EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 CERN-EP-2018-330 LHCb-PAPER-2018-043

Model-independent observation of exotic contributions to
${{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{+}}{{\pi}^{-}}$decays

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

An angular analysis of
${{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{+}}{{\pi}^{-}}$ decays is performed, using proton-proton
collision data corresponding to an integrated luminosity of
3$\text{\,fb}^{-1}$ collected with the LHCb detector. The
$m({{K}^{+}}{{\pi}^{-}})$ spectrum is divided into fine bins. In each
$m({{K}^{+}}{{\pi}^{-}})$ bin, the hypothesis that the three-dimensional
angular distribution can be described by structures induced only by $K^{\ast}$
resonances is examined, making minimal assumptions about the $K^{+}\pi^{-}$
system. The data reject the $K^{\ast}$-only hypothesis with a large
significance, implying the observation of exotic contributions in a model-
independent fashion. Inspection of the
$m({{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{{\pi}^{-}})$ versus
$m({{K}^{+}}{{\pi}^{-}})$ plane suggests structures near
$m({{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{{\pi}^{-}})=4200$ MeV and
4600  MeV.

Published in Phys. Rev. Lett. 122, 152002 (2019)

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

In the Standard Model, the quark model allows for hadrons comprising any
number of valence quarks, as long as they are colour-singlet states. Yet,
after decades of searches, the reason why the vast majority of hadrons are
built out of only quark-antiquark (meson) or three-quark (baryon) combinations
remains a mystery. The best known exception is the $Z(4430)^{-}$ resonance
with spin-parity $1^{-}$ and width $\Gamma=172\pm 13$ MeV [1, 2],111Natural
units with $\hslash=c=1$ are used throughout the document. which has minimal
quark content $c\bar{c}\bar{u}\bar{d}$, and is therefore manifestly exotic,
i.e., has components that are neither quark-antiquark or three-quark
combinations. The only confirmed decay of the $Z(4430)^{-}$ state is via
${Z(4430)^{-}\rightarrow{\psi{(2S)}}\pi^{-}}$, as seen in
${B^{0}\rightarrow{\psi{(2S)}}K^{+}\pi^{-}}$ decays [1].222The inclusion of
charge-conjugate decay modes is implied throughout. The corresponding
${Z(4430)^{-}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\pi^{-}}$ decay rate is suppressed by at least a factor of ten [3]. The
authors of Ref. [4] surmise that in a dynamical diquark picture, this is
because of a larger overlap of the $Z(4430)^{-}$ radial wavefunction with the
excited state $\psi{(2S)}$ than with the ground state
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$. For the
$B^{0}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}K^{+}\pi^{-}$
channel, the Belle collaboration [3] has reported the observation of a new
exotic $Z(4200)^{-}$ resonance decaying to
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\pi^{-}$, that might correspond
to the structure in $m({\psi{(2S)}}{{\pi}^{-}})$ seen in Ref. [1] at around
the same mass.

A generic concern in searches for broad exotic states like the $Z(4430)^{-}$
resonance is disentangling contributions from non-exotic components. For
$B^{0}\rightarrow\psi^{(^{\prime})}K^{+}\pi^{-}$ decays,333Here $\psi$ denotes
the ground state ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}$ and
$\psi^{\prime}$ denotes the excited state $\psi{(2S)}$. the latter comprise
different $K^{\ast}_{J}$ resonances with spin $J$, that decay to
$K^{+}\pi^{-}$. Figure 1 shows the $K^{\ast}_{J}$ spectrum, which has
multiple, overlapping, and poorly measured states. The bulk of the
measurements come from the LASS $K^{+}\pi^{-}$ scattering experiment [5]. In
particular, the decay $B^{0}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}K^{+}{{\pi}^{-}}$ is known to be dominated by $K^{\ast}_{J}$
resonances, with an exotic fit fraction of only $2.4\%$ [3], compared to a
$10.3\%$ contribution from the $Z(4430)^{-}$ for
$B^{0}\rightarrow{\psi{(2S)}}K^{+}{{\pi}^{-}}$ [6]. This smaller exotic fit
fraction for the ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ case makes it
pertinent to study the evidence of exotic contributions in a manner
independent of the dominant but poorly understood $K^{\ast}_{J}$ spectrum.

Figure 1: Spectrum of $K^{\ast}_{J}$ resonances from Ref. [7], with the
vertical span of the boxes indicating $\pm\Gamma_{0}$, where $\Gamma_{0}$ is
the width of each resonance. The horizontal dashed lines mark the
$m({{K}^{+}}{{\pi}^{-}})$ physical region for
${B^{0}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}K^{+}\pi^{-}}$
decays, while the dot-dashed lines mark the specific region,
${m({{K}^{+}}{{\pi}^{-}})\in[1085,1445]}$ MeV, employed for determining the
significance of exotic contributions.

The BaBar collaboration [8] has performed a model-independent analysis of
${B^{0}\rightarrow\psi^{(^{\prime})}K^{+}\pi^{-}}$ decays making minimal
assumptions about the $K^{\ast}_{J}$ spectrum, using two-dimensional (2D)
moments in the variables $m({{K}^{+}}{{\pi}^{-}})$ and the $K^{+}$ helicity
angle, $\theta_{V}$. The key feature of this approach is that no information
on the exact content of the $K^{\ast}_{J}$ states, including their masses,
widths and $m({{K}^{+}}{{\pi}^{-}})$-dependent lineshapes, is required. An
amplitude analysis would require the accurate description of the
$K^{\ast}_{J}$ lineshapes which depend on the underlying production dynamics.
The model-independent procedure bypasses these problems, requiring only
knowledge of the highest spin, $J_{\rm max}$, among all the contributing
$K^{\ast}_{J}$ states, for a given $m({{K}^{+}}{{\pi}^{-}})$ bin. Within
uncertainties, the $m({{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\pi^{-})$
spectrum in the BaBar data was found to be adequately described using just
$K^{\ast}_{J}$ states, without the need for exotic contributions.

In this Letter, a four-dimensional (4D) angular analysis of
$B^{0}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}K^{+}\pi^{-}$
decays with ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\rightarrow{\mu^{+}}{\mu^{-}}$ is reported, employing the Run 1 LHCb
dataset. The data sample corresponds to a signal yield approximately $40$ and
$20$ times larger than those of the corresponding BaBar [8] and Belle [6]
analyses, respectively. The larger sample size allows analysis of the
differential rate as a function of the four variables,
$m({{K}^{+}}{{\pi}^{-}})$, $\theta_{V}$, $\theta_{l}$ and $\chi$, that fully
describe the decay topology. The lepton helicity angle, $\theta_{l}$, and the
azimuthal angle, $\chi$, between the $({\mu^{+}}{\mu^{-}})$ and
$(K^{+}\pi^{-})$ decay planes, were integrated over in the BaBar 2D analysis
[8]. The present 4D analysis therefore benefits from a significantly better
sensitivity to exotic components than the previous 2D analysis.

The LHCb detector is a single-arm forward spectrometer covering the
pseudorapidity range $2<\eta<5$ and is described in detail in Ref. [9].
Samples of simulated events are used to obtain the detector efficiency and
optimise the selection. The $pp$ collisions are generated using Pythia [10,
*Sjostrand:2007gs] with a specific LHCb configuration [12]. Decays of hadronic
particles are described by EvtGen [13], in which final-state radiation is
generated using Photos [14]. Dedicated control samples are employed to
calibrate the simulation for agreement with the data.

The selection procedure is the same as in Refs. [15, 16] for the rare decay
${B^{0}\rightarrow\mu^{+}\mu^{-}K^{+}\pi^{-}}$, with the additional
requirement that the $m(\mu^{+}\mu^{-})$ mass is constrained to the known
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ mass via a kinematic fit [17].
The data sample is divided into 35 fine bins in $m({{K}^{+}}{{\pi}^{-}})$ such
that the $m({{K}^{+}}{{\pi}^{-}})$-dependence can be neglected inside a given
bin, and each subsample is processed independently. The bin-widths vary
depending on the data sample size in a given $m({{K}^{+}}{{\pi}^{-}})$ region.
Backgrounds from $B^{+}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}K^{+}$, $B^{0}_{s}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}K^{+}K^{-}$ and ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}pK^{-}$ decays are reduced to a level below $1\%$ of the signal yield
at the selection stage using the excellent tracking and particle-
identification capabilities of the LHCb detector, and are subsequently removed
by a background subtraction procedure. The
$B^{0}_{(s)}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}K^{+}\pi^{-}$ signal lineshape in the
$m({{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}K^{+}\pi^{-})$ spectrum is
described by a bifurcated Gaussian core and exponential tails on both sides. A
sum of two such lineshapes is used for the signal template for the mass fit,
while the background lineshape is a falling exponential. The exponential tails
in the signal lineshape are fixed from the simulation and all other parameters
are allowed to vary in the fit, performed as a binned $\chi^{2}$ minimisation.
An example mass fit result is given in the Appendix. The cumulative signal
yield in the $m({{K}^{+}}{{\pi}^{-}})\in[745,1545]$ MeV region is
$554,\\!500\pm 800$.

The strategy in this analysis is to examine the hypothesis that non-exotic
$K^{\ast}_{J}$ contributions alone can explain all features of the data. Under
the approximation that the muon mass can be neglected and within a narrow
$m({{K}^{+}}{{\pi}^{-}})$ bin, the $C\\!P$-averaged transition matrix element
squared is [18, 19]

$\displaystyle\\!\\!|\mathcal{M}|^{2}$
$\displaystyle=\\!\sum_{\eta}\Big{|}\sum_{\lambda,J}\sqrt{2J+1}\mathcal{H}^{\eta,J}_{\lambda}d^{J}_{\lambda,0}(\theta_{V})d^{1}_{\lambda,\eta}(\theta_{l})e^{i\lambda\chi}\Big{|}^{2},$
(1)

where $\mathcal{H}^{\eta,J}_{\lambda}$ are the $K^{\ast}_{J}$ helicity
amplitudes and $d^{j}_{m^{\prime},m}$ are Wigner rotation matrix elements. The
helicities of the outgoing lepton and $K^{\ast}_{J}$ are ${\eta=\pm 1}$ and
${\lambda\in\\{0,\pm 1\\}}$, respectively. Parity conservation in the
electromagnetic ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\rightarrow{\mu^{-}}{\mu^{+}}$ decay leads to the relation
${\mathcal{H}^{+,J}_{\lambda}=\mathcal{H}^{-,J}_{\lambda}\equiv\mathcal{H}^{J}_{\lambda}}$.
The differential decay rate of
${{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}(\rightarrow{\mu^{+}}{\mu^{-}}){{K}^{+}}{{\pi}^{-}}$ with the ${K}^{+}$
${\pi}^{-}$ system including spin-$J$ partial waves with $J\leq J^{k}_{\rm
max}$ can be written as

$\left[\frac{\mathrm{d}\Gamma^{k}}{\mathrm{d}\Omega^{\phantom{k}}}\right]_{J_{\rm
max}^{k}}\propto\sum^{n_{\rm max}^{k}}_{i=1}f_{i}(\Omega)\Gamma^{k}_{i},$ (2)

where the angular part in Eq. 1 has been expanded in an orthonormal basis of
angular functions, $f_{i}(\Omega)$. Here, $k$ enumerates the
$m({{K}^{+}}{{\pi}^{-}})$ bin under consideration and
${\mathrm{d}\Omega=\mathrm{d}\\!\cos\theta_{\ell}\,\mathrm{d}\\!\cos\theta_{V}\,\mathrm{d}\chi}$
is the angular phase space differential element. The angular basis functions,
$f_{i}(\Omega)$, are constructed from spherical harmonics, $Y^{m}_{l}\equiv
Y^{m}_{l}(\theta_{l},\chi)$, and reduced spherical harmonics,
${P^{m}_{l}\equiv\sqrt{2\pi}Y^{m}_{l}(\theta_{V},0)}$, and are given in are
given in the Appendix.

The $\Gamma^{k}_{i}$ moments are observables that have an overall
$m({{K}^{+}}{{\pi}^{-}})$ dependence, but within a narrow
$m({{K}^{+}}{{\pi}^{-}})$ bin, this dependence can be neglected. The number of
moments for the $k^{\rm th}$ bin, $n_{\rm max}^{k}$, depends on the allowed
spin of the highest partial wave, $J_{\rm max}^{k}$, and is given by [19]

$n_{\rm max}^{k}=28+12\times(J_{\rm max}^{k}-2),\text{ for }J_{\rm
max}^{k}>2.$ (3)

Thus, for spin 3 onward, each additional higher spin component leads to 12
additional moments. In contrast to previous analyses,
$\mathrm{d}\\!\cos\theta_{\ell}\,\mathrm{d}\chi$ is not integrated over, which
would have resulted in integrating over 10 out of these 12 moments, for each
additional spin. Due to the orthonormality of the $f_{i}(\Omega)$ basis
functions, the angular observables, $\Gamma^{k}_{i}$, can be determined from
the data in an unbiased fashion using a simple counting measurement [18]. For
the $k^{\rm th}$ $m({{K}^{+}}{{\pi}^{-}})$ bin, the background-subtracted raw
moments are estimated as

$\Gamma^{k}_{i,{\rm raw}}=\sum_{p=1}^{n^{k}_{\rm
sig}}f_{i}(\Omega_{p})-x^{k}\sum_{p=1}^{n^{k}_{\rm bkg}}f_{i}(\Omega_{p}),$
(4)

where $\Omega_{p}$ refers to the set of angles for a given event in this
$m({{K}^{+}}{{\pi}^{-}})$ bin. The corresponding covariance matrix is

$\\!\\!C^{k}_{ij,{\rm raw}}=\sum_{p=1}^{n^{k}_{\rm
sig}}f_{i}(\Omega_{p})f_{j}(\Omega_{p})+(x^{k})^{2}\sum_{p=1}^{n^{k}_{\rm
bkg}}f_{i}(\Omega_{p})f_{j}(\Omega_{p}).$ (5)

Here, $n^{k}_{\rm sig}$ and $n^{k}_{\rm bkg}$ correspond to the number of
candidates in the signal and background regions, respectively. The signal
region is defined within $\pm 15$ MeV of the known ${B}^{0}$ mass, and the
background region spans the range $m({{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{+}}{{\pi}^{-}})\in[5450,5560]$ MeV. The scale factor, $x^{k}$, is
the ratio of the estimated number of background candidates in the signal
region divided by the number of candidates in the background region and is
used to normalise the background subtraction.

To unfold effects from the detector efficiency including event reconstruction
and selection, an efficiency matrix, $E^{k}_{ij}$, is used. It is obtained
from simulated signal events generated according to a phase space
distribution, uniform in $\Omega$, as

$E^{k}_{ij}=\sum_{p=1}^{n^{k}_{\rm
sim}}w^{k}_{p}f_{i}(\Omega_{p})f_{j}(\Omega_{p}).$ (6)

The $w^{k}_{p}$ weight factors correct for differences between data and
simulation, and the summation is over simulated and reconstructed events. They
are derived using the
${{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}K^{\ast}(892)^{0}$ control mode, as described in Refs. [15, 16]. The
efficiency-corrected moments and covariance matrices are estimated as

$\displaystyle\Gamma^{k}_{i}$
$\displaystyle=\left(\left(E^{k}\right)^{-1}\right)_{il}\Gamma^{k}_{l,{\rm
raw}},$ (7) $\displaystyle C^{k}_{ij}$
$\displaystyle=\left(\left(E^{k}\right)^{-1}\right)_{il}C^{k}_{lm,{\rm
raw}}\left(\left(E^{k}\right)^{-1}\right)_{jm}.$ (8)

The first moment, $\Gamma^{k}_{1}$, corresponds to the overall rate. The
remaining moments and the covariance matrix are normalised to this overall
rate as $\overline{\Gamma}^{k}_{i}\equiv\Gamma^{k}_{i}/\Gamma^{k}_{1}$ and

$\displaystyle\overline{C}^{k}_{ij,{\rm stat}}$
$\displaystyle=\left[\frac{C^{k}_{ij}}{\left(\Gamma_{1}^{k}\right)^{2}}+\frac{\Gamma^{k}_{i}\Gamma^{k}_{j}}{\left(\Gamma^{k}_{1}\right)^{4}}C^{k}_{11}-\frac{\Gamma^{k}_{i}C^{k}_{1j}+\Gamma^{k}_{j}C^{k}_{1i}}{\Gamma^{k}_{1}\left(\Gamma_{1}^{k}\right)^{2}}\right],$
(9)

for $i,j\in\\{2,\ldots,n^{k}_{\rm max}\\}$.

The normalisation with respect to the total rate renders the analysis
insensitive to any overall systematic effect not correlated with
$\mathrm{d}\Omega$ in a given $m({{K}^{+}}{{\pi}^{-}})$ bin. The uncertainty
from limited knowledge of the background is included in the second term in Eq.
5. The effect on the normalised moments, $\overline{\Gamma}^{k}_{i}$, due to
the uncertainty in the $x^{k}$ scale factors from the mass fit, is found to be
negligible. The effect due to the limited simulation sample size compared to
the data is small and accounted for using pseudoexperiments. The last source
of systematic uncertainty is the effect of finite resolution in the
reconstructed angles. The estimated biases in the measured
$\overline{\Gamma}^{k}_{i}$ moments are added as additional uncertainties.

The dominant contributions to
${{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{+}}{{\pi}^{-}}$ are from the $K^{\ast}(892)^{0}$ and
$K^{\ast}_{2}(1430)^{0}$ states. To maximise the sensitivity to any exotic
component, the dominant $K^{\ast}(892)^{0}$ region that serves as a background
for any non-$K^{\ast}_{J}$ component, the analysis is performed on the
${m({{K}^{+}}{{\pi}^{-}})\in[1085,1445]}$ MeV region, as marked by the dot-
dashed lines in Fig. 1. The value of $J^{k}_{\rm max}$ depends on
$m({{K}^{+}}{{\pi}^{-}})$, with higher spin states suppressed at lower
$m({{K}^{+}}{{\pi}^{-}})$ values, due to the orbital angular momentum barrier
factor [20]. As seen from Fig. 1, only states with spin $J=\\{0,1\\}$
contribute below $m({{K}^{+}}{{\pi}^{-}})\sim 1300$ MeV and spin
$J=\\{0,1,2\\}$ below $m({{K}^{+}}{{\pi}^{-}})\sim 1600$ MeV. As a
conservative choice, $J^{k}_{\rm max}$ is taken to be one unit larger than
these expectations,

$\displaystyle\\!\\!J^{k}_{\rm max}=\begin{cases}2{\rm\;\;for\;\;}1085\leq
m({{K}^{+}}{{\pi}^{-}})<1265~{}{\rm\text{\,Me\kern-1.00006ptV}},\\\
3{\rm\;\;for\;\;}1265\leq
m({{K}^{+}}{{\pi}^{-}})<1445~{}{\rm\text{\,Me\kern-1.00006ptV}}.\end{cases}$
(10)

Any exotic component in the ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{\pi}^{-}}$ or ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{+}}$ system will reflect onto the entire basis of $K^{\ast}_{J}$
partial waves and give rise to nonzero contributions from
$P_{l}(\cos\theta_{V})$ components for $l$ larger than those needed to account
for $K^{\ast}_{J}$ resonances. From the completeness of the $f_{i}(\Omega)$
basis, a model with large enough $J^{k}_{\rm max}$ also describes any exotic
component in the data. For a given value of $m({{K}^{+}}{{\pi}^{-}})$, there
is a one-to-one correspondence between $\cos\theta_{V}$ and the variables
$m({{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{{\pi}^{-}})$ or
$m({{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{{K}^{+}})$. Therefore a
complete basis of $P_{l}(\cos\theta_{V})$ partial waves also describes any
arbitrary shape in $m({{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{\pi}^{-}})$ or $m({{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{+}})$, for a given $m({{K}^{+}}{{\pi}^{-}})$ bin. The series is
truncated at a value large enough to describe the relevant features of the
distribution in data, but not so large that it follows bin-by-bin statistical
fluctuations. A value of $J^{k}_{\rm max}=15$ is found to be suitable.

For the $k^{\rm th}$ $m({{K}^{+}}{{\pi}^{-}})$ bin, the probability density
function (pdf) for the $J^{k}_{\rm max}$ model is

$\displaystyle\mathcal{P}_{J^{k}_{\rm max}}(\Omega)$
$\displaystyle=\displaystyle\frac{1}{\sqrt{8\pi}}\left[\frac{1}{\sqrt{8\pi}}+\sum_{i=2}^{n^{k}_{J_{\rm
max}}}\overline{\Gamma}^{k}_{i}f_{i}(\Omega)\right].$ (11)

Simulated events generated uniformly in $\Omega$, after incorporating detector
efficiency effects and weighting by the pdf in Eq. 11, are expected to match
the background-subtracted data. The background subtraction is performed using
the $sPlot$ technique [21], where the weights are determined from fits to the
invariant $m({{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}K^{+}\pi^{-})$
distributions described previously. Figure 2 shows this comparison between the
background-subtracted data and weighted simulated events in the
$m({{K}^{+}}{{\pi}^{-}})\in[1085,1265]$ MeV region. The $J^{k}_{\rm max}=2$
model clearly misses the peaking structures in the data around
$m({{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\pi^{-})=4200$ MeV and $4600$
MeV. This inability of the $J^{k}_{\rm max}=2$ model to describe the data,
even though the first spin 2 state, $K^{\ast}_{2}(1430)^{0}$, lies beyond this
mass region, strongly points toward the presence of exotic components. These
could be four-quark bound states, meson molecules, or possibly dynamically
generated features such as cusps.

Figure 2: Comparison of $m(J\psi\pi^{-})$ in the
$m({{K}^{+}}{{\pi}^{-}})\in[1085,1265]$ MeV region between the background-
subtracted data and simulated events weighted by moments models with
$J^{k}_{\rm max}=2$ and $J^{k}_{\rm max}=15$.

To obtain a numerical estimate of the significance of exotic states, the
likelihood ratio test is employed between the null hypothesis
($K^{\ast}_{J}$-only, from Eq. 10) and the exotic hypothesis ($J^{k}_{\rm
max}=15$) pdfs, denoted ${\cal P}^{k}_{K^{\ast}_{J}}$ and ${\cal P}^{k}_{\rm
exotic}$, respectively. The test statistic used in the likelihood ratio test
is defined as

$\displaystyle\Delta(-2\log{\cal
L})\Big{|}_{k}\equiv-\displaystyle\phantom{x^{k}}\sum_{p=1}^{n^{k}_{\rm
sig}}2\left[\log\left(\frac{{\cal P}^{k}_{K^{\ast}_{J}}(\Omega_{p})}{{\cal
P}^{k}_{\rm exotic}(\Omega_{p})}\right)\right]+\displaystyle
x^{k}\sum_{p=1}^{n^{k}_{\rm bkg}}2\left[\log\left(\frac{{\cal
P}^{k}_{K^{\ast}_{J}}(\Omega_{p})}{{\cal P}^{k}_{\rm
exotic}(\Omega_{p})}\right)\right]+$ $\displaystyle\hskip
113.81102pt2\times(n^{k}_{\rm sig}-x^{k}n^{k}_{\rm
bkg})\times\log\left(\frac{\int{\cal
P}^{k}_{K^{\ast}_{J}}(\Omega)\epsilon(\Omega)\mathrm{d}\Omega}{\int{\cal
P}^{k}_{\rm exotic}(\Omega)\epsilon(\Omega)\mathrm{d}\Omega}\right),$ (12)

for the $k^{\rm th}$ $m({{K}^{+}}{{\pi}^{-}})$ bin, where $\epsilon(\Omega)$
denotes the 3-dimensional angular detector efficiency in this bin, derived
from the simulation weighted to match the data in the ${{B}^{0}}$ production
kinematics. The last term in Eq. S0.Ex1 ensures normalization of the relevant
pdf and is calculated from simulated events that pass the reconstruction and
selection criteria

$\displaystyle E^{k}_{i}$
$\displaystyle\equiv\displaystyle\sum_{p=1}^{n^{k}_{\rm
sim}}w^{k}_{p}f_{i}(\Omega_{p}),$ (13) $\displaystyle\int{\cal P}_{J^{k}_{\rm
max}}(\Omega)\epsilon(\Omega)\mathrm{d}\Omega$
$\displaystyle\propto\displaystyle\sum_{i=1}^{n^{k}_{\rm
max}}\Gamma^{k}_{i}E^{k}_{i}.$ (14)

Results from individual $m({{K}^{+}}{{\pi}^{-}})$ bins are combined to give
the final test statistic ${\Delta(-2\log{\cal
L})=\displaystyle\sum_{k}\Delta(-2\log{\cal L})\Big{|}_{k}}$.

From Eq. 3 the number of degrees-of-freedom (ndf) increases by 12 for each
additional spin-$J$ wave in each $m({{K}^{+}}{{\pi}^{-}})$ bin. From Eq. 10,
for the $J^{k}_{\rm max}=2$ and $3$ choices, $\Delta{\rm
ndf}=12\times(15-2)=156$ and $12\times(15-3)=144$, respectively, between the
exotic and $K^{\ast}_{J}$-only pdf’s for each $m({{K}^{+}}{{\pi}^{-}})$ bin.
Each additional degree-of-freedom between the exotic and $K^{\ast}_{J}$-only
pdf adds approximately one unit to the computed $\Delta(-2\log{\cal L})$ in
the data due to increased sensitivity to the statistical fluctuations, and
$\Delta(-2\log{\cal L})$ is therefore not expected to be zero even if there is
no exotic contribution in the data. The expected $\Delta(-2\log{\cal L})$
distribution in the absence of exotic activity is evaluated using a large
number of pseudoexperiments. For each $m({{K}^{+}}{{\pi}^{-}})$ bin, 11,000
pseudoexperiments are generated according to the $K^{\ast}_{J}$-only model
with the moments varied according to the covariance matrix. The number of
signal and background events for each pseudoexperiment are taken to be those
measured in the data. The detector efficiency obtained from simulation is
parameterised in 4D. Each pseudoexperiment is analyzed in exactly the same way
as the data, where an independent efficiency matrix is generated for each
pseudoexperiment. This accounts for the limited sample size of the simulation
for the efficiency unfolding. The pseudoexperiments therefore represent the
data faithfully at every step of the processing.

Figure 3: Likelihood-ratio test for exotic significance. The data shows a
$10\sigma$ deviation from the pseudoexperiments generated according to the
null hypothesis ($K^{\ast}_{J}$-only contributions).

Figure 3 shows the distribution of $\Delta(-2\log{\cal L})$ from the
pseudoexperiments in the $m({{K}^{+}}{{\pi}^{-}})\in[1085,1445]$ MeV region
comprising six $m({{K}^{+}}{{\pi}^{-}})$ bins each with the $J^{k}_{\rm
max}=2$ or $3$ choice. A fit to a Gaussian profile gives $\Delta(-2\log{\cal
L})\approx 2051$ between the null and exotic hypothesis, even in the absence
of any exotic contributions. This value is consistent with the naïve
expectation $\Delta({\rm ndf})=1800$ from the counting discussed earlier. The
value of $\Delta(-2\log{\cal L})$ for the data, as marked by the vertical line
in Fig. 3, shows a deviation of more than $10\sigma$ from the null hypothesis,
corresponding to the distribution of the pseudoexperiments. The uncertainty
due to the quality of the Gaussian profile fit in Fig. 3 is found to be
negligible. The choice of large $J^{k}_{\rm max}$ for ${\cal P}^{k}_{\rm
exotic}$, as well as the detector efficiency and calibration of the
simulation, are systematically varied in pseudoexperiments, with significance
for exotic components in excess of $6\sigma$ observed in each case.

Figure 4: Background-subtracted 2D distribution of
$m({{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\pi^{-})$ versus
$m({{K}^{+}}{{\pi}^{-}})$ in the region
${m({{K}^{+}}{{\pi}^{-}})\in[745,1545]}$ MeV. The intensity ($z$-axis) scale
has been highly truncated to limit the strong $K^{\ast}(892)^{0}$
contribution.

In summary, employing the Run 1 LHCb dataset, non-$K^{\ast}_{J}$ contributions
in ${B^{0}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}K^{+}\pi^{-}}$ are observed with overwhelming significance. Compared to
the previous BaBar analysis [8] of the same channel, the current study
benefits from a 40-fold increase in signal yield and a full angular analysis
of the decay topology. The method relies on a novel orthonormal angular
moments expansion and, aside from a conservative limit on the highest allowed
$K^{\ast}_{J}$ spin for a given $m({{K}^{+}}{{\pi}^{-}})$ invariant mass,
makes no other assumption about the $K^{+}\pi^{-}$ system. Figure 4 shows a
scatter plot of $m({{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\pi^{-})$
against $m({{K}^{+}}{{\pi}^{-}})$ in the background-subtracted data. While the
model-independent analysis performed here does not identify the origin of the
non-$K^{\ast}_{J}$ contributions, structures are visible at
${m({{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\pi^{-})\approx 4200}$ MeV,
close to the exotic state reported previously by Belle [3], and at
$m({{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\pi^{-})\approx 4600$ MeV. To
interpret these structures as exotic tetraquark resonances and measure their
properties will require a future model-dependent amplitude analysis of the
data.

## 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); 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
(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); ANR, Labex P2IO and OCEVU,
and Région Auvergne-Rhône-Alpes (France); Key Research Program of Frontier
Sciences of CAS, CAS PIFI, and the Thousand Talents Program (China); RFBR, RSF
and Yandex LLC (Russia); GVA, XuntaGal and GENCAT (Spain); the Royal Society
and the Leverhulme Trust (United Kingdom); Laboratory Directed Research and
Development program of LANL (USA).

Appendix

A. Angle conventions

Figure 5: Angle conventions as described in Ref. [18] for (a) ${{\kern
1.79993pt\overline{\kern-1.79993ptB}}{}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}(\rightarrow{\mu^{-}}{\mu^{+}}){{K}^{-}}{{\pi}^{+}}$ and (b)
${{{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}(\rightarrow{\mu^{+}}{\mu^{-}}){{K}^{+}}{{\pi}^{-}}}$. The leptonic
(${\mu^{+}}{\mu^{-}}$) and hadronic ($K^{+}\pi^{-}$) frames are back-to-back
with a common $\hat{y}$ axis.

The four kinematic variables for the process
${{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}(\rightarrow{\mu^{+}}{\mu^{-}}){{K}^{+}}{{\pi}^{-}}$ are the invariant
mass $m({{K}^{+}}{{\pi}^{-}})$, and the three angles
$\\{\theta_{l},\theta_{V},\chi\\}$. The angle conventions for ${{B}^{0}}$ and
${{\kern 1.79993pt\overline{\kern-1.79993ptB}}{}^{0}}$ are depicted in Fig. 5.
Assuming negligible direct $C\\!P$ violation and production asymmetry, the
rate expression remains the same between the charge-conjugate modes.

B. Example mass fit result in a particular bin

Figure 6: Fit to the invariant mass $m({{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}K^{+}\pi^{-})$ in the $m({{K}^{+}}{{\pi}^{-}})\in[1235,1265]$ MeV bin.

Figure 6 shows an example mass fit result for the
$m({{K}^{+}}{{\pi}^{-}})\in[1235,1265]$ MeV bin.

C. Further comparison between the $\bm{J^{k}_{\rm max}=2}$ and $\bm{J^{k}_{\rm
max}=15}$ models

Figure 7: Comparison of $m(J/\psi\pi^{-})$ in the
$m(K^{+}\pi^{-})\in[880,910]$ MeV region between the background-subtracted
data and simulation data weighted by moments models with $J^{k}_{\rm max}=2$
and $J^{k}_{\rm max}=15$.

Figure 7 shows a comparison between the $J^{k}_{\rm max}=2$ and $J^{k}_{\rm
max}=15$ moments models in the $m(K^{+}\pi^{-})=895\pm 15$ MeV bin. Since the
spin-1 $K^{\ast}(892)^{0}$ resonance strongly dominates here, the two models
are compatible.

Figure 8: Comparison of $m(J/\psi\pi^{-})$ in the
$m(K^{+}\pi^{-})\in[1265,1445]$ MeV region between the background-subtracted
data and simulation data weighted by moments models with $J^{k}_{\rm max}=2$
and $J^{k}_{\rm max}=15$.

Figure 8 shows a comparison between the $J^{k}_{\rm max}=2$ and $J^{k}_{\rm
max}=15$ moments models in the $m({{K}^{+}}{{\pi}^{-}})\in[1265,1445]$ MeV.

D. Angular moments definitions

The transversity basis amplitudes, $\mathcal{H}^{J}_{\\{\parallel,\perp\\}}$,
are defined as

$\displaystyle\mathcal{H}^{J}_{\pm}$
$\displaystyle=(\mathcal{H}^{J}_{\parallel}\pm\mathcal{H}^{J}_{\perp})/\sqrt{2}$
(15)

and the amplitudes for spin $J\in\\{0,1,2\\}$ are denoted as $S$,
$H_{\\{0,\parallel,\perp\\}}$ and $D_{\\{0,\parallel,\perp\\}}$, respectively.
For $K^{\ast}_{J}$ contributions up to $J=2$, there are 28 angular moments
from the expansion of Eq. 1, as explicitly listed in Table 1 in terms of the
transversity amplitudes. The addition of $K^{\ast}_{J}$ states from spin-3
onward results in 12 moments for each additional spin. The form of the moments
are listed in Table 2, leading to the expression appearing in Eq. 3 of the
main text. Further details can be obtained from Refs. [18, 19].

Table 1: The transversity-basis moments of the 28 orthonormal angular
functions $f_{i}(\Omega)$ in Eq. 2 till spin-2 in the ${{K}^{+}}{{\pi}^{-}}$
system.

$i$ | $f_{i}(\Omega)$ | $\Gamma^{{\rm tr}}_{i}({q^{2}})$
---|---|---
1 | $P^{0}_{0}Y^{0}_{0}$ | $\left[|H_{0}|^{2}+|H_{\parallel}|^{2}+|H_{\perp}|^{2}+|S|^{2}+|D_{0}|^{2}+|D_{\parallel}|^{2}+|D_{\perp}|^{2}\right]$
2 | $P^{0}_{1}Y^{0}_{0}$ | $2\left[\frac{2}{\sqrt{5}}Re(H_{0}D^{\ast}_{0})+Re(SH_{0}^{\ast})+\sqrt{\frac{3}{5}}\,Re(H_{\parallel}D^{\ast}_{\parallel}+H_{\perp}D^{\ast}_{\perp})\right]$
3 | $P^{0}_{2}Y^{0}_{0}$ |  $\frac{\sqrt{5}}{7}$ ($|D_{\parallel}|^{2}$ \+ $|D_{\perp}|^{2}$) - $\frac{1}{\sqrt{5}}$ ($|H_{\parallel}|^{2}$ \+ $|H_{\perp}|^{2}$) + $\frac{2}{\sqrt{5}}$ $|H_{0}|^{2}$ \+ $\frac{10}{7\sqrt{5}}$ $|D_{0}|^{2}$ \+ $2$ $Re(SD_{0}^{\ast})$
4 | $P^{0}_{3}Y^{0}_{0}$ | $\frac{6}{\sqrt{35}}\left[-\,Re(H_{\parallel}D^{\ast}_{\parallel}+H_{\perp}D^{\ast}_{\perp})+\sqrt{3}Re(H_{0}D^{\ast}_{0})\right]$
5 | $P^{0}_{4}Y^{0}_{0}$ | $\frac{2}{7}\left[-2(|D_{\parallel}|^{2}+|D_{\perp}|^{2})+3|D_{0}|^{2}\right]$
6 | $P^{0}_{0}Y^{0}_{2}$ | $\frac{1}{2\sqrt{5}}\left[(|D_{\parallel}|^{2}+|D_{\perp}|^{2})+(|H_{\parallel}|^{2}+|H_{\perp}|^{2})-2|S|^{2}-2|D_{0}|^{2}-2|H_{0}|^{2}\right]$
7 | $P^{0}_{1}Y^{0}_{2}$ | $\left[\frac{\sqrt{3}}{5}\,Re(H_{\parallel}D^{\ast}_{\parallel}+H_{\perp}D^{\ast}_{\perp})-\frac{2}{\sqrt{5}}\,Re(SH^{\ast}_{0})-\frac{4}{5}\,Re(H_{0}D^{\ast}_{0})\right]$
8 | $P^{0}_{2}Y^{0}_{2}$ | $\left[\frac{1}{14}(|D_{\parallel}|^{2}+|D_{\perp}|^{2})-\frac{2}{7}|D_{0}|^{2}-\frac{1}{10}(|H_{\parallel}|^{2}+|H_{\perp}|^{2})-\frac{2}{5}|H_{0}|^{2}-\frac{2}{\sqrt{5}}Re(SD_{0}^{\ast})\right]$
9 | $P^{0}_{3}Y^{0}_{2}$ | $-\frac{3}{5\sqrt{7}}\left[\,Re(H_{\parallel}D^{\ast}_{\parallel}+H_{\perp}D^{\ast}_{\perp})+2\sqrt{3}\,Re(H_{0}D^{\ast}_{0})\right]$
10 | $P^{0}_{4}Y^{0}_{2}$ | $-\frac{2}{7\sqrt{5}}\left[|D_{\parallel}|^{2}+|D_{\perp}|^{2}+3|D_{0}|^{2}\right]$
11 | $P^{1}_{1}\sqrt{2}\,Re(Y^{1}_{2})$ | $-\frac{3}{\sqrt{10}}\left[\sqrt{\frac{2}{3}}\,Re(H_{\parallel}S^{\ast})-\sqrt{\frac{2}{15}}\,Re(H_{\parallel}D^{\ast}_{0})+\sqrt{\frac{2}{5}}\,Re(D_{\parallel}H^{\ast}_{0})\right]$
12 | $P^{1}_{2}\sqrt{2}\,Re(Y^{1}_{2})$ | $-\frac{3}{5}\left[\,Re(H_{\parallel}H^{\ast}_{0})+\sqrt{\frac{5}{3}}\,Re(D_{\parallel}S^{\ast})+\frac{5}{7\sqrt{3}}\,Re(D_{\parallel}D^{\ast}_{0})\right]$
13 | $P^{1}_{3}\sqrt{2}\,Re(Y^{1}_{2})$ | $-\frac{6}{5\sqrt{14}}\left[2\,Re(D_{\parallel}H^{\ast}_{0})+\sqrt{3}\,Re(H_{\parallel}D^{\ast}_{0})\right]$
14 | $P^{1}_{4}\sqrt{2}\,Re(Y^{1}_{2})$ | $-\frac{6}{7\sqrt{2}}\,Re(D_{\parallel}D^{\ast}_{0})$
15 | $P^{1}_{1}\sqrt{2}\,Im(Y^{1}_{2})$ | $3\left[\frac{1}{\sqrt{15}}\,Im(H_{\perp}S^{\ast})+\frac{1}{5}\,Im(D_{\perp}H^{\ast}_{0})-\frac{1}{5\sqrt{3}}\,Im(H_{\perp}D^{\ast}_{0})\right]$
16 | $P^{1}_{2}\sqrt{2}\,Im(Y^{1}_{2})$ | $3\left[\frac{1}{7\sqrt{3}}\,Im(D_{\perp}D^{\ast}_{0})+\frac{1}{5}\,Im(H_{\perp}H^{\ast}_{0})+\frac{1}{\sqrt{15}}\,Im(D_{\perp}S^{\ast})\right]$
17 | $P^{1}_{3}\sqrt{2}\,Im(Y^{1}_{2})$ | $\frac{6}{5\sqrt{14}}\left[2\,Im(D_{\perp}H^{\ast}_{0})+\sqrt{3}\,Im(H_{\perp}D^{\ast}_{0})\right]$
18 | $P^{1}_{4}\sqrt{2}\,Im(Y^{1}_{2})$ | $\frac{6}{7\sqrt{2}}\,Im(D_{\perp}D^{\ast}_{0})$
19 | $P^{0}_{0}\sqrt{2}\,Re(Y^{2}_{2})$ | $-\frac{3}{2\sqrt{15}}\left[(|H_{\parallel}|^{2}-|H_{\perp}|^{2})+(|D_{\parallel}|^{2}-|D_{\perp}|^{2})\right]$
20 | $P^{0}_{1}\sqrt{2}\,Re(Y^{2}_{2})$ | $-\frac{3}{5}\left[\,Re(H_{\parallel}D^{\ast}_{\parallel})-\,Re(D_{\perp}H^{\ast}_{\perp})\right]$
21 | $P^{0}_{2}\sqrt{2}\,Re(Y^{2}_{2})$ | $\frac{\sqrt{3}}{2}\left[-\frac{1}{7}(|D_{\parallel}|^{2}-|D_{\perp}|^{2})+\frac{1}{5}(|H_{\parallel}|^{2}-|H_{\perp}|^{2})\right]$
22 | $P^{0}_{3}\sqrt{2}\,Re(Y^{2}_{2})$ | $\frac{3}{5}\sqrt{\frac{3}{7}}\left[\,Re(H_{\parallel}D^{\ast}_{\parallel})-\,Re(D_{\perp}H^{\ast}_{\perp})\right]$
23 | $P^{0}_{4}\sqrt{2}\,Re(Y^{2}_{2})$ | $\frac{2}{7}\sqrt{\frac{3}{5}}(|D_{\parallel}|^{2}-|D_{\perp}|^{2})$
24 | $P^{0}_{0}\sqrt{2}\,Im(Y^{2}_{2})$ | $\sqrt{\frac{3}{5}}\left[\,Im(H_{\perp}H^{\ast}_{\parallel})+\,Im(D_{\perp}D^{\ast}_{\parallel})\right]$
25 | $P^{0}_{1}\sqrt{2}\,Im(Y^{2}_{2})$ | $\frac{3}{5}\,Im(H_{\perp}D^{\ast}_{\parallel}+D_{\perp}H^{\ast}_{\parallel})$
26 | $P^{0}_{2}\sqrt{2}\,Im(Y^{2}_{2})$ | $\sqrt{3}\left[\frac{1}{7}\,Im(D_{\perp}D^{\ast}_{\parallel})-\frac{1}{5}\,Im(H_{\perp}H^{\ast}_{\parallel})\right]$
27 | $P^{0}_{3}\sqrt{2}\,Im(Y^{2}_{2})$ | $-\frac{3}{5}\sqrt{\frac{3}{7}}\,Im(D_{\perp}H^{\ast}_{\parallel}+H_{\perp}D^{\ast}_{\parallel})$
28 | $P^{0}_{4}\sqrt{2}\,Im(Y^{2}_{2})$ | $-\frac{4}{7}\sqrt{\frac{3}{5}}\,Im(D_{\perp}D^{\ast}_{\parallel})$

Table 2: The 12 angular terms for each additional spin-$J$ wave in the ${{K}^{+}}{{\pi}^{-}}$ system, for $J\geq 3$. $i$ | $f_{i}(\Omega)$
---|---
$1$ | $P^{0}_{2J-1}Y^{0}_{0}$
$2$ | $P^{0}_{2J\phantom{-1}}Y^{0}_{0}$
$3$ | $P^{0}_{2J-1}Y^{0}_{2}$
$4$ | $P^{0}_{2J\phantom{-1}}Y^{0}_{2}$
$5$ | $P^{1}_{2J-1}\sqrt{2}Re(Y^{1}_{2})$
$6$ | $P^{1}_{2J\phantom{-1}}\sqrt{2}Re(Y^{1}_{2})$
$7$ | $P^{1}_{2J-1}\sqrt{2}Im(Y^{1}_{2})$
$8$ | $P^{1}_{2J\phantom{-1}}\sqrt{2}Im(Y^{1}_{2})$
$9$ | $P^{0}_{2J-1}\sqrt{2}Re(Y^{2}_{2})$
$10$ | $P^{0}_{2J\phantom{-1}}\sqrt{2}Re(Y^{2}_{2})$
$11$ | $P^{0}_{2J-1}\sqrt{2}Im(Y^{2}_{2})$
$12$ | $P^{0}_{2J\phantom{-1}}\sqrt{2}Im(Y^{2}_{2})$

## References

  * [1] LHCb collaboration, R. Aaij et al., _Observation of the resonant character of the $Z(4430)^{-}$ state_, Phys. Rev. Lett. 112 (2014) 222002, arXiv:1404.1903
  * [2] Belle collaboration, S. K. Choi et al., _Observation of a resonance-like structure in the $\pi^{\pm}\psi^{\prime}$ mass distribution in exclusive $B\rightarrow K\pi^{\pm}\psi^{\prime}$ decays_, Phys. Rev. Lett. 100 (2008) 142001, arXiv:0708.1790
  * [3] Belle collaboration, K. Chilikin et al., _Observation of a new charged charmoniumlike state in $\bar{B}^{0}\rightarrow J/\psi K^{-}\pi^{+}$ decays_, Phys. Rev. D90 (2014) 112009, arXiv:1408.6457
  * [4] S. J. Brodsky, D. S. Hwang, and R. F. Lebed, _Dynamical picture for the formation and decay of the exotic $XYZ$ mesons_, Phys. Rev. Lett. 113 (2014) 112001, arXiv:1406.7281
  * [5] LASS collaboration, D. Aston et al., _A study of $K^{-}\pi^{+}$ scattering in the reaction $K^{-}p\rightarrow K^{-}\pi^{+}n$ at 11 GeV/c_, Nucl. Phys. B296 (1988) 493
  * [6] Belle collaboration, K. Chilikin et al., _Experimental constraints on the spin and parity of the $Z(4430)^{+}$_, Phys. Rev. D88 (2013) 074026, arXiv:1306.4894
  * [7] Particle Data Group, M. Tanabashi et al., _Review of particle physics_ , Phys. Rev. D98 (2018) 030001
  * [8] BaBar collaboration, B. Aubert et al., _Search for the $Z(4430)^{-}$ at BABAR_, Phys. Rev. D79 (2009) 112001, arXiv:0811.0564
  * [9] LHCb collaboration, A. A. Alves Jr. et al., _The LHCb detector at the LHC_, JINST 3 (2008) S08005
  * [10] T. Sjöstrand, S. Mrenna, and P. Skands, _PYTHIA 6.4 physics and manual_ , JHEP 05 026
  * [11] T. Sjöstrand, S. Mrenna, and P. Skands, _A brief introduction to PYTHIA 8.1_ , Comput. Phys. Commun. 178 (2008) 852, arXiv:0710.3820
  * [12] I. Belyaev et al., _Handling of the generation of primary events in Gauss, the LHCb simulation framework_ , J. Phys. Conf. Ser. 331 (2011) 032047
  * [13] D. J. Lange, _The EvtGen particle decay simulation package_ , Nucl. Instrum. Meth. A462 (2001) 152
  * [14] P. Golonka and Z. Was, _PHOTOS Monte Carlo: A precision tool for QED corrections in $Z$ and $W$ decays_, Eur. Phys. J. C45 (2006) 97, arXiv:hep-ph/0506026
  * [15] LHCb collaboration, R. Aaij et al., _Angular analysis of the $B^{0}\rightarrow K^{*0}\mu^{+}\mu^{-}$ decay using 3 fb-1 of integrated luminosity_, JHEP 02 (2016) 104, arXiv:1512.04442
  * [16] LHCb collaboration, R. Aaij et al., _Differential branching fraction and angular moments analysis of the decay $B^{0}\rightarrow K^{+}\pi^{-}\mu^{+}\mu^{-}$ in the $K^{*}_{0,2}(1430)^{0}$ region_, JHEP 12 (2016) 065, arXiv:1609.04736
  * [17] W. D. Hulsbergen, _Decay chain fitting with a Kalman filter_ , Nucl. Instrum. Meth. A552 (2005) 566, arXiv:physics/0503191
  * [18] B. Dey, _Angular analyses of exclusive $\bar{B}\rightarrow{X}\ell_{1}\ell_{2}$ with complex helicity amplitudes_, Phys. Rev. D92 (2015) 033013, arXiv:1505.02873
  * [19] B. Dey, _Angular analyses of exclusive $\bar{B}\rightarrow X_{J}\ell_{1}\ell_{2}$ decays for spin $J\leq 4$_, Phys. Rev. D95 (2017) 033004, arXiv:1609.06115
  * [20] F. von Hippel and C. Quigg, _Centrifugal-barrier effects in resonance partial decay widths, shapes, and production amplitudes_ , Phys. Rev. D5 (1972) 624
  * [21] M. Pivk and F. R. Le Diberder, _sPlot: A statistical tool to unfold data distributions_ , Nucl. Instrum. Meth. A555 (2005) 356, arXiv:physics/0402083

LHCb Collaboration

R. Aaij29, C. Abellán Beteta46, B. Adeva43, M. Adinolfi50, C.A. Aidala77, Z.
Ajaltouni7, S. Akar61, P. Albicocco20, J. Albrecht12, F. Alessio44, M.
Alexander55, A. Alfonso Albero42, G. Alkhazov41, P. Alvarez Cartelle57, A.A.
Alves Jr43, S. Amato2, S. Amerio25, Y. Amhis9, L. An19, L. Anderlini19, G.
Andreassi45, M. Andreotti18, J.E. Andrews62, F. Archilli29, J. Arnau Romeu8,
A. Artamonov40, M. Artuso63, K. Arzymatov38, E. Aslanides8, M. Atzeni46, B.
Audurier24, S. Bachmann14, J.J. Back52, S. Baker57, V. Balagura9,b, W.
Baldini18, A. Baranov38, R.J. Barlow58, S. Barsuk9, W. Barter58, M.
Bartolini21, F. Baryshnikov73, V. Batozskaya33, B. Batsukh63, A. Battig12, V.
Battista45, A. Bay45, J. Beddow55, F. Bedeschi26, I. Bediaga1, A. Beiter63,
L.J. Bel29, S. Belin24, N. Beliy4, V. Bellee45, N. Belloli22,i, K. Belous40,
I. Belyaev35, G. Bencivenni20, E. Ben-Haim10, S. Benson29, S. Beranek11, A.
Berezhnoy36, R. Bernet46, D. Berninghoff14, E. Bertholet10, A. Bertolin25, C.
Betancourt46, F. Betti17,44, M.O. Bettler51, Ia. Bezshyiko46, S. Bhasin50, J.
Bhom31, S. Bifani49, P. Billoir10, A. Birnkraut12, A. Bizzeti19,u, M. Bjørn59,
M.P. Blago44, T. Blake52, F. Blanc45, S. Blusk63, D. Bobulska55, V. Bocci28,
O. Boente Garcia43, T. Boettcher60, A. Bondar39,x, N. Bondar41, S.
Borghi58,44, M. Borisyak38, M. Borsato43, F. Bossu9, M. Boubdir11, T.J.V.
Bowcock56, C. Bozzi18,44, S. Braun14, M. Brodski44, J. Brodzicka31, A. Brossa
Gonzalo52, D. Brundu24,44, E. Buchanan50, A. Buonaura46, C. Burr58, A.
Bursche24, J. Buytaert44, W. Byczynski44, S. Cadeddu24, H. Cai67, R.
Calabrese18,g, R. Calladine49, M. Calvi22,i, M. Calvo Gomez42,m, A.
Camboni42,m, P. Campana20, D.H. Campora Perez44, L. Capriotti17,e, A.
Carbone17,e, G. Carboni27, R. Cardinale21, A. Cardini24, P. Carniti22,i, K.
Carvalho Akiba2, G. Casse56, L. Cassina22, M. Cattaneo44, G. Cavallero21, R.
Cenci26,p, M.G. Chapman50, M. Charles10, Ph. Charpentier44, G.
Chatzikonstantinidis49, M. Chefdeville6, V. Chekalina38, C. Chen3, S. Chen24,
S.-G. Chitic44, V. Chobanova43, M. Chrzaszcz44, A. Chubykin41, P. Ciambrone20,
X. Cid Vidal43, G. Ciezarek44, F. Cindolo17, P.E.L. Clarke54, M. Clemencic44,
H.V. Cliff51, J. Closier44, V. Coco44, J.A.B. Coelho9, J. Cogan8, E.
Cogneras7, L. Cojocariu34, P. Collins44, T. Colombo44, A. Comerma-Montells14,
A. Contu24, G. Coombs44, S. Coquereau42, G. Corti44, M. Corvo18,g, C.M. Costa
Sobral52, B. Couturier44, G.A. Cowan54, D.C. Craik60, A. Crocombe52, M. Cruz
Torres1, R. Currie54, F. Da Cunha Marinho2, C.L. Da Silva78, E. Dall’Occo29,
J. Dalseno43,v, C. D’Ambrosio44, A. Danilina35, P. d’Argent14, A. Davis3, O.
De Aguiar Francisco44, K. De Bruyn44, S. De Capua58, M. De Cian45, J.M. De
Miranda1, L. De Paula2, M. De Serio16,d, P. De Simone20, J.A. de Vries29, C.T.
Dean55, D. Decamp6, L. Del Buono10, B. Delaney51, H.-P. Dembinski13, M.
Demmer12, A. Dendek32, D. Derkach74, O. Deschamps7, F. Desse9, F. Dettori56,
B. Dey68, A. Di Canto44, P. Di Nezza20, S. Didenko73, H. Dijkstra44, F.
Dordei24, M. Dorigo44,y, A.C. dos Reis1, A. Dosil Suárez43, L. Douglas55, A.
Dovbnya47, K. Dreimanis56, L. Dufour44, G. Dujany10, P. Durante44, J.M.
Durham78, D. Dutta58, R. Dzhelyadin40, M. Dziewiecki14, A. Dziurda31, A.
Dzyuba41, S. Easo53, U. Egede57, V. Egorychev35, S. Eidelman39,x, S.
Eisenhardt54, U. Eitschberger12, R. Ekelhof12, L. Eklund55, S. Ely63, A.
Ene34, S. Escher11, S. Esen29, T. Evans61, A. Falabella17, C. Färber44, N.
Farley49, S. Farry56, D. Fazzini22,44,i, M. Féo44, P. Fernandez Declara44, A.
Fernandez Prieto43, F. Ferrari17, L. Ferreira Lopes45, F. Ferreira Rodrigues2,
M. Ferro-Luzzi44, S. Filippov37, R.A. Fini16, M. Fiorini18,g, M. Firlej32, C.
Fitzpatrick45, T. Fiutowski32, F. Fleuret9,b, M. Fontana44, F. Fontanelli21,h,
R. Forty44, V. Franco Lima56, M. Frank44, C. Frei44, J. Fu23,q, W. Funk44, E.
Gabriel54, A. Gallas Torreira43, D. Galli17,e, S. Gallorini25, S. Gambetta54,
Y. Gan3, M. Gandelman2, P. Gandini23, Y. Gao3, L.M. Garcia Martin76, J. García
Pardiñas46, B. Garcia Plana43, J. Garra Tico51, L. Garrido42, D. Gascon42, C.
Gaspar44, L. Gavardi12, G. Gazzoni7, D. Gerick14, E. Gersabeck58, M.
Gersabeck58, T. Gershon52, D. Gerstel8, Ph. Ghez6, V. Gibson51, O.G. Girard45,
P. Gironella Gironell42, L. Giubega34, K. Gizdov54, V.V. Gligorov10, C.
Göbel65, D. Golubkov35, A. Golutvin57,73, A. Gomes1,a, I.V. Gorelov36, C.
Gotti22,i, E. Govorkova29, J.P. Grabowski14, R. Graciani Diaz42, L.A. Granado
Cardoso44, E. Graugés42, E. Graverini46, G. Graziani19, A. Grecu34, R.
Greim29, P. Griffith24, L. Grillo58, L. Gruber44, B.R. Gruberg Cazon59, O.
Grünberg70, C. Gu3, E. Gushchin37, A. Guth11, Yu. Guz40,44, T. Gys44, T.
Hadavizadeh59, C. Hadjivasiliou7, G. Haefeli45, C. Haen44, S.C. Haines51, B.
Hamilton62, X. Han14, T.H. Hancock59, S. Hansmann-Menzemer14, N. Harnew59, T.
Harrison56, C. Hasse44, M. Hatch44, J. He4, M. Hecker57, K. Heinicke12, A.
Heister12, K. Hennessy56, L. Henry76, M. Heß70, J. Heuel11, A. Hicheur64, R.
Hidalgo Charman58, D. Hill59, M. Hilton58, P.H. Hopchev45, J. Hu14, W. Hu68,
W. Huang4, Z.C. Huard61, W. Hulsbergen29, T. Humair57, M. Hushchyn74, D.
Hutchcroft56, D. Hynds29, P. Ibis12, M. Idzik32, P. Ilten49, A. Inglessi41, A.
Inyakin40, K. Ivshin41, R. Jacobsson44, J. Jalocha59, E. Jans29, B.K.
Jashal76, A. Jawahery62, F. Jiang3, M. John59, D. Johnson44, C.R. Jones51, C.
Joram44, B. Jost44, N. Jurik59, S. Kandybei47, M. Karacson44, J.M. Kariuki50,
S. Karodia55, N. Kazeev74, M. Kecke14, F. Keizer51, M. Kelsey63, M. Kenzie51,
T. Ketel30, E. Khairullin38, B. Khanji44, C. Khurewathanakul45, K.E. Kim63, T.
Kirn11, V.S. Kirsebom45, S. Klaver20, K. Klimaszewski33, T. Klimkovich13, S.
Koliiev48, M. Kolpin14, R. Kopecna14, P. Koppenburg29, I. Kostiuk29, S.
Kotriakhova41, M. Kozeiha7, L. Kravchuk37, M. Kreps52, F. Kress57, P.
Krokovny39,x, W. Krupa32, W. Krzemien33, W. Kucewicz31,l, M. Kucharczyk31, V.
Kudryavtsev39,x, A.K. Kuonen45, T. Kvaratskheliya35,44, D. Lacarrere44, G.
Lafferty58, A. Lai24, D. Lancierini46, G. Lanfranchi20, C. Langenbruch11, T.
Latham52, C. Lazzeroni49, R. Le Gac8, R. Lefèvre7, A. Leflat36, F. Lemaitre44,
O. Leroy8, T. Lesiak31, B. Leverington14, P.-R. Li4,ab, Y. Li5, Z. Li63, X.
Liang63, T. Likhomanenko72, R. Lindner44, F. Lionetto46, V. Lisovskyi9, G.
Liu66, X. Liu3, D. Loh52, A. Loi24, I. Longstaff55, J.H. Lopes2, G.H.
Lovell51, D. Lucchesi25,o, M. Lucio Martinez43, A. Lupato25, E. Luppi18,g, O.
Lupton44, A. Lusiani26, X. Lyu4, F. Machefert9, F. Maciuc34, V. Macko45, P.
Mackowiak12, S. Maddrell-Mander50, O. Maev41,44, K. Maguire58, D.
Maisuzenko41, M.W. Majewski32, S. Malde59, B. Malecki44, A. Malinin72, T.
Maltsev39,x, G. Manca24,f, G. Mancinelli8, D. Marangotto23,q, J. Maratas7,w,
J.F. Marchand6, U. Marconi17, C. Marin Benito9, M. Marinangeli45, P. Marino45,
J. Marks14, P.J. Marshall56, G. Martellotti28, M. Martinelli44, D. Martinez
Santos43, F. Martinez Vidal76, A. Massafferri1, M. Materok11, R. Matev44, A.
Mathad52, Z. Mathe44, C. Matteuzzi22, A. Mauri46, E. Maurice9,b, B. Maurin45,
M. McCann57,44, A. McNab58, R. McNulty15, J.V. Mead56, B. Meadows61, C.
Meaux8, N. Meinert70, D. Melnychuk33, M. Merk29, A. Merli23,q, E. Michielin25,
D.A. Milanes69, E. Millard52, M.-N. Minard6, L. Minzoni18,g, D.S. Mitzel14, A.
Mödden12, A. Mogini10, R.D. Moise57, T. Mombächer12, I.A. Monroy69, S.
Monteil7, M. Morandin25, G. Morello20, M.J. Morello26,t, O. Morgunova72, J.
Moron32, A.B. Morris8, R. Mountain63, F. Muheim54, M. Mukherjee68, M.
Mulder29, D. Müller44, J. Müller12, K. Müller46, V. Müller12, C.H. Murphy59,
D. Murray58, P. Naik50, T. Nakada45, R. Nandakumar53, A. Nandi59, T. Nanut45,
I. Nasteva2, M. Needham54, N. Neri23,q, S. Neubert14, N. Neufeld44, R.
Newcombe57, T.D. Nguyen45, C. Nguyen-Mau45,n, S. Nieswand11, R. Niet12, N.
Nikitin36, A. Nogay72, N.S. Nolte44, A. Oblakowska-Mucha32, V. Obraztsov40, S.
Ogilvy55, D.P. O’Hanlon17, R. Oldeman24,f, C.J.G. Onderwater71, A. Ossowska31,
J.M. Otalora Goicochea2, T. Ovsiannikova35, P. Owen46, A. Oyanguren76, P.R.
Pais45, T. Pajero26,t, A. Palano16, M. Palutan20, G. Panshin75, A.
Papanestis53, M. Pappagallo54, L.L. Pappalardo18,g, W. Parker62, C.
Parkes58,44, G. Passaleva19,44, A. Pastore16, M. Patel57, C. Patrignani17,e,
A. Pearce44, A. Pellegrino29, G. Penso28, M. Pepe Altarelli44, S. Perazzini44,
D. Pereima35, P. Perret7, L. Pescatore45, K. Petridis50, A. Petrolini21,h, A.
Petrov72, S. Petrucci54, M. Petruzzo23,q, B. Pietrzyk6, G. Pietrzyk45, M.
Pikies31, M. Pili59, D. Pinci28, J. Pinzino44, F. Pisani44, A. Piucci14, V.
Placinta34, S. Playfer54, J. Plews49, M. Plo Casasus43, F. Polci10, M. Poli
Lener20, A. Poluektov52, N. Polukhina73,c, I. Polyakov63, E. Polycarpo2, G.J.
Pomery50, S. Ponce44, A. Popov40, D. Popov49,13, S. Poslavskii40, E. Price50,
J. Prisciandaro43, C. Prouve43, V. Pugatch48, A. Puig Navarro46, H. Pullen59,
G. Punzi26,p, W. Qian4, J. Qin4, R. Quagliani10, B. Quintana7, N.V. Raab15, B.
Rachwal32, J.H. Rademacker50, M. Rama26, M. Ramos Pernas43, M.S. Rangel2, F.
Ratnikov38,74, G. Raven30, M. Ravonel Salzgeber44, M. Reboud6, F. Redi45, S.
Reichert12, F. Reiss10, C. Remon Alepuz76, Z. Ren3, V. Renaudin59, S.
Ricciardi53, S. Richards50, K. Rinnert56, P. Robbe9, A. Robert10, A.B.
Rodrigues45, E. Rodrigues61, J.A. Rodriguez Lopez69, M. Roehrken44, S.
Roiser44, A. Rollings59, V. Romanovskiy40, A. Romero Vidal43, M. Rotondo20,
M.S. Rudolph63, T. Ruf44, J. Ruiz Vidal76, J.J. Saborido Silva43, N.
Sagidova41, B. Saitta24,f, V. Salustino Guimaraes65, C. Sanchez Gras29, C.
Sanchez Mayordomo76, B. Sanmartin Sedes43, R. Santacesaria28, C. Santamarina
Rios43, M. Santimaria20,44, E. Santovetti27,j, G. Sarpis58, A. Sarti20,k, C.
Satriano28,s, A. Satta27, M. Saur4, D. Savrina35,36, S. Schael11, M.
Schellenberg12, M. Schiller55, H. Schindler44, M. Schmelling13, T.
Schmelzer12, B. Schmidt44, O. Schneider45, A. Schopper44, H.F. Schreiner61, M.
Schubiger45, S. Schulte45, M.H. Schune9, R. Schwemmer44, B. Sciascia20, A.
Sciubba28,k, A. Semennikov35, E.S. Sepulveda10, A. Sergi49, N. Serra46, J.
Serrano8, L. Sestini25, A. Seuthe12, P. Seyfert44, M. Shapkin40, Y.
Shcheglov41,†, T. Shears56, L. Shekhtman39,x, V. Shevchenko72, E. Shmanin73,
B.G. Siddi18, R. Silva Coutinho46, L. Silva de Oliveira2, G. Simi25,o, S.
Simone16,d, I. Skiba18, N. Skidmore14, T. Skwarnicki63, M.W. Slater49, J.G.
Smeaton51, E. Smith11, I.T. Smith54, M. Smith57, M. Soares17, l. Soares
Lavra1, M.D. Sokoloff61, F.J.P. Soler55, B. Souza De Paula2, B. Spaan12, E.
Spadaro Norella23,q, P. Spradlin55, F. Stagni44, M. Stahl14, S. Stahl44, P.
Stefko45, S. Stefkova57, O. Steinkamp46, S. Stemmle14, O. Stenyakin40, M.
Stepanova41, H. Stevens12, A. Stocchi9, S. Stone63, B. Storaci46, S.
Stracka26, M.E. Stramaglia45, M. Straticiuc34, U. Straumann46, S. Strokov75,
J. Sun3, L. Sun67, Y. Sun62, K. Swientek32, A. Szabelski33, T. Szumlak32, M.
Szymanski4, Z. Tang3, A. Tayduganov8, T. Tekampe12, G. Tellarini18, F.
Teubert44, E. Thomas44, M.J. Tilley57, V. Tisserand7, S. T’Jampens6, M.
Tobin32, S. Tolk44, L. Tomassetti18,g, D. Tonelli26, D.Y. Tou10, R. Tourinho
Jadallah Aoude1, E. Tournefier6, M. Traill55, M.T. Tran45, A. Trisovic51, A.
Tsaregorodtsev8, G. Tuci26,p, A. Tully51, N. Tuning29,44, A. Ukleja33, A.
Usachov9, A. Ustyuzhanin38,74, U. Uwer14, A. Vagner75, V. Vagnoni17, A.
Valassi44, S. Valat44, G. Valenti17, M. van Beuzekom29, E. van Herwijnen44, J.
van Tilburg29, M. van Veghel29, A. Vasiliev40, R. Vazquez Gomez44, P. Vazquez
Regueiro43, C. Vázquez Sierra29, S. Vecchi18, J.J. Velthuis50, M. Veltri19,r,
G. Veneziano59, A. Venkateswaran63, M. Vernet7, M. Veronesi29, M.
Vesterinen52, J.V. Viana Barbosa44, D. Vieira4, M. Vieites Diaz43, H.
Viemann70, X. Vilasis-Cardona42,m, A. Vitkovskiy29, M. Vitti51, V. Volkov36,
A. Vollhardt46, D. Vom Bruch10, B. Voneki44, A. Vorobyev41, V. Vorobyev39,x,
N. Voropaev41, R. Waldi70, J. Walsh26, J. Wang5, M. Wang3, Y. Wang68, Z.
Wang46, D.R. Ward51, H.M. Wark56, N.K. Watson49, D. Websdale57, A. Weiden46,
C. Weisser60, M. Whitehead11, G. Wilkinson59, M. Wilkinson63, I. Williams51,
M. Williams60, M.R.J. Williams58, T. Williams49, F.F. Wilson53, M. Winn9, W.
Wislicki33, M. Witek31, G. Wormser9, S.A. Wotton51, K. Wyllie44, D. Xiao68, Y.
Xie68, A. Xu3, M. Xu68, Q. Xu4, Z. Xu6, Z. Xu3, Z. Yang3, Z. Yang62, Y. Yao63,
L.E. Yeomans56, H. Yin68, J. Yu68,aa, X. Yuan63, O. Yushchenko40, K.A.
Zarebski49, M. Zavertyaev13,c, D. Zhang68, L. Zhang3, W.C. Zhang3,z, Y.
Zhang44, A. Zhelezov14, Y. Zheng4, X. Zhu3, V. Zhukov11,36, J.B. Zonneveld54,
S. Zucchelli17,e.

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
4University of Chinese Academy of Sciences, Beijing, China
5Institute Of High Energy Physics (ihep), Beijing, China
6Univ. Grenoble Alpes, Univ. Savoie Mont Blanc, CNRS, IN2P3-LAPP, Annecy,
France
7Université Clermont Auvergne, CNRS/IN2P3, LPC, Clermont-Ferrand, France
8Aix Marseille Univ, CNRS/IN2P3, CPPM, Marseille, France
9LAL, Univ. Paris-Sud, CNRS/IN2P3, Université Paris-Saclay, Orsay, France
10LPNHE, Sorbonne Université, Paris Diderot Sorbonne Paris Cité, CNRS/IN2P3,
Paris, France
11I. Physikalisches Institut, RWTH Aachen University, Aachen, Germany
12Fakultät Physik, Technische Universität Dortmund, Dortmund, Germany
13Max-Planck-Institut für Kernphysik (MPIK), Heidelberg, Germany
14Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg,
Germany
15School of Physics, University College Dublin, Dublin, Ireland
16INFN Sezione di Bari, Bari, Italy
17INFN Sezione di Bologna, Bologna, Italy
18INFN Sezione di Ferrara, Ferrara, Italy
19INFN Sezione di Firenze, Firenze, Italy
20INFN Laboratori Nazionali di Frascati, Frascati, Italy
21INFN Sezione di Genova, Genova, Italy
22INFN Sezione di Milano-Bicocca, Milano, Italy
23INFN Sezione di Milano, Milano, Italy
24INFN Sezione di Cagliari, Monserrato, Italy
25INFN Sezione di Padova, Padova, Italy
26INFN Sezione di Pisa, Pisa, Italy
27INFN Sezione di Roma Tor Vergata, Roma, Italy
28INFN Sezione di Roma La Sapienza, Roma, Italy
29Nikhef National Institute for Subatomic Physics, Amsterdam, Netherlands
30Nikhef National Institute for Subatomic Physics and VU University Amsterdam,
Amsterdam, Netherlands
31Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of
Sciences, Kraków, Poland
32AGH - University of Science and Technology, Faculty of Physics and Applied
Computer Science, Kraków, Poland
33National Center for Nuclear Research (NCBJ), Warsaw, Poland
34Horia Hulubei National Institute of Physics and Nuclear Engineering,
Bucharest-Magurele, Romania
35Institute of Theoretical and Experimental Physics NRC Kurchatov Institute
(ITEP NRC KI), Moscow, Russia, Moscow, Russia
36Institute of Nuclear Physics, Moscow State University (SINP MSU), Moscow,
Russia
37Institute for Nuclear Research of the Russian Academy of Sciences (INR RAS),
Moscow, Russia
38Yandex School of Data Analysis, Moscow, Russia
39Budker Institute of Nuclear Physics (SB RAS), Novosibirsk, Russia
40Institute for High Energy Physics NRC Kurchatov Institute (IHEP NRC KI),
Protvino, Russia, Protvino, Russia
41Petersburg Nuclear Physics Institute NRC Kurchatov Institute (PNPI NRC KI),
Gatchina, Russia , St.Petersburg, Russia
42ICCUB, Universitat de Barcelona, Barcelona, Spain
43Instituto Galego de Física de Altas Enerxías (IGFAE), Universidade de
Santiago de Compostela, Santiago de Compostela, Spain
44European Organization for Nuclear Research (CERN), Geneva, Switzerland
45Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL),
Lausanne, Switzerland
46Physik-Institut, Universität Zürich, Zürich, Switzerland
47NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine
48Institute for Nuclear Research of the National Academy of Sciences (KINR),
Kyiv, Ukraine
49University of Birmingham, Birmingham, United Kingdom
50H.H. Wills Physics Laboratory, University of Bristol, Bristol, United
Kingdom
51Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom
52Department of Physics, University of Warwick, Coventry, United Kingdom
53STFC Rutherford Appleton Laboratory, Didcot, United Kingdom
54School of Physics and Astronomy, University of Edinburgh, Edinburgh, United
Kingdom
55School of Physics and Astronomy, University of Glasgow, Glasgow, United
Kingdom
56Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom
57Imperial College London, London, United Kingdom
58School of Physics and Astronomy, University of Manchester, Manchester,
United Kingdom
59Department of Physics, University of Oxford, Oxford, United Kingdom
60Massachusetts Institute of Technology, Cambridge, MA, United States
61University of Cincinnati, Cincinnati, OH, United States
62University of Maryland, College Park, MD, United States
63Syracuse University, Syracuse, NY, United States
64Laboratory of Mathematical and Subatomic Physics , Constantine, Algeria,
associated to 2
65Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), Rio de
Janeiro, Brazil, associated to 2
66South China Normal University, Guangzhou, China, associated to 3
67School of Physics and Technology, Wuhan University, Wuhan, China, associated
to 3
68Institute of Particle Physics, Central China Normal University, Wuhan,
Hubei, China, associated to 3
69Departamento de Fisica , Universidad Nacional de Colombia, Bogota, Colombia,
associated to 10
70Institut für Physik, Universität Rostock, Rostock, Germany, associated to 14
71Van Swinderen Institute, University of Groningen, Groningen, Netherlands,
associated to 29
72National Research Centre Kurchatov Institute, Moscow, Russia, associated to
35
73National University of Science and Technology “MISIS”, Moscow, Russia,
associated to 35
74National Research University Higher School of Economics, Moscow, Russia,
associated to 38
75National Research Tomsk Polytechnic University, Tomsk, Russia, associated to
35
76Instituto de Fisica Corpuscular, Centro Mixto Universidad de Valencia -
CSIC, Valencia, Spain, associated to 42
77University of Michigan, Ann Arbor, United States, associated to 63
78Los Alamos National Laboratory (LANL), Los Alamos, United States, associated
to 63

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, Vietnam
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
vH.H. Wills Physics Laboratory, University of Bristol, Bristol, United Kingdom
wMSU - Iligan Institute of Technology (MSU-IIT), Iligan, Philippines
xNovosibirsk State University, Novosibirsk, Russia
ySezione INFN di Trieste, Trieste, Italy
zSchool of Physics and Information Technology, Shaanxi Normal University
(SNNU), Xi’an, China
aaPhysics and Micro Electronic College, Hunan University, Changsha City, China
abLanzhou University, Lanzhou, China
†Deceased