\mathit{325}$ $\mathit{4143.0}$ fixed $\mathit{11.7}$ fixed $\mathit{1.9}$
CDF [26] $\mathit{115}$ $\mathit{\\!4143.4{{}^{+2.9}_{-3.0}}\\!\pm\\!\\!0.6}$
$\mathit{15.3\\!^{+10.4}_{-\phantom{0}6.1}\\!\\!\pm\\!\\!2.5}$ $\mathit{5.0}$
$\mathit{15\\!\\!\pm\\!\\!4\\!\\!\pm\\!\\!2}$ LHCb [21] $346$ $4143.4$ fixed
$15.3$ fixed $1.4$ $<\phantom{0}7$ CMS [23] $\\!2480$
$4148.0\\!\pm\\!2.4\\!\pm\\!6.3$
$28\phantom{.0}\,^{+15\phantom{.0}}_{-11\phantom{.0}}\pm 19$ $5.0$
$10\\!\pm\\!3$ D0 [25] $215$ $4159.0\\!\pm\\!4.3\\!\pm\\!6.6$
$19.9\\!\pm\\!12.6\,^{+1.0}_{-8.0}$ $3.1$ $21\\!\pm\\!8\\!\pm\\!4$ BaBar [22]
$189$ $4143.4$ fixed $15.3$ fixed $1.6$ $<13$ D0 [24] –
$4152.5\\!\pm\\!1.7\,^{+6.2}_{-5.4}$ $16.3\\!\pm\\!5.6\\!\pm\\!\\!11.4$
4.7–5.7 – Average $4147.1\\!\pm\\!2.4$ $15.7\\!\pm\\!6.3$

In an unpublished update to their analysis [26], the CDF collaboration
presented $3.1\sigma$ evidence for a second relatively narrow
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\phi$ mass peak near
$4274\mathrm{\,Me\kern-1.00006ptV}$. A second peak was also observed by the
CMS collaboration at a mass which is higher by $3.2$ standard deviations, but
its statistical significance was not determined [23]. The Belle collaboration
obtained $3.2\sigma$ evidence for a narrow
($\Gamma=13\,^{+18}_{-\phantom{0}9}\pm 4\mathrm{\,Me\kern-1.00006ptV}$)
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\phi$ peak at
$4350.6\,^{+4.6}_{-5.1}\pm 0.7\mathrm{\,Me\kern-1.00006ptV}$ in two-photon
collisions, which implies $J^{PC}=0^{++}$ or $2^{++}$, and found no signal for
$X(4140)$ [27].

The $X(4140)$ and $X(4274)$ states are the only known candidates for four-
quark systems that contain neither of the light $u$ and $d$ quarks. Their
confirmation, and determination of their quantum numbers, would allow new
insights into the binding mechanisms present in multi-quark systems, and help
improve understanding of QCD in the non-perturbative regime.

The data sample used in this work corresponds to an integrated luminosity of
$3$ fb-1 collected with the LHCb detector in $pp$ collisions at center-of-mass
energies 7 and 8 TeV. The LHCb detector is a single-arm forward spectrometer
covering the pseudorapidity range $2<\eta<5$, described in detail in Refs.
[28, 29]. Thanks to the larger signal yield, corresponding to $4289\pm 151$
reconstructed $B^{+}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\phi K^{+}$ decays, the roughly uniform efficiency and the relatively
low background across the entire ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\phi$ mass range, this data sample offers the best sensitivity to date,
not only to probe for the previously claimed
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\phi$ structures, but also to
inspect the high mass region for the first time. All previous analyses were
based on naive ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\phi$ mass
($m_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\phi}$) fits, with
Breit–Wigner (BW) signal peaks on top of incoherent background described by
ad-hoc functional shapes (e.g. the three-body phase space distribution in
$B^{+}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\phi K^{+}$
decays). While the $m_{\phi K}$ distribution has been observed to be smooth,
several resonant contributions from kaon excitations (denoted generically as
$K^{*}$) are expected. It is important to prove that any
$m_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\phi}$ peaks are not merely
reflections of $K^{*}$ states. If genuine
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\phi$ states are present, it is
crucial to determine their quantum numbers to aid their theoretical
interpretation. Both of these tasks call for a proper amplitude analysis of
$B^{+}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\phi K^{+}$
decays, in which the observed $m_{\phi K}$ and
$m_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\phi}$ masses are analyzed
simultaneously with the distributions of decay angles, without which the
resolution of different resonant contributions is difficult, if not
impossible.

In this Letter, results with a focus on
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\phi$ mass structures are
presented from the first amplitude analysis of
$B^{+}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\phi K^{+}$
decays. A detailed description of the analysis with more extensive discussion
of the results on kaon spectroscopy can be found in Ref. [30]. The data
selection is similar to that described in Ref. [21], with modifications [30]
that increase the $B^{+}$ signal yield per unit luminosity by about 50% at the
expense of larger background. A $K^{+}K^{-}$ pair with mass within $\pm
15\mathrm{\,Me\kern-1.00006ptV}$ of the known $\phi$ mass [31] is accepted as
a $\phi$ candidate. To avoid reconstruction ambiguities, we require that there
is exactly one $\phi$ candidate per ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}K^{+}K^{-}K^{+}$ combination, which reduces the $B^{+}$ yield by
$3.2\%$. A fit to the mass distribution of
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\phi K^{+}$ candidates yields
$4289\pm 151$ $B^{+}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\phi K^{+}$ events, with a background fraction ($\beta$) of $23\%$ in
the region used in the amplitude analysis (twice the $B^{+}$ mass resolution
on each side of its peak). The non-$\phi$
$B^{+}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}K^{+}K^{-}K^{+}$ background is small ($2.1\%$) and neglected in the
amplitude model, but considered as a source of systematic uncertainty.

We first try to describe the data with kaon excitations alone. We construct an
amplitude model ($\mathcal{M}$) using the helicity formalism [32, 33, 34] in
which the six independent variables fully describing the
$B^{+}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}K^{*+}$,
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\rightarrow\mu^{+}\mu^{-}$,
$K^{*+}\rightarrow\phi K^{+}$, $\phi\rightarrow K^{+}K^{-}$ decay chain are
$m_{\phi K}$, $\theta_{{{K}^{*}}}$,
$\theta_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}}$, $\theta_{\phi}$,
$\Delta{\phi}_{{{K}^{*}},{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}}$ and
$\Delta{\phi}_{{{K}^{*}},\phi}$, where $\theta$ denotes helicity angles, and
$\Delta\phi$ angles between decay planes. The set of angles is denoted by
$\Omega$. The matrix element for a single $K^{*+}$ resonance ($j$) with mass
${M_{0}}^{j}$ and width ${\Gamma_{0}}^{j}$ is assumed to factorize,
$\mathcal{M}_{K^{*}}\,^{j}{}_{\Delta\lambda_{\mu}}=R(m_{\phi
K}|{M_{0}}^{j},{\Gamma_{0}}^{j})\,H_{\Delta\lambda_{\mu}}(\Omega|\\{A^{j}\\})$,
where $R(m_{\phi K}|{M_{0}}^{j},{\Gamma_{0}}^{j})$ is a complex BW function
and $H_{\Delta\lambda_{\mu}}(\Omega|\\{A^{j}\\})$ describes the angular
correlations, with $\\{A^{j}\\}$ being a set of complex helicity couplings
which are determined from the data (1–4 independent couplings depending on
$J^{P}$), where $\Delta\lambda_{\mu}=\lambda_{\mu^{+}}-\lambda_{\mu^{-}}$, and
$\lambda$ denotes the helicity. The total matrix element sums coherently over
all possible ${{K}^{*}}$ resonances:
$\left|\mathcal{M}\right|^{2}=\sum_{\Delta\lambda_{\mu}=\pm
1}\left|\sum_{j}\mathcal{M}^{K^{*}\,j}_{\Delta\lambda_{\mu}}\right|^{2}$.
Detailed definitions of $R(m_{\phi K}|{M_{0}}^{j},{\Gamma_{0}}^{j})$ and of
$H_{\Delta\lambda_{\mu}}(\Omega|\\{A^{j}\\})$ are given in Ref. [30]. The free
parameters are determined from the data by minimizing the unbinned six-
dimensional (6D) negative log-likelihood ($-\\!\ln{\cal L}$), where the
probability density function (PDF) is proportional to
$(1-\beta)\left|\mathcal{M}\right|^{2}$, multiplied by the detection
efficiency, plus a background term. The signal PDF is normalized by summing
over $B^{+}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\phi
K^{+}$ events generated [35, 36] uniformly in decay phase space, followed by
detector simulation [37] and data selection. This procedure accounts for the
6D efficiency in the reconstruction of the signal decays [30]. We use $B^{+}$
mass sidebands to obtain a 6D parameterization of the background PDF [30].

Figure 1: Distribution of $m_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\phi}$ for the data and the fit results with a model containing only
$K^{*+}\rightarrow\phi K^{+}$ contributions.

Past experiments on $K^{*}$ states decaying to $\phi K$ [38, 39, 40] had
limited precision, gave somewhat inconsistent results, and provided evidence
for only a few of the states expected from the quark model in the
$1513$–$2182\mathrm{\,Me\kern-1.00006ptV}$ range probed in our data. We have
used the predictions of the relativistic potential model by Godfrey–Isgur [41]
(horizontal black lines in Fig. 2) as a guide to the quantum numbers of the
$K^{*+}$ states to be included in the amplitude model. The masses and widths
of all states are left free; thus our fits do not depend on details of the
predictions, nor on previous measurements. We also include a constant
nonresonant amplitude with $J^{P}=1^{+}$, since such $\phi K^{+}$
contributions can be produced, and can decay, in S-wave. Allowing the
magnitude of the nonresonant amplitude to vary with $m_{\phi K}$ does not
improve fit qualities. While it is possible to describe the $m_{\phi K}$ and
$m_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}K}$ distributions well with
${{K}^{*}}$ contributions alone, the fit projections onto
$m_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\phi}$ do not provide an
acceptable description of the data. For illustration we show in Fig. 1 the
projection of a fit with the following composition: a nonresonant term plus
candidates for two $2{\rm P}_{1}$, two $1{\rm D}_{2}$, and one of each of
$1{}^{3}{\rm F}_{3}$, $1{}^{3}{\rm D}_{1}$, $3{}^{3}{\rm S}_{1}$, $3{}^{1}{\rm
S}_{0}$, $2{}^{3}{\rm P}_{2}$, $1{}^{3}{\rm F}_{2}$, $1{}^{3}{\rm D}_{3}$ and
$1{}^{3}{\rm F}_{4}$ states, labeled here with their intrinsic quantum numbers
$n{}^{2S+1}L_{J}$ ($n$ is the radial quantum number, $S$ the total spin of the
valence quarks, $L$ the orbital angular momentum between quarks, and $J$ the
total angular momentum of the bound state). The fit contains 104 free
parameters. The $\chi^{2}$ value (144.9/68 bins) between the fit projection
and the observed $m_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\phi}$
distribution corresponds to a p-value below $10^{-7}$. Adding even more
resonances does not change the conclusion that non-${{K}^{*}}$ contributions
are needed.

The matrix element for $B^{+}\rightarrow XK^{+}$,
$X\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\phi$ decays can be
parameterized using $m_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\phi}$
and the $\theta_{X}$, $\theta_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}}^{X}$, $\theta_{\phi}^{X}$,
$\Delta\phi_{X,{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}}$,
$\Delta\phi_{X,\phi}$ angles. The angles
$\theta_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}}^{X}$ and
$\theta_{\phi}^{X}$ are not the same as in the ${{K}^{*}}$ decay chain since
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}$ and $\phi$ are produced in
decays of different particles. For the same reason, the muon helicity states
are different between the two decay chains, and an azimuthal rotation by an
angle $\alpha^{X}$ is needed to align them [42, 30]. The parameters needed to
characterize the $X$ decay chain, including $\alpha^{X}$, do not constitute
new degrees of freedom since they can all be derived from $m_{\phi K}$ and
$\Omega$. We also consider possible contributions from $B^{+}\rightarrow
Z^{+}\phi$, $Z^{+}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}K^{+}$ decays, which can be parameterized in a similar way [30]. The
total matrix element is obtained by summing all possible $K^{*+}$ ($j$), $X$
($k$) and $Z^{+}$ ($n$) contributions:
$\left|\mathcal{M}\right|^{2}=\sum_{\Delta\lambda_{\mu}=\pm
1}\left|\sum_{j}\mathcal{M}^{K^{*}\,j}_{\Delta\lambda_{\mu}}+\right.$
$e^{i\,\Delta\lambda_{\mu}\,\alpha^{X}}\sum_{k}\mathcal{M}^{X\,k}_{\Delta\lambda_{\mu}}+$
$\left.e^{i\,\Delta\lambda_{\mu}\,\alpha^{Z}}\sum_{n}\mathcal{M}^{Z\,n}_{\Delta\lambda_{\mu}}\right|^{2}$.

Figure 2: Masses of kaon excitations obtained in the default amplitude fit to
the LHCb data, shown as red points with statistical (thicker bars) and total
(thinner bars) errors, compared with the predictions by Godfrey–Isgur [41]
(horizontal black lines) for the most likely spectroscopic interpretations
labeled with $n{}^{2S+1}L_{J}$ (see the text). Experimentally established
states are also shown with narrower solid blue boxes extending to $\pm
1\sigma$ in mass and labeled with their PDG names [31]. Unconfirmed states are
shown with dashed green boxes. The long horizontal red lines indicate the
$\phi K$ mass range probed in
$B^{+}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\phi K^{+}$
decays. Decays of the $2{}^{3}{\rm P}_{0}$ state ($J^{P}=0^{+}$) to $\phi
K^{+}$ are forbidden.

We have explored adding $X$ and $Z^{+}$ contributions of various quantum
numbers to the fit models. Only $X$ contributions lead to significant
improvements in the description of the data. The default resonance model is
summarized in Table 2. It contains seven $K^{*+}$ states (Fig. 2), four $X$
states, and $\phi K^{+}$ and ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\phi$ nonresonant components. There are 98 free parameters in this fit.
Additional $K^{*+}$, $X$ or $Z^{+}$ states are not significant. Projections of
the fit onto the mass variables are displayed in Fig. 3. The $\chi^{2}$ value
(71.5/68 bins) between the fit projection and the observed
$m_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\phi}$ distribution
corresponds to a p-value of 22%, where the effective number of degrees of
freedom has been obtained with simulations of pseudoexperiments generated from
the default amplitude model. Projections onto angular variables, and onto
masses in different regions of the Dalitz plot, can be found in Ref. [30].

The systematic uncertainties [30] are obtained from the sum in quadrature of
the changes observed in the fit results when: the $K^{*+}$ and $X(4140)$
models are varied (the dominant errors); the BW amplitude parameterization is
modified; only the left or right $B^{+}$ mass peak sidebands are used for the
background parameterization; the $\phi$ mass selection is changed; the signal
and background shapes are varied in the fit to
$m_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\phi K}$ which determines
$\beta$; the weights assigned to simulated events, in order to improve
agreement with the data on $B^{+}$ production characteristics and detector
efficiency, are removed.

The significance of each (non)resonant contribution is calculated from the
change in log-likelihood between fits with and without the contribution
included. The distribution of $\Delta(\\!-\\!2\ln{\cal L})$ between the two
hypothesis should follow a $\chi^{2}$ distribution with number of degrees of
freedom equal to the number of free parameters in its parameterization
(doubled when $M_{0}$ and $\Gamma_{0}$ are free parameters). The validity of
this assumption has been verified using simulated pseudoexperiments. The
significances of the $X$ contributions are given after accounting for
systematic uncertainties.

Table 2: Results for significances, masses, widths and fit fractions (FF) of
the components included in the default amplitude model. The first (second)
errors are statistical (systematic). Possible interpretations in terms of kaon
excitation levels are given for the resonant $\phi K^{+}$ fit components.
Comparisons with the previously experimentally observed kaon excitations [31]
and $X\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\phi$
structures are also given.

Contri- Sign. Fit results bution or Ref. $M_{0}$
[$\mathrm{\,Me\kern-1.00006ptV}$ ] $\Gamma_{0}$
[$\mathrm{\,Me\kern-1.00006ptV}$ ] FF % All $K(1^{+})$ $8.0\sigma$
$42\\!\pm\\!\phantom{8}8\,^{+\phantom{8}5}_{-\phantom{8}9}$ ${\rm NR}_{\phi
K}\phantom{2{}^{1}{\rm P}_{1}}$ $16\\!\pm\\!13\,^{+35}_{-\phantom{8}6}$
$K(1^{+})\,2{}^{1}{\rm P}_{1}$ $7.6\sigma$ $1793\\!\pm\\!59\,^{+153}_{-101}$
$365\\!\pm\\!157\,^{+138}_{-215}$ $12\\!\pm\\!10\,^{+17}_{-\phantom{8}6}$
$K_{1}(1650)$ [31] $1650\\!\pm\\!50$ $150\\!\pm\\!\phantom{2}50$
$K^{{}^{\prime}}(1^{+})\,2{}^{3}{\rm P}_{1}$ $1.9\sigma$
$1968\\!\pm\\!65\,^{+\phantom{8}70}_{-172}$ $396\\!\pm\\!170\,^{+174}_{-178}$
$23\\!\pm\\!20\,^{+31}_{-29}$ All $K(2^{-})$ $5.6\sigma$
$11\\!\pm\\!\phantom{8}3\,^{+\phantom{8}2}_{-\phantom{8}5}$
$K(2^{-})\,1{}^{1}{\rm D}_{2}$ $5.0\sigma$
$1777\\!\pm\\!35\,^{+122}_{-\phantom{8}77}$ $217\\!\pm\\!116\,^{+221}_{-154}$
${\small K_{2}(1770)}$ [31] $1773\\!\pm\\!\phantom{2}8$
$188\\!\pm\\!\phantom{2}14$ $K^{{}^{\prime}}(2^{-})\,1{}^{3}{\rm D}_{2}$
$3.0\sigma$ $1853\\!\pm\\!27\,^{+\phantom{2}18}_{-\phantom{2}35}$
$167\\!\pm\\!\phantom{2}58\,^{+\phantom{2}82}_{-\phantom{2}72}$ ${\small
K_{2}(1820)}$ [31] $1816\\!\pm\\!13$ $276\\!\pm\\!\phantom{2}35$
$K^{*}(1^{-})\,1{}^{3}{\rm D}_{1}$ $8.5\sigma$
$1722\\!\pm\\!20\,^{+\phantom{8}33}_{-109}$
$354\\!\pm\\!\phantom{2}75\,^{+140}_{-181}$ $6.7\\!\pm\\!1.9\,^{+3.2}_{-3.9}$
${\small K^{*}(1680)}$ [31] $1717\\!\pm\\!27$ $322\\!\pm\\!110$
$K^{*}(2^{+})\,2{}^{3}{\rm P}_{2}$ $5.4\sigma$
$2073\\!\pm\\!94\,^{+245}_{-240}$
$678\\!\pm\\!311\,^{+1153}_{-\phantom{2}559}$
$2.9\\!\pm\\!0.8\,^{+1.7}_{-0.7}$ ${K^{*}_{2}(1980)}$ [31] $1973\\!\pm\\!26$
$373\\!\pm\\!\phantom{2}69$ $K(0^{-})\,3{}^{1}{\rm S}_{0}$ $3.5\sigma$
$1874\\!\pm\\!43\,^{+\phantom{2}59}_{-115}$
$168\\!\pm\\!\phantom{2}90\,^{+280}_{-104}$ $2.6\\!\pm\\!1.1\,^{+2.3}_{-1.8}$
${K(1830)}$ [31] $\sim 1830$ $\sim 250\phantom{\pm 888}$ All $X(1^{+})$
$16\\!\pm\\!3\phantom{2}\phantom{2}\,^{+\phantom{2}6}_{-\phantom{2}2}$
$X(4140)$ $8.4\sigma$ $4146.5\\!\pm\\!4.5\,^{+4.6}_{-2.8}$
$83\\!\pm\\!21\,^{+21}_{-14}$ $13.0\\!\pm\\!3.2\,^{+4.7}_{-2.0}$ ave.
Table 1 $4147.1\\!\pm\\!2.4$ $15.7\\!\pm\\!6.3$ $X(4274)$ $6.0\sigma$
$4273.3\\!\pm\\!8.3\,^{+17.2}_{-\phantom{2}3.6}$
$56\\!\pm\\!11\,^{+\phantom{0}8}_{-11}$ $7.1\\!\pm\\!2.5\,^{+3.5}_{-2.4}$ CDF
[26] $4274.4\,^{+8.4}_{-6.7}\pm 1.9$ $32\,^{+22}_{-15}\pm 8$ CMS [23]
$4313.8\\!\pm\\!5.3\\!\pm\\!7.3$ $38\,^{+30}_{-15}\pm 16$ All $X(0^{+})$
$28\\!\pm\\!\phantom{2}5\\!\pm\\!\phantom{2}7$ ${\rm
NR}_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\phi}$ $6.4\sigma$
$46\\!\pm\\!11\phantom{2}\,^{+11}_{-21}$ $X(4500)$ $6.1\sigma$
$4506\\!\pm\\!11\,^{+12}_{-15}$ $\phantom{8}92\\!\pm\\!21\,^{+21}_{-20}$
$6.6\\!\pm\\!2.4\,^{+3.5}_{-2.3}$ $X(4700)$ $5.6\sigma$
$4704\\!\pm\\!10\,^{+14}_{-24}$ $120\\!\pm\\!31\,^{+42}_{-33}$
$12\\!\pm\\!\phantom{2}5\phantom{2}\,^{+\phantom{2}9}_{-\phantom{2}5}$

The $K^{*+}$ composition of our amplitude model is in good agreement with the
expectations for the $\bar{s}u$ states [41], and also in agreement with
previous experimental results on $K^{*}$ states in this mass range [31] as
illustrated in Fig. 2 and in Table 2. Effects of adding extra insignificant
$K^{*+}$ resonances of various $J^{P}$, as well as of removing the least
significant $K^{*+}$ contributions, are included among the systematic
variations of the fit amplitude. More detailed discussion of our results for
kaon excitations can be found in Ref. [30].

A near-threshold ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\phi$
structure in our data is the most significant ($8.4\sigma$) exotic
contribution to our model. We determine its quantum numbers to be
$J^{PC}=1^{++}$ at $5.7\sigma$ significance from the change in $-\\!2\ln{\cal
L}$ relative to other $J^{P}$ assignments [43] including systematic
variations. When fitted as a resonance, its mass ($4146.5\pm
4.5\,^{+4.6}_{-2.8}\mathrm{\,Me\kern-1.00006ptV}$) is in excellent agreement
with previous measurements for the $X(4140)$ state, although the width ($83\pm
21\,^{+21}_{-14}\mathrm{\,Me\kern-1.00006ptV}$) is substantially larger. The
upper limit previously set for production of a narrow
($\Gamma=15.3\mathrm{\,Me\kern-1.00006ptV}$) $X(4140)$ state based on a small
subset of our present data [21] does not apply to such a broad resonance, thus
the present results are consistent with our previous analysis. The statistical
power of the present data sample is not sufficient to study its phase motion
[44]. A model-dependent study discussed in Ref. [30] suggests that the
$X(4140)$ structure may be affected by the nearby $D_{s}^{\pm}D_{s}^{*\mp}$
coupled-channel threshold. However, larger data samples will be required to
resolve this issue.

We establish the existence of the $X(4274)$ structure with statistical
significance of $6.0\sigma$, at a mass of $4273.3\pm
8.3\,^{+17.2}_{-\phantom{8}3.6}\mathrm{\,Me\kern-1.00006ptV}$ and a width of
$56.2\pm 10.9\,^{+\phantom{8}8.4}_{-11.1}\mathrm{\,Me\kern-1.00006ptV}$. Its
quantum numbers are determined to be $J^{PC}=1^{++}$ at $5.8\sigma$
significance. Due to interference effects, the data peak above the pole mass,
underlining the importance of proper amplitude analysis.

Figure 3: Distributions of (top left) $\phi K^{+}$, (top right)
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}K^{+}$ and (bottom)
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\phi$ invariant masses for the
$B^{+}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\phi K^{+}$
candidates (black data points) compared with the results of the default
amplitude fit containing eight $K^{*+}\rightarrow\phi K^{+}$ and five
$X\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\phi$
contributions. The total fit is given by the red points with error bars.
Individual fit components are also shown.

The high $J/\psi\phi$ mass region also shows structures that cannot be
described in a model containing only $K^{*+}$ states. These features are best
described in our model by two $J^{PC}=0^{++}$ resonances, $X(4500)$
($6.1\sigma$) and $X(4700)$ ($5.6\sigma$), with parameters given in Table 2.
The resonances interfere with a nonresonant $J^{PC}=0^{++}$
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\phi$ contribution that is also
significant ($6.4\sigma$). The significances of the quantum number
determinations for the high mass states are $4.0\sigma$ and $4.5\sigma$,
respectively.

In summary, we have performed the first amplitude analysis of
$B^{+}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\phi K^{+}$
decays. We have obtained a good description of the data in the 6D phase space
composed of invariant masses and decay angles. The $K^{*+}$ amplitude model
extracted from our data is consistent with expectations from the quark model
and from the previous experimental results on such resonances. We determine
the $J^{PC}$ quantum numbers of the $X(4140)$ structure to be $1^{++}$. This
has a large impact on its possible interpretations, in particular ruling out
the $0^{++}$ or $2^{++}$ $D_{s}^{*+}D_{s}^{*-}$ molecular models [3, 4, 5, 6,
7, 8]. The $X(4140)$ width is substantially larger than previously determined.
The below-${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\phi$-threshold
$D_{s}^{\pm}D_{s}^{*\mp}$ cusp [18, 9] may have an impact on the $X(4140)$
structure, but more data will be required to address this issue, as discussed
in more detail in the companion article [30]. The existence of the $X(4274)$
structure is established and its quantum numbers are determined to be
$1^{++}$. Molecular bound-states or cusps cannot account for these $J^{PC}$
values. A hybrid charmonium state would have $1^{-+}$ [15, 16]. Some
tetraquark models expected $0^{-+}$, $1^{-+}$ [11] or $0^{++}$, $2^{++}$ [12]
state(s) in this mass range. A tetraquark model implemented by Stancu [10] not
only correctly assigned $1^{++}$ to $X(4140)$, but also predicted a second
$1^{++}$ state at mass not much higher than the $X(4274)$ mass. Calculations
by Anisovich et al. [13] based on the diquark tetraquark model predicted only
one $1^{++}$ state at a somewhat higher mass. Lebed–Polosa [14] predicted the
$X(4140)$ peak to be a $1^{++}$ tetraquark, although they expected the
$X(4274)$ peak to be a $0^{-+}$ state in the same model. A lattice QCD
calculation with diquark operators found no evidence for a $1^{++}$ tetraquark
below $4.2\mathrm{\,Ge\kern-1.00006ptV}$ [45].

The high ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\phi$ mass region is
investigated for the first time with good sensitivity and shows very
significant structures, which can be described as two $0^{++}$ resonances:
$X(4500)$ and $X(4700)$. The work of Wang et al. [46] predicted a virtual
$0^{++}$ $D_{s}^{*+}D_{s}^{*-}$ state at $4.48\pm
0.17\mathrm{\,Ge\kern-1.00006ptV}$. None of the observed
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\phi$ states is consistent with
the state seen in two-photon collisions by the Belle collaboration [27].

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); NSFC
(China); CNRS/IN2P3 (France); BMBF, DFG and MPG (Germany); INFN (Italy); FOM
and NWO (The Netherlands); MNiSW and NCN (Poland); MEN/IFA (Romania); MinES
and FASO (Russia); MinECo (Spain); SNSF and SER (Switzerland); NASU (Ukraine);
STFC (United Kingdom); NSF (USA). We acknowledge the computing resources that
are provided by CERN, IN2P3 (France), KIT and DESY (Germany), INFN (Italy),
SURF (The Netherlands), PIC (Spain), GridPP (United Kingdom), RRCKI and Yandex
LLC (Russia), CSCS (Switzerland), IFIN-HH (Romania), CBPF (Brazil), PL-GRID
(Poland) and OSC (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 AvH Foundation (Germany), EPLANET, Marie
Skłodowska-Curie Actions and ERC (European Union), Conseil Général de Haute-
Savoie, Labex ENIGMASS and OCEVU, Région Auvergne (France), RFBR and Yandex
LLC (Russia), GVA, XuntaGal and GENCAT (Spain), Herchel Smith Fund, The Royal
Society, Royal Commission for the Exhibition of 1851 and the Leverhulme Trust
(United Kingdom).

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LHCb collaboration

R. Aaij39, B. Adeva38, M. Adinolfi47, Z. Ajaltouni5, S. Akar6, J. Albrecht10,
F. Alessio39, M. Alexander52, S. Ali42, G. Alkhazov31, P. Alvarez Cartelle54,
A.A. Alves Jr58, S. Amato2, S. Amerio23, Y. Amhis7, L. An40, L. Anderlini18,
G. Andreassi40, M. Andreotti17,g, J.E. Andrews59, R.B. Appleby55, O. Aquines
Gutierrez11, F. Archilli1, P. d’Argent12, J. Arnau Romeu6, A. Artamonov36, M.
Artuso60, E. Aslanides6, G. Auriemma26, M. Baalouch5, I. Babuschkin55, S.
Bachmann12, J.J. Back49, A. Badalov37, C. Baesso61, W. Baldini17, R.J.
Barlow55, C. Barschel39, S. Barsuk7, W. Barter39, V. Batozskaya29, B.
Batsukh60, V. Battista40, A. Bay40, L. Beaucourt4, J. Beddow52, F. Bedeschi24,
I. Bediaga1, L.J. Bel42, V. Bellee40, N. Belloli21,i, K. Belous36, I.
Belyaev32, E. Ben-Haim8, G. Bencivenni19, S. Benson39, J. Benton47, A.
Berezhnoy33, R. Bernet41, A. Bertolin23, F. Betti15, M.-O. Bettler39, M. van
Beuzekom42, I. Bezshyiko41, S. Bifani46, P. Billoir8, T. Bird55, A.
Birnkraut10, A. Bitadze55, A. Bizzeti18,u, T. Blake49, F. Blanc40, J. Blouw11,
S. Blusk60, V. Bocci26, T. Boettcher57, A. Bondar35, N. Bondar31,39, W.
Bonivento16, A. Borgheresi21,i, S. Borghi55, M. Borisyak67, M. Borsato38, F.
Bossu7, M. Boubdir9, T.J.V. Bowcock53, E. Bowen41, C. Bozzi17,39, S. Braun12,
M. Britsch12, T. Britton60, J. Brodzicka55, E. Buchanan47, C. Burr55, A.
Bursche2, J. Buytaert39, S. Cadeddu16, R. Calabrese17,g, M. Calvi21,i, M.
Calvo Gomez37,m, P. Campana19, D. Campora Perez39, L. Capriotti55, A.
Carbone15,e, G. Carboni25,j, R. Cardinale20,h, A. Cardini16, P. Carniti21,i,
L. Carson51, K. Carvalho Akiba2, G. Casse53, L. Cassina21,i, L. Castillo
Garcia40, M. Cattaneo39, Ch. Cauet10, G. Cavallero20, R. Cenci24,t, M.
Charles8, Ph. Charpentier39, G. Chatzikonstantinidis46, M. Chefdeville4, S.
Chen55, S.-F. Cheung56, V. Chobanova38, M. Chrzaszcz41,27, X. Cid Vidal38, G.
Ciezarek42, P.E.L. Clarke51, M. Clemencic39, H.V. Cliff48, J. Closier39, V.
Coco58, J. Cogan6, E. Cogneras5, V. Cogoni16,f, L. Cojocariu30, G.
Collazuol23,o, P. Collins39, A. Comerma-Montells12, A. Contu39, A. Cook47, S.
Coquereau8, G. Corti39, M. Corvo17,g, C.M. Costa Sobral49, B. Couturier39,
G.A. Cowan51, D.C. Craik51, A. Crocombe49, M. Cruz Torres61, S. Cunliffe54, R.
Currie54, C. D’Ambrosio39, E. Dall’Occo42, J. Dalseno47, P.N.Y. David42, A.
Davis58, O. De Aguiar Francisco2, K. De Bruyn6, S. De Capua55, M. De Cian12,
J.M. De Miranda1, L. De Paula2, M. De Serio14,d, P. De Simone19, C.-T. Dean52,
D. Decamp4, M. Deckenhoff10, L. Del Buono8, M. Demmer10, D. Derkach67, O.
Deschamps5, F. Dettori39, B. Dey22, A. Di Canto39, H. Dijkstra39, F. Dordei39,
M. Dorigo40, A. Dosil Suárez38, A. Dovbnya44, K. Dreimanis53, L. Dufour42, G.
Dujany55, K. Dungs39, P. Durante39, R. Dzhelyadin36, A. Dziurda39, A.
Dzyuba31, N. Déléage4, S. Easo50, U. Egede54, V. Egorychev32, S. Eidelman35,
S. Eisenhardt51, U. Eitschberger10, R. Ekelhof10, L. Eklund52, Ch. Elsasser41,
S. Ely60, S. Esen12, H.M. Evans48, T. Evans56, A. Falabella15, N. Farley46, S.
Farry53, R. Fay53, D. Fazzini21,i, D. Ferguson51, V. Fernandez Albor38, F.
Ferrari15,39, F. Ferreira Rodrigues1, M. Ferro-Luzzi39, S. Filippov34, R.A.
Fini14, M. Fiore17,g, M. Fiorini17,g, M. Firlej28, C. Fitzpatrick40, T.
Fiutowski28, F. Fleuret7,b, K. Fohl39, M. Fontana16, F. Fontanelli20,h, D.C.
Forshaw60, R. Forty39, M. Frank39, C. Frei39, J. Fu22,q, E. Furfaro25,j, C.
Färber39, A. Gallas Torreira38, D. Galli15,e, S. Gallorini23, S. Gambetta51,
M. Gandelman2, P. Gandini56, Y. Gao3, J. García Pardiñas38, J. Garra Tico48,
L. Garrido37, P.J. Garsed48, D. Gascon37, C. Gaspar39, L. Gavardi10, G.
Gazzoni5, D. Gerick12, E. Gersabeck12, M. Gersabeck55, T. Gershon49, Ph.
Ghez4, S. Gianì40, V. Gibson48, O.G. Girard40, L. Giubega30, K. Gizdov51, V.V.
Gligorov8, D. Golubkov32, A. Golutvin54,39, A. Gomes1,a, I.V. Gorelov33, C.
Gotti21,i, M. Grabalosa Gándara5, R. Graciani Diaz37, L.A. Granado Cardoso39,
E. Graugés37, E. Graverini41, G. Graziani18, A. Grecu30, P. Griffith46, L.
Grillo21, B.R. Gruberg Cazon56, O. Grünberg65, E. Gushchin34, Yu. Guz36, T.
Gys39, C. Göbel61, T. Hadavizadeh56, C. Hadjivasiliou5, G. Haefeli40, C.
Haen39, S.C. Haines48, S. Hall54, B. Hamilton59, X. Han12, S. Hansmann-
Menzemer12, N. Harnew56, S.T. Harnew47, J. Harrison55, M. Hatch39, J. He62, T.
Head40, A. Heister9, K. Hennessy53, P. Henrard5, L. Henry8, J.A. Hernando
Morata38, E. van Herwijnen39, M. Heß65, A. Hicheur2, D. Hill56, C. Hombach55,
W. Hulsbergen42, T. Humair54, M. Hushchyn67, N. Hussain56, D. Hutchcroft53, M.
Idzik28, P. Ilten57, R. Jacobsson39, A. Jaeger12, J. Jalocha56, E. Jans42, A.
Jawahery59, M. John56, D. Johnson39, C.R. Jones48, C. Joram39, B. Jost39, N.
Jurik60, S. Kandybei44, W. Kanso6, M. Karacson39, J.M. Kariuki47, S.
Karodia52, M. Kecke12, M. Kelsey60, I.R. Kenyon46, M. Kenzie39, T. Ketel43, E.
Khairullin67, B. Khanji21,39,i, C. Khurewathanakul40, T. Kirn9, S. Klaver55,
K. Klimaszewski29, S. Koliiev45, M. Kolpin12, I. Komarov40, R.F. Koopman43, P.
Koppenburg42, A. Kozachuk33, M. Kozeiha5, L. Kravchuk34, K. Kreplin12, M.
Kreps49, P. Krokovny35, F. Kruse10, W. Krzemien29, W. Kucewicz27,l, M.
Kucharczyk27, V. Kudryavtsev35, A.K. Kuonen40, K. Kurek29, T.
Kvaratskheliya32,39, D. Lacarrere39, G. Lafferty55,39, A. Lai16, D. Lambert51,
G. Lanfranchi19, C. Langenbruch9, B. Langhans39, T. Latham49, C. Lazzeroni46,
R. Le Gac6, J. van Leerdam42, J.-P. Lees4, A. Leflat33,39, J. Lefrançois7, R.
Lefèvre5, F. Lemaitre39, E. Lemos Cid38, O. Leroy6, T. Lesiak27, B.
Leverington12, Y. Li7, T. Likhomanenko67,66, R. Lindner39, C. Linn39, F.
Lionetto41, B. Liu16, X. Liu3, D. Loh49, I. Longstaff52, J.H. Lopes2, D.
Lucchesi23,o, M. Lucio Martinez38, H. Luo51, A. Lupato23, E. Luppi17,g, O.
Lupton56, A. Lusiani24, X. Lyu62, F. Machefert7, F. Maciuc30, O. Maev31, K.
Maguire55, S. Malde56, A. Malinin66, T. Maltsev35, G. Manca7, G. Mancinelli6,
P. Manning60, J. Maratas5,v, J.F. Marchand4, U. Marconi15, C. Marin Benito37,
P. Marino24,t, J. Marks12, G. Martellotti26, M. Martin6, M. Martinelli40, D.
Martinez Santos38, F. Martinez Vidal68, D. Martins Tostes2, L.M. Massacrier7,
A. Massafferri1, R. Matev39, A. Mathad49, Z. Mathe39, C. Matteuzzi21, A.
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McNulty13, B. Meadows58, F. Meier10, M. Meissner12, D. Melnychuk29, M. Merk42,
A. Merli22,q, E. Michielin23, D.A. Milanes64, M.-N. Minard4, D.S. Mitzel12, J.
Molina Rodriguez61, I.A. Monroy64, S. Monteil5, M. Morandin23, P. Morawski28,
A. Mordà6, M.J. Morello24,t, J. Moron28, A.B. Morris51, R. Mountain60, F.
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C. Nguyen-Mau40,n, S. Nieswand9, R. Niet10, N. Nikitin33, T. Nikodem12, A.
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A. Pistone20, A. Piucci12, S. Playfer51, M. Plo Casasus38, T. Poikela39, F.
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J. Prisciandaro38, A. Pritchard53, C. Prouve47, V. Pugatch45, A. Puig
Navarro40, G. Punzi24,p, W. Qian56, R. Quagliani7,47, B. Rachwal27, J.H.
Rademacker47, M. Rama24, M. Ramos Pernas38, M.S. Rangel2, I. Raniuk44, G.
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Molina37, P. Robbe7,39, A.B. Rodrigues1, E. Rodrigues58, J.A. Rodriguez
Lopez64, P. Rodriguez Perez55, A. Rogozhnikov67, S. Roiser39, V.
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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
4LAPP, Université Savoie Mont-Blanc, CNRS/IN2P3, Annecy-Le-Vieux, France
5Clermont Université, Université Blaise Pascal, CNRS/IN2P3, LPC, Clermont-
Ferrand, France
6CPPM, Aix-Marseille Université, CNRS/IN2P3, Marseille, France
7LAL, Université Paris-Sud, CNRS/IN2P3, Orsay, France
8LPNHE, Université Pierre et Marie Curie, Université Paris Diderot,
CNRS/IN2P3, Paris, France
9I. Physikalisches Institut, RWTH Aachen University, Aachen, Germany
10Fakultät Physik, Technische Universität Dortmund, Dortmund, Germany
11Max-Planck-Institut für Kernphysik (MPIK), Heidelberg, Germany
12Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg,
Germany
13School of Physics, University College Dublin, Dublin, Ireland
14Sezione INFN di Bari, Bari, Italy
15Sezione INFN di Bologna, Bologna, Italy
16Sezione INFN di Cagliari, Cagliari, Italy
17Sezione INFN di Ferrara, Ferrara, Italy
18Sezione INFN di Firenze, Firenze, Italy
19Laboratori Nazionali dell’INFN di Frascati, Frascati, Italy
20Sezione INFN di Genova, Genova, Italy
21Sezione INFN di Milano Bicocca, Milano, Italy
22Sezione INFN di Milano, Milano, Italy
23Sezione INFN di Padova, Padova, Italy
24Sezione INFN di Pisa, Pisa, Italy
25Sezione INFN di Roma Tor Vergata, Roma, Italy
26Sezione INFN di Roma La Sapienza, Roma, Italy
27Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of
Sciences, Kraków, Poland
28AGH - University of Science and Technology, Faculty of Physics and Applied
Computer Science, Kraków, Poland
29National Center for Nuclear Research (NCBJ), Warsaw, Poland
30Horia Hulubei National Institute of Physics and Nuclear Engineering,
Bucharest-Magurele, Romania
31Petersburg Nuclear Physics Institute (PNPI), Gatchina, Russia
32Institute of Theoretical and Experimental Physics (ITEP), Moscow, Russia
33Institute of Nuclear Physics, Moscow State University (SINP MSU), Moscow,
Russia
34Institute for Nuclear Research of the Russian Academy of Sciences (INR RAN),
Moscow, Russia
35Budker Institute of Nuclear Physics (SB RAS) and Novosibirsk State
University, Novosibirsk, Russia
36Institute for High Energy Physics (IHEP), Protvino, Russia
37ICCUB, Universitat de Barcelona, Barcelona, Spain
38Universidad de Santiago de Compostela, Santiago de Compostela, Spain
39European Organization for Nuclear Research (CERN), Geneva, Switzerland
40Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland
41Physik-Institut, Universität Zürich, Zürich, Switzerland
42Nikhef National Institute for Subatomic Physics, Amsterdam, The Netherlands
43Nikhef National Institute for Subatomic Physics and VU University Amsterdam,
Amsterdam, The Netherlands
44NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine
45Institute for Nuclear Research of the National Academy of Sciences (KINR),
Kyiv, Ukraine
46University of Birmingham, Birmingham, United Kingdom
47H.H. Wills Physics Laboratory, University of Bristol, Bristol, United
Kingdom
48Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom
49Department of Physics, University of Warwick, Coventry, United Kingdom
50STFC Rutherford Appleton Laboratory, Didcot, United Kingdom
51School of Physics and Astronomy, University of Edinburgh, Edinburgh, United
Kingdom
52School of Physics and Astronomy, University of Glasgow, Glasgow, United
Kingdom
53Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom
54Imperial College London, London, United Kingdom
55School of Physics and Astronomy, University of Manchester, Manchester,
United Kingdom
56Department of Physics, University of Oxford, Oxford, United Kingdom
57Massachusetts Institute of Technology, Cambridge, MA, United States
58University of Cincinnati, Cincinnati, OH, United States
59University of Maryland, College Park, MD, United States
60Syracuse University, Syracuse, NY, United States
61Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), Rio de
Janeiro, Brazil, associated to 2
62University of Chinese Academy of Sciences, Beijing, China, associated to 3
63Institute of Particle Physics, Central China Normal University, Wuhan,
Hubei, China, associated to 3
64Departamento de Fisica , Universidad Nacional de Colombia, Bogota, Colombia,
associated to 8
65Institut für Physik, Universität Rostock, Rostock, Germany, associated to 12
66National Research Centre Kurchatov Institute, Moscow, Russia, associated to
32
67Yandex School of Data Analysis, Moscow, Russia, associated to 32
68Instituto de Fisica Corpuscular (IFIC), Universitat de Valencia-CSIC,
Valencia, Spain, associated to 37
69Van Swinderen Institute, University of Groningen, Groningen, The
Netherlands, associated to 42

aUniversidade Federal do Triângulo Mineiro (UFTM), Uberaba-MG, Brazil
bLaboratoire Leprince-Ringuet, Palaiseau, France
cP.N. Lebedev Physical Institute, Russian Academy of Science (LPI RAS),
Moscow, Russia
dUniversità di Bari, Bari, Italy
eUniversità di Bologna, Bologna, Italy
fUniversità di Cagliari, Cagliari, Italy
gUniversità di Ferrara, Ferrara, Italy
hUniversità di Genova, Genova, Italy
iUniversità di Milano Bicocca, Milano, Italy
jUniversità di Roma Tor Vergata, Roma, Italy
kUniversità di Roma La Sapienza, Roma, Italy
lAGH - University of Science and Technology, Faculty of Computer Science,
Electronics and Telecommunications, Kraków, Poland
mLIFAELS, La Salle, Universitat Ramon Llull, Barcelona, Spain
nHanoi University of Science, Hanoi, Viet Nam
oUniversità di Padova, Padova, Italy
pUniversità di Pisa, Pisa, Italy
qUniversità degli Studi di Milano, Milano, Italy
rUniversità di Urbino, Urbino, Italy
sUniversità della Basilicata, Potenza, Italy
tScuola Normale Superiore, Pisa, Italy
uUniversità di Modena e Reggio Emilia, Modena, Italy
vIligan Institute of Technology (IIT), Iligan, Philippines