EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 CERN-EP-2016-086 LHCb-PAPER-2016-009 April 19, 2016

Model-independent evidence for $J/\psi p$ contributions to ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow J/\psi pK^{-}$ decays

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

The data sample of ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}pK^{-}$ decays acquired with the LHCb detector from 7 and 8 TeV $pp$
collisions, corresponding to an integrated luminosity of 3 $\mbox{\,fb}^{-1}$,
is inspected for the presence of ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}p$ or ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}K^{-}$
contributions with minimal assumptions about $K^{-}p$ contributions. It is
demonstrated at more than 9 standard deviations that ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}pK^{-}$ decays cannot be described with $K^{-}p$ contributions alone,
and that ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}p$ contributions play
a dominant role in this incompatibility. These model-independent results
support the previously obtained model-dependent evidence for
$P_{c}^{+}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}p$
charmonium-pentaquark states in the same data sample.

Submitted to Physical Review Letters

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

From the birth of the quark model, it has been anticipated that baryons could
be constructed not only from three quarks, but also from four quarks and an
antiquark [1, 2], hereafter referred to as pentaquarks. The distribution of
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}p$ mass
($m_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}p}$) in ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}pK^{-}$, ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\rightarrow\mu^{+}\mu^{-}$ decays observed with the LHCb detector at
the LHC shows a narrow peak suggestive of $uudc\bar{c}$ pentaquark formation,
amidst the dominant formation of various excitations of the ${\mathchar
28931\relax}$ $[uds]$ baryon (${{\mathchar 28931\relax}^{*}}$) decaying to
$K^{-}p$ [3]. (The inclusion of charge conjugate states is implied in this
Letter.) Amplitude analyses were performed on all relevant masses and decay
angles of the six-dimensional (6D) data, using the helicity formalism and
Breit-Wigner amplitudes to describe all resonances. In addition to the
previously well established ${{\mathchar 28931\relax}^{*}}$ resonances, two
pentaquark resonances $P_{c}(4380)^{+}$ ($9\,\sigma$ significance) and
$P_{c}(4450)^{+}$ ($12\,\sigma$) were required in the model for a good
description of the data. The mass, width and fit fractions were determined to
be $4380\pm 8\pm 29$$\mathrm{\,Me\kern-1.00006ptV}$, $205\pm 18\pm
86$$\mathrm{\,Me\kern-1.00006ptV}$, $(8.4\pm 0.7\pm 4.3)\%$, and $4450\pm 2\pm
3$$\mathrm{\,Me\kern-1.00006ptV}$, $39\pm 5\pm
19$$\mathrm{\,Me\kern-1.00006ptV}$, $(4.1\pm 0.5\pm 1.1)\%$, respectively.

The addition of further ${{\mathchar 28931\relax}^{*}}$ states beyond the
well-established ones, and of nonresonant contributions, did not remove the
need for two pentaquark states in the model to describe the data. Yet
${{\mathchar 28931\relax}^{*}}$ spectroscopy is a complex problem, as pointed
out in a recent reanalysis of $\overline{K}N$ scattering data [4], in which
the well-established ${\mathchar 28931\relax}(1800)$ state was not seen, and
evidence for a few previously unidentified states was obtained. Theoretical
models of ${{\mathchar 28931\relax}^{*}}$ baryons [5, 6, 7, 8, 9, 10] predict
a much larger number of higher mass excitations than is established
experimentally [11]. The high density of predicted states, presumably with
large widths, would make it difficult to identify them experimentally.
Nonresonant contributions with non-trivial $K^{-}p$ mass-dependence may also
be present. Therefore, it is worth inspecting the ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}pK^{-}$ data with an approach that is model-independent with respect to
$K^{-}p$ contributions. Such a method was introduced by the BaBar
collaboration [12] and later improved upon by the LHCb collaboration [13].
There it was used to examine $B^{0}\rightarrow\psi(2S)\pi^{+}K^{-}$ decays,
which are dominated by kaon excitations decaying to $K^{-}\pi^{+}$, in order
to understand whether the data require the presence of the tetraquark
candidate decay, $Z(4430)^{+}\rightarrow\psi(2S)\pi^{+}$. In this Letter, this
method is applied to the same ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}pK^{-}$ sample previously analyzed in the amplitude analysis [3]. The
sensitivity of the model-independent approach to exotic resonances is
investigated with simulation studies.

The LHCb detector is a single-arm forward spectrometer covering the
pseudorapidity range $2<\eta<5$, described in detail in Ref. [14]. The data
selection is described in Ref. [3]. A mass window of $\pm 2\,\sigma$
($\sigma=7.5$ MeV) around the ${{\mathchar 28931\relax}^{0}_{b}}$ mass peak is
selected, leaving $n_{\rm cand}^{\rm sig}=27\,469$ ${\mathchar
28931\relax}^{0}_{b}$ candidates for further analysis, with background
fraction ($\beta$) equal to 5.4%. The background is subtracted using $n_{\rm
cand}^{\rm side}=10\,259$ candidates from the ${{\mathchar
28931\relax}^{0}_{b}}$ sidebands, which extend from $\pm 38$ to $\pm
140\mathrm{\,Me\kern-1.00006ptV}$ from the peak (see the supplemental
material).

The aim of this analysis is to assess the level of consistency of the data
with the hypothesis that all ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}pK^{-}$ decays proceed via ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{\mathchar 28931\relax}^{*}}$, ${{\mathchar
28931\relax}^{*}}\rightarrow pK^{-}$, with minimal assumptions about the spin
and lineshape of possible ${{\mathchar 28931\relax}^{*}}$ contributions. This
will be referred to as the null-hypothesis $H_{0}$. Here, ${{\mathchar
28931\relax}^{*}}$ denotes not only excitations of the ${\mathchar
28931\relax}$ baryon, but also nonresonant $K^{-}p$ contributions or
excitations of the ${\mathchar 28934\relax}$ baryon. The latter contributions
are expected to be small[15]. The analysis method is two-dimensional and uses
the information contained in the Dalitz variables,
$(m_{Kp}^{2},m_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}p}^{2})$, or
equivalently in $(m_{Kp},\cos\theta_{{{\mathchar 28931\relax}^{*}}})$, where
$\theta_{{{\mathchar 28931\relax}^{*}}}$ is the helicity angle of the $K^{-}p$
system, defined as the angle between the $\vec{p}_{K}$ and
$-\vec{p}_{{{\mathchar 28931\relax}^{0}_{b}}}$ (or
$-\vec{p}_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}}$) directions in the
$K^{-}p$ rest frame.

The $(m_{Kp},\cos\theta_{{{\mathchar 28931\relax}^{*}}})$ plane is
particularly suited for implementing constraints stemming from the $H_{0}$
hypothesis by expanding the $\cos\theta_{{{\mathchar 28931\relax}^{*}}}$
angular distribution in Legendre polynomials $P_{l}$:

$dN/d\cos\theta_{{{\mathchar 28931\relax}^{*}}}=\sum_{l=0}^{l_{\rm
max}}\langle P_{l}^{U}\rangle P_{l}(\cos\theta_{{{\mathchar
28931\relax}^{*}}}),$

where $N$ is the efficiency-corrected and background-subtracted signal yield,
and $\langle P_{l}^{U}\rangle$ is an unnormalized Legendre moment of rank $l$,

$\langle P_{l}^{U}\rangle=\int_{-1}^{+1}d\cos\theta_{{{\mathchar
28931\relax}^{*}}}\,P_{l}(\cos\theta_{{{\mathchar
28931\relax}^{*}}})\,dN/d\cos\theta_{{{\mathchar 28931\relax}^{*}}}.$

Under the $H_{0}$ hypothesis, $K^{-}p$ components cannot contribute to moments
of rank higher than $2\,J_{\rm max}$, where $J_{\rm max}$ is the highest spin
of any $K^{-}p$ contribution at the given $m_{Kp}$ value. This requirement
sets the appropriate $l_{\rm max}$ value, which can be deduced from the
lightest experimentally known ${{\mathchar 28931\relax}^{*}}$ resonances for
each $J$, or from the quark model, as in Fig. 1.

Figure 1: Excitations of the ${\mathchar 28931\relax}$ baryon. States
predicted in Ref. [7] are shown as short horizontal bars (black) and
experimentally well-established ${{\mathchar 28931\relax}^{*}}$ states are
shown as green boxes covering the mass ranges from $M_{0}-\Gamma_{0}$ to
$M_{0}+\Gamma_{0}$. The $m_{Kp}$ mass range probed in ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}p{{K}^{-}}$ decays is shown by long horizontal lines (blue). The
$l_{\rm max}(m_{Kp})$ filter is shown as a stepped line (red). All
contributions from ${{\mathchar 28931\relax}^{*}}$ states with $J^{P}$ values
to the left of the red line are accepted by the filter. The filter works well
also for the excitations of the ${\mathchar 28934\relax}$ baryon [11, 7] (not
shown).

An $l_{\rm max}(m_{Kp})$ function is formed, guided by the values of resonance
masses ($M_{0}$) lowered by two units of their widths ($\Gamma_{0}$): $l_{\rm
max}=3$ for $m_{Kp}$ up to $1.64$ $\mathrm{\,Ge\kern-1.00006ptV}$, 5 up to
$1.70$ $\mathrm{\,Ge\kern-1.00006ptV}$, 7 up to $2.05$
$\mathrm{\,Ge\kern-1.00006ptV}$ and 9 for higher masses as visualized in Fig.
1.

Reflections from other channels, ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow
P_{c}^{+}K^{-}$, $P_{c}^{+}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}p$ or ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow Z_{c}^{-}p$,
$Z_{c}^{-}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}K^{-}$,
would introduce both low and high rank moments (see the supplemental material
for an illustration). The narrower the resonance, the narrower the reflection
and the higher the rank $l$ of Legendre polynomials required to describe such
a structure.

Selection criteria and backgrounds can also produce high-$l$ structures in the
$\cos\theta_{{{\mathchar 28931\relax}^{*}}}$ distribution. Therefore, the data
are efficiency-corrected and the background is subtracted. Even though testing
the $H_{0}$ hypothesis involves only two dimensions, the selection efficiency
has some dependence on the other phase-space dimensions, namely the
${{\mathchar 28931\relax}^{0}_{b}}$ and
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}$ helicity angles, as well as
angles between the ${{\mathchar 28931\relax}^{0}_{b}}$ decay plane and the
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}$ and ${{\mathchar
28931\relax}^{*}}$ decay planes. Averaging the efficiency over these
additional dimensions ($\Omega_{a}$) would introduce biases dependent on the
exact dynamics of the ${{\mathchar 28931\relax}^{*}}$ decays. Therefore, a
six-dimensional efficiency correction is used. The efficiency
parameterization, $\epsilon(m_{Kp},\cos\theta_{{{\mathchar
28931\relax}^{*}}},\Omega_{a})$, is the same as that used in the amplitude
analysis and is described in Sec. 5 of the supplement of Ref. [3].

In order to make the analysis as model-independent as possible, no
interpretations are imposed on the $m_{Kp}$ distribution. Instead, the
observed efficiency-corrected and background-subtracted histogram of $m_{Kp}$
is used. To obtain a continuous probability density function, ${\cal
F}(m_{Kp}|H_{0})$, a quadratic interpolation of the histogram is performed, as
shown in Fig. 2. The essential part of this analysis method is to incorporate
the $l\leq l_{\rm max}(m_{Kp})$ constraint on the ${{\mathchar
28931\relax}^{*}}$ helicity angle distribution: ${\cal
F}(m_{Kp},\cos\theta_{{{\mathchar 28931\relax}^{*}}}|H_{0})={\cal
F}(m_{Kp}|H_{0})\,{\cal F}(\cos\theta_{{{\mathchar
28931\relax}^{*}}}|H_{0},m_{Kp})$, where ${\cal F}(\cos\theta_{{{\mathchar
28931\relax}^{*}}}|H_{0},m_{Kp})$ is obtained via linear interpolation between
neighboring $m_{Kp}$ bins of

${\cal F}(\cos\theta_{{{\mathchar
28931\relax}^{*}}}|H_{0},{m_{Kp}}^{k})=\sum_{l=0}^{l_{\rm
max}({m_{Kp}}^{k})}\langle P_{l}^{N}\rangle^{k}P_{l}(\cos\theta_{{{\mathchar
28931\relax}^{*}}}),$

where $k$ is the bin index. Here the Legendre moments $\langle
P_{l}^{N}\rangle^{k}$ are normalized by the yield in the corresponding
$m_{Kp}$ bin, since the overall normalization of ${\cal
F}(\cos\theta_{{{\mathchar 28931\relax}^{*}}}|H_{0},m_{Kp})$ to the data is
already contained in the ${\cal F}(m_{Kp}|H_{0})$ definition. The data are
used to determine

$\langle P_{l}^{U}\rangle^{k}=\sum_{i=1}^{{n_{\rm
cand}}^{k}}(w_{i}/\epsilon_{i})P_{l}(\cos\theta_{{{\mathchar
28931\relax}^{*}}}^{i}).$

Here the index $i$ runs over selected ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}pK^{-}$ candidates in the signal and sideband regions for the $k^{th}$
bin of $m_{Kp}$ (${n_{\rm cand}}^{k}$ is their total number),
$\epsilon_{i}=\epsilon({m_{Kp}}^{i},\cos{\theta_{{{\mathchar
28931\relax}^{*}}}}^{i},{\Omega_{a}}^{i})$ is the efficiency correction, and
$w_{i}$ is the background subtraction weight, which equals 1 for events in the
signal region and $-\beta\,n_{\rm cand}^{\rm sig}/n_{\rm cand}^{\rm side}$ for
events in the sideband region. Values of $\langle P_{l}^{U}\rangle^{k}$ are
shown in Fig. 3.

Figure 2: Efficiency-corrected and background-subtracted $m_{Kp}$ distribution
of the data (black points with error bars), with ${\cal F}(m_{Kp}|H_{0})$
superimposed (solid blue line). ${\cal F}(m_{Kp}|H_{0})$ fits the data by
construction.  Figure 3: Legendre moments of $\cos\theta_{{{\mathchar
28931\relax}^{*}}}$ as a function of $m_{Kp}$ in the data. Regions excluded by
the $l\leq l_{\rm max}(m_{Kp})$ filter are shaded.

Instead of using the two-dimensional (2D) distribution of
$(m_{Kp},\cos\theta_{{{\mathchar 28931\relax}^{*}}})$ to evaluate the
consistency of the data with the $H_{0}$ hypothesis, now expressed by the
$l\leq l_{\rm max}(m_{Kp})$ requirement, it is more convenient to use the
$m_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}p}$
($m_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}K}$) distribution, as any
deviations from $H_{0}$ should appear in the mass region of potential
pentaquark (tetraquark) resonances. The projection of ${\cal
F}(m_{Kp},\cos\theta_{{{\mathchar 28931\relax}^{*}}}|H_{0})$ onto
$m_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}p}$ involves replacing
$\cos\theta_{{{\mathchar 28931\relax}^{*}}}$ with
$m_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}p}$ and integrating over
$m_{Kp}$. This integration is carried out numerically, by generating large
numbers of simulated events uniformly distributed in $m_{Kp}$ and
$\cos\theta_{{{\mathchar 28931\relax}^{*}}}$, calculating the corresponding
value of $m_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}p}$, and then
filling a histogram with ${\cal F}(m_{Kp},\cos\theta_{{{\mathchar
28931\relax}^{*}}}|H_{0})$ as a weight. In Fig. 4, ${\cal
F}({m_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}p}}|H_{0})$ is compared
to the directly obtained efficiency-corrected and background-subtracted
$m_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}p}$ distribution in the
data.

Figure 4: Efficiency-corrected and background-subtracted
$m_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}p}$ distribution of the data
(black points with error bars), with ${\cal
F}(m_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}p}|H_{0})$ (solid blue
line) and ${\cal F}(m_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}p}|H_{1})$ (dashed black line) superimposed.

To probe the compatibility of ${\cal
F}(m_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}p}|H_{0})$ with the data,
a sensitive test can be constructed by making a specific alternative
hypothesis ($H_{1}$). Following the method discussed in Ref. [13] $H_{1}$ is
defined as $l\leq l_{\rm large}$, where $l_{\rm large}$ is not dependent on
$m_{Kp}$ and large enough to reproduce structures induced by
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}p$ or
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}K$ contributions. The
significance of the $l_{\rm max}(m_{Kp})\leq l\leq l_{\rm large}$ Legendre
moments is probed using the likelihood ratio test:

${\Delta(\\!-2\ln L\\!)}=\sum_{i=1}^{n_{\rm cand}^{\rm sig}+n_{\rm cand}^{\rm
side}}w_{i}\ln\frac{{\cal F}({m_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}p}}^{i}|H_{0})/I_{H_{0}}}{{\cal
F}({m_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}p}}^{i}|H_{1})/I_{H_{1}}},$

with normalizations $I_{H_{0,1}}$ determined via Monte Carlo integration. Note
that the explicit event-by-event efficiency factor cancels in the likelihood
ratio, but enters the likelihood normalizations. In order for the test to have
optimal sensitivity, the value $l_{\rm large}$ should be set such that the
statistically significant features of the data are properly described. Beyond
that the power of the test deteriorates. The limit $l_{\rm
large}\rightarrow\infty$ would result in a perfect description of the data,
but a weak test since then the test statistic would pick up the fluctuations
in the data. For the same reason it is also important to choose $l_{\rm
large}$ independently of the actual data. Here $l_{\rm large}=31$ is taken,
one unit larger than the value used in the model-independent analysis of
$B^{0}\rightarrow\psi(2S)\pi^{+}K^{-}$ [13], as baryons have half-integer
spins. The result for ${\cal F}(m_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}p}|H_{1})$ is shown in Fig. 4, where it is seen that $l_{\rm large}=31$
is sufficient. To make ${\cal F}(m_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}p}|H_{0,1})$ continuous, quadratic splines are used to interpolate
between nearby $m_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}p}$ bins.

The numerical representations of $H_{0}$ and of $H_{1}$ contain a large number
of parameters, requiring extensive statistical simulations to determine the
distribution of the test variable for the $H_{0}$ hypothesis: ${\cal
F}_{t}({\Delta(\\!-2\ln L\\!)}|H_{0})$. A large number of pseudoexperiments
are generated with $n_{\rm cand}^{\rm sig}$ and $n_{\rm cand}^{\rm side}$
equal to those obtained in the data. The signal events, contributing a
fraction $(1-\beta)$ to the signal region sample, are generated according to
the ${\cal F}(m_{Kp},\cos\theta_{{{\mathchar 28931\relax}^{*}}}|H_{0})$
function with parameters determined from the data. They are then shaped
according to the $\epsilon(m_{Kp},\cos\theta_{{{\mathchar
28931\relax}^{*}}},\Omega_{a})$ function, with the $\Omega_{a}$ angles
generated uniformly in phase space. The latter is an approximation, whose
possible impact is discussed later. Background events in sideband and signal
regions are generated according to the 6D background parameterization
previously developed in the amplitude analysis of the same data (Ref. [3]
supplement). The pseudoexperiments are subject to the same analysis procedure
as the data. The distribution of values of ${\Delta(\\!-2\ln L\\!)}$ over more
than 10 000 pseudoexperiments determines the form of ${\cal
F}_{t}({\Delta(\\!-2\ln L\\!)}|H_{0})$, which can then be used to convert the
${\Delta(\\!-2\ln L\\!)}$ value obtained from data into a corresponding
$p$-value. A small $p$-value indicates non-${{\mathchar 28931\relax}^{*}}$
contributions in the data. A large $p$-value means that the data are
consistent with the ${{\mathchar 28931\relax}^{*}}$-only hypothesis, but does
not rule out other contributions.

Before applying this method to the data, it is useful to study its sensitivity
with the help of amplitude models. Pseudoexperiments are generated according
to the 6D amplitude model containing only ${{\mathchar 28931\relax}^{*}}$
resonances (the reduced model in Table 1 of Ref. [3]), along with efficiency
effects. The distribution of ${\Delta(\\!-2\ln L\\!)}$ values is close to that
expected from ${\cal F}_{t}({\Delta(\\!-2\ln L\\!)}|H_{0})$ (black open and
red falling hatched histograms in Fig. 5), thus verifying the 2D model-
independent procedure on one example of the ${{\mathchar 28931\relax}^{*}}$
model. They also indicate that the non-uniformities in $\epsilon(\Omega_{a})$
are small enough not to significantly bias the ${\cal F}_{t}({\Delta(\\!-2\ln
L\\!)}|H_{0})$ distribution when approximating the $\Omega_{a}$ probability
density via a uniform distribution. To test the sensitivity of the method to
an exotic $P_{c}^{+}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}p$ resonance, the amplitude model described in Ref. [3] is used, but
with the $P_{c}(4450)^{+}$ contribution removed. Generating many
pseudoexperiments from this amplitude model produces a distribution of
${\Delta(\\!-2\ln L\\!)}$, which is almost indistinguishable from the ${\cal
F}_{t}({\Delta(\\!-2\ln L\\!)}|H_{0})$ distribution (blue dotted and red
falling hatched histograms in Fig. 5), thus predicting that for such a broad
$P_{c}(4380)^{+}$ resonance ($\Gamma_{0}=205$ $\mathrm{\,Me\kern-1.00006ptV}$)
the false $H_{0}$ hypothesis is expected to be accepted (type II error),
because the $P_{c}(4380)^{+}$ contribution inevitably feeds into the numerical
representation of $H_{0}$. Simulations are then repeated while reducing the
$P_{c}(4380)^{+}$ width by subsequent factors of two, showing a dramatic
increase in the power of the test (histograms peaking at 60 and 300). Figure 5
also shows the ${\Delta(\\!-2\ln L\\!)}$ distribution obtained with the narrow
$P_{c}(4450)^{+}$ state restored in the amplitude model and $P_{c}(4380)^{+}$
at its nominal $205$ $\mathrm{\,Me\kern-1.00006ptV}$ width (black rising
hatched histogram). The separation from ${\cal F}_{t}({\Delta(\\!-2\ln
L\\!)}|H_{0})$ is smaller than that of the simulation with a $P_{c}(4380)^{+}$
of comparable width ($51\mathrm{\,Me\kern-1.00006ptV}$) due to the smaller
$P_{c}(4450)^{+}$ fit fraction.

Figure 5: Distributions of ${\Delta(\\!-2\ln L\\!)}$ in the model-independent
pseudoexperiments corresponding to $H_{0}$ (red falling hatched) compared to
the distributions for pseudoexperiments generated from various amplitude
models and, in the inset, to the bifurcated Gaussian fit function (solid line)
and the value obtained for the data (vertical bar).

Nevertheless, the separation from ${\cal F}_{t}({\Delta(\\!-2\ln
L\\!)}|H_{0})$ is clear; thus, if this amplitude model is a good
representation of the data, the $H_{0}$ hypothesis is expected to essentially
always be rejected.

The value of the ${\Delta(\\!-2\ln L\\!)}$ test variable obtained from the
data is significantly above the ${\cal F}_{t}({\Delta(\\!-2\ln L\\!)}|H_{0})$
distribution (see the inset of Fig. 5). To estimate a $p$-value the simulated
${\cal F}_{t}({\Delta(\\!-2\ln L\\!)}|H_{0})$ distribution is fitted with a
bifurcated Gaussian function (asymmetric widths); the significance of the
$H_{0}$ rejection is $10.1\,\sigma$ standard deviations.

To test the sensitivity of the result to possible biases from the background
subtraction, either the left or the right sideband is exclusively used, and
the weakest obtained rejection of $H_{0}$ is $9.8\,\sigma$. As a further
check, the sideband subtraction is performed with the sPlot technique [16], in
which the $w_{i}$ weights are obtained from the fit to the
$m_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}pK}$ distribution for
candidates in the entire fit range. This increases the significance of the
$H_{0}$ rejection to $10.4\,\sigma$. Loosening the cut on the boosted decision
tree variable discussed in Ref. [3] increases the signal efficiency by 14%,
while doubling the background fraction $\beta$, and causes the significance of
the $H_{0}$ rejection to increase to $11.1\,\sigma$. Replacing the uniform
generation of the $\Omega_{a}$ angles in the $H_{0}$ pseudoexperiments with
that of the amplitude model without the $P_{c}(4380)^{+}$ and
$P_{c}(4450)^{+}$ states, but generating $(m_{Kp},\cos\theta_{{{\mathchar
28931\relax}^{*}}})$ in the model-independent way, results in a $9.9\,\sigma$
$H_{0}$ rejection.

Figure 6: Efficiency-corrected and background-subtracted
$m_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}K}$ distribution of the data
(black points with error bars), with ${\cal
F}(m_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}K}|H_{0})$ (solid blue
line) and ${\cal F}(m_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}K}|H_{1})$ (dashed black line) superimposed.

Figure 4 indicates that the rejection of the $H_{0}$ hypothesis has to do with
a narrow peak in the data near $4450$ $\mathrm{\,Me\kern-1.00006ptV}$.
Determination of any $P_{c}^{+}$ parameters is not possible without a model-
dependent analysis, because $P_{c}^{+}$ states feed into the numerical
representation of $H_{0}$ in an intractable manner.

The $H_{0}$ testing is repeated using
$m_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}K}$ instead of
$m_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}p}$. The
$m_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}K}$ distribution, with
${\cal F}(m_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}K}|H_{0})$ and
${\cal F}(m_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}K}|H_{1})$
superimposed, is shown in Fig. 6. The ${\Delta(\\!-2\ln L\\!)}$ test gives a
$5.3\,\sigma$ rejection of $H_{0}$, which is lower than the rejection obtained
using $m_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}p}$, thus providing
model-independent evidence that non-${{\mathchar 28931\relax}^{*}}$
contributions are more likely of the
$P_{c}^{+}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}p$ type.
Further, in the model-dependent amplitude analysis [3], it was seen that the
$P_{c}$ states reflected into the $m_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}K}$ distribution in the region in which ${\cal
F}(m_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}K}|H_{0})$ disagrees with
the data.

In summary, it has been demonstrated at more than $9$ standard deviations that
the ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}pK^{-}$ decays cannot all be attributed to $K^{-}p$ resonant or
nonresonant contributions. The analysis requires only minimal assumptions on
the mass and spin of the $K^{-}p$ contributions; no assumptions on their
number, their resonant or nonresonant nature, or their lineshapes have been
made. Non-$K^{-}p$ contributions, which must be present in the data, can be
either of the exotic hadron type, or due to rescattering effects among
ordinary hadrons. This result supports the amplitude model-dependent
observation of the ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}p$
resonances presented previously [3].

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 FANO (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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## Appendix: Supplemental material

##  1 Data sample

The definition of the signal and sideband regions is illustrated in Fig. 7.
The background-subtracted and efficiency-corrected distribution of the data on
the rectangular Dalitz plane $(m_{Kp},\cos\theta_{{{\mathchar
28931\relax}^{*}}})$ is shown in Fig. 8.

Figure 7: Distribution of $m_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}pK}$ in the data with the fit of signal and background components
superimposed [3]. The fit is used to determine the background fraction $\beta$
in the $\pm 2\sigma$ signal region around the ${{\mathchar
28931\relax}^{0}_{b}}$ peak (shown by the vertical red bars). The sidebands
used in the background subtraction are also shown.  Figure 8:  Background-
subtracted and efficiency-corrected distribution of the cosine of the
${{\mathchar 28931\relax}^{*}}$ helicity angle versus $m_{Kp}$ for the data.

##  2 Simulations based on amplitude models

The rectangular Dalitz plane $(m_{Kp},\cos\theta_{{{\mathchar
28931\relax}^{*}}})$ distributions for the large statistics pseudo-samples
generated from the amplitude model with only the ${{\mathchar
28931\relax}^{*}}$ resonances and from the amplitude model with only the
$P_{c}(4380)^{+}$ and $P_{c}(4450)^{+}$ resonances are shown in Figs. 9 and
10, respectively. Parameters of the models, without and with the $P_{c}^{+}$
states, were determined by fitting the amplitude models to the data as
described in Ref. [3].

The Legendre moments of $\cos\theta_{{{\mathchar 28931\relax}^{*}}}$
distributions ($\langle P_{l}^{U}\rangle^{k}$) in various bins of $m_{Kp}$ are
compared between these two simulated pseudo-samples in Fig. 11. The $l\leq
l_{\rm max}(m_{Kp})$ filter, used in forming a numerical representation of the
hypothesis that only $K^{-}p$ contributions are present ($H_{0}$), is also
illustrated in Fig. 11: moments in the shaded regions ($l>l_{\rm
max}(m_{Kp})$) are neglected. The pentaquark resonances can induce significant
values of the moments in these regions, as illustrated with the example
amplitude model containing only $P_{c}^{+}$ states. The $P_{c}^{+}$ states
also contribute significantly to the unshaded $l\leq l_{\rm max}(m_{Kp})$
regions, thus feeding into the numerical representation of the $H_{0}$
hypothesis, and decreasing the sensitivity of the model-independent approach
to exotic hadron contributions. This is especially true for wide resonances,
which contribute very little to high moments, as illustrated for the
$P_{c}(4380)^{+}$ state in Fig. 12. The example amplitude model with only
${{\mathchar 28931\relax}^{*}}$ resonances contributes to the unshaded regions
only, as expected.

Figure 9:  Distribution in a pseudoexperiment of the cosine of the
${{\mathchar 28931\relax}^{*}}$ helicity angle versus $m_{Kp}$ for the
amplitude model with ${{\mathchar 28931\relax}^{*}}$ resonances only.  Figure
10:  Distribution in a pseudoexperiment of the cosine of the ${{\mathchar
28931\relax}^{*}}$ helicity angle versus $m_{Kp}$ for the amplitude model with
the $P_{c}(4380)^{+}$ and $P_{c}(4450)^{+}$ resonances only.  Figure 11:
Legendre moments of $\cos\theta_{{{\mathchar 28931\relax}^{*}}}$ as a function
of $m_{Kp}$ for the simulated data from the amplitude models with only
${{\mathchar 28931\relax}^{*}}$ (solid blue lines) and with only
$P_{c}(4380)^{+}$, $P_{c}(4450)^{+}$ contributions (dashed red lines), scaled
by $0.5$. The regions excluded by the $l\leq l_{\rm max}(m_{Kp})$ filter are
shaded.  Figure 12: Legendre moments of $\cos\theta_{{{\mathchar
28931\relax}^{*}}}$ as a function of $m_{Kp}$ for the simulated data from
amplitude models with only $P_{c}(4380)^{+}$ (solid blue lines) and only
$P_{c}(4450)^{+}$ contributions (dashed red line).

LHCb collaboration

R. Aaij39, C. Abellán Beteta41, 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.
An3,40, L. Anderlini18, G. Andreassi40, M. Andreotti17,g, J.E. Andrews59, R.B.
Appleby55, O. Aquines Gutierrez11, F. Archilli39, P. d’Argent12, A.
Artamonov36, M. Artuso60, E. Aslanides6, G. Auriemma26,n, M. Baalouch5, S.
Bachmann12, J.J. Back49, A. Badalov37, C. Baesso61, S. Baker54, W. Baldini17,
R.J. Barlow55, C. Barschel39, S. Barsuk7, W. Barter39, V. Batozskaya29, V.
Battista40, A. Bay40, L. Beaucourt4, J. Beddow52, F. Bedeschi24, I. Bediaga1,
L.J. Bel42, V. Bellee40, N. Belloli21,k, 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, S. Bifani46, P.
Billoir8, T. Bird55, A. Birnkraut10, A. Bizzeti18,i, T. Blake49, F. Blanc40,
J. Blouw11, S. Blusk60, V. Bocci26, A. Bondar35, N. Bondar31,39, W.
Bonivento16, A. Borgheresi21,k, S. Borghi55, M. Borisyak67, M. Borsato38, 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,k, M.
Calvo Gomez37,p, P. Campana19, D. Campora Perez39, L. Capriotti55, A.
Carbone15,e, G. Carboni25,l, R. Cardinale20,j, A. Cardini16, P. Carniti21,k,
L. Carson51, K. Carvalho Akiba2, G. Casse53, L. Cassina21,k, 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 Vidal39, 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,r, P. Collins39, A. Comerma-Montells12, A. Contu39, A. Cook47, S.
Coquereau8, G. Corti39, M. Corvo17,g, 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, P. De Simone19, C.-T. Dean52, D. Decamp4, M.
Deckenhoff10, L. Del Buono8, N. Déléage4, M. Demmer10, A. Dendek28, 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, S. Easo50,39, U. Egede54, V.
Egorychev32, S. Eidelman35, S. Eisenhardt51, U. Eitschberger10, R. Ekelhof10,
L. Eklund52, I. El Rifai5, Ch. Elsasser41, S. Ely60, S. Esen12, H.M. Evans48,
T. Evans56, A. Falabella15, C. Färber39, N. Farley46, S. Farry53, R. Fay53, D.
Fazzini21,k, D. Ferguson51, V. Fernandez Albor38, F. Ferrari15,39, F. Ferreira
Rodrigues1, M. Ferro-Luzzi39, S. Filippov34, M. Fiore17,g, M. Fiorini17,g, M.
Firlej28, C. Fitzpatrick40, T. Fiutowski28, F. Fleuret7,b, K. Fohl39, M.
Fontana16, F. Fontanelli20,j, D. C. Forshaw60, R. Forty39, M. Frank39, C.
Frei39, M. Frosini18, J. Fu22, E. Furfaro25,l, 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, V.V. Gligorov8, C. Göbel61, D. Golubkov32, A.
Golutvin54,39, A. Gomes1,a, C. Gotti21,k, M. Grabalosa Gándara5, R. Graciani
Diaz37, L.A. Granado Cardoso39, E. Graugés37, E. Graverini41, G. Graziani18,
A. Grecu30, P. Griffith46, L. Grillo12, O. Grünberg65, E. Gushchin34, Yu.
Guz36,39, T. Gys39, T. Hadavizadeh56, C. Hadjivasiliou60, G. Haefeli40, C.
Haen39, S.C. Haines48, S. Hall54, B. Hamilton59, X. Han12, S. Hansmann-
Menzemer12, N. Harnew56, S.T. Harnew47, J. Harrison55, J. He39, T. Head40, A.
Heister9, K. Hennessy53, P. Henrard5, L. Henry8, J.A. Hernando Morata38, E.
van Herwijnen39, M. Heß65, A. Hicheur2, D. Hill56, M. Hoballah5, C. Hombach55,
L. Hongming40, 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, T.M.
Karbach39,†, S. Karodia52, M. Kecke12, M. Kelsey60, I.R. Kenyon46, M.
Kenzie39, T. Ketel43, E. Khairullin67, B. Khanji21,39,k, C. Khurewathanakul40,
T. Kirn9, S. Klaver55, K. Klimaszewski29, M. Kolpin12, I. Komarov40, R.F.
Koopman43, P. Koppenburg42, M. Kozeiha5, L. Kravchuk34, K. Kreplin12, M.
Kreps49, P. Krokovny35, F. Kruse10, W. Krzemien29, W. Kucewicz27,o, M.
Kucharczyk27, V. Kudryavtsev35, A. K. Kuonen40, K. Kurek29, T.
Kvaratskheliya32, D. Lacarrere39, G. Lafferty55,39, A. Lai16, D. Lambert51, G.
Lanfranchi19, C. Langenbruch49, B. Langhans39, T. Latham49, C. Lazzeroni46, R.
Le Gac6, J. van Leerdam42, J.-P. Lees4, R. Lefèvre5, A. Leflat33,39, J.
Lefrançois7, 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,r, M. Lucio Martinez38, H. Luo51, A. Lupato23, E. Luppi17,g, O.
Lupton56, N. Lusardi22, A. Lusiani24, X. Lyu62, F. Machefert7, F. Maciuc30, O.
Maev31, K. Maguire55, S. Malde56, A. Malinin66, G. Manca7, G. Mancinelli6, P.
Manning60, A. Mapelli39, J. Maratas5, 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. Mauri41, B. Maurin40, A. Mazurov46, M. McCann54, J.
McCarthy46, A. McNab55, R. McNulty13, B. Meadows58, F. Meier10, M. Meissner12,
D. Melnychuk29, M. Merk42, A Merli22,u, 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.
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K. Müller41, V. Müller10, M. Mussini15, B. Muster40, P. Naik47, T. Nakada40,
R. Nandakumar50, A. Nandi56, I. Nasteva2, M. Needham51, N. Neri22, S.
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Olloqui37, B. Pietrzyk4, M. Pikies27, D. Pinci26, A. Pistone20, A. Piucci12,
S. Playfer51, M. Plo Casasus38, T. Poikela39, F. Polci8, A. Poluektov49,35, I.
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Potterat2, E. Price47, J.D. Price53, J. Prisciandaro38, A. Pritchard53, C.
Prouve47, V. Pugatch45, A. Puig Navarro40, G. Punzi24,s, W. Qian56, R.
Quagliani7,47, B. Rachwal27, J.H. Rademacker47, M. Rama24, M. Ramos Pernas38,
M.S. Rangel2, I. Raniuk44, G. Raven43, F. Redi54, S. Reichert10, A.C. dos
Reis1, V. Renaudin7, S. Ricciardi50, S. Richards47, M. Rihl39, K.
Rinnert53,39, V. Rives Molina37, P. Robbe7, A.B. Rodrigues1, E. Rodrigues58,
J.A. Rodriguez Lopez64, P. Rodriguez Perez55, A. Rogozhnikov67, S. Roiser39,
V. Romanovsky36, A. Romero Vidal38, J. W. Ronayne13, M. Rotondo23, T. Ruf39,
P. Ruiz Valls68, J.J. Saborido Silva38, N. Sagidova31, B. Saitta16,f, V.
Salustino Guimaraes2, C. Sanchez Mayordomo68, B. Sanmartin Sedes38, R.
Santacesaria26, C. Santamarina Rios38, M. Santimaria19, E. Santovetti25,l, A.
Sarti19,m, C. Satriano26,n, A. Satta25, D.M. Saunders47, D. Savrina32,33, S.
Schael9, M. Schiller39, H. Schindler39, M. Schlupp10, M. Schmelling11, T.
Schmelzer10, B. Schmidt39, O. Schneider40, A. Schopper39, M. Schubiger40,
M.-H. Schune7, R. Schwemmer39, B. Sciascia19, A. Sciubba26,m, A. Semennikov32,
A. Sergi46, N. Serra41, J. Serrano6, L. Sestini23, P. Seyfert21, M. Shapkin36,
I. Shapoval17,44,g, Y. Shcheglov31, T. Shears53, L. Shekhtman35, V.
Shevchenko66, A. Shires10, B.G. Siddi17, R. Silva Coutinho41, L. Silva de
Oliveira2, G. Simi23,s, M. Sirendi48, N. Skidmore47, T. Skwarnicki60, E.
Smith54, I.T. Smith51, J. Smith48, M. Smith55, H. Snoek42, M.D. Sokoloff58,
F.J.P. Soler52, F. Soomro40, D. Souza47, B. Souza De Paula2, B. Spaan10, P.
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Vagnoni15,39, S. Valat39, G. Valenti15, A. Vallier7, R. Vazquez Gomez19, P.
Vazquez Regueiro38, C. Vázquez Sierra38, S. Vecchi17, M. van Veghel42, J.J.
Velthuis47, M. Veltri18,h, G. Veneziano40, M. Vesterinen12, B. Viaud7, D.
Vieira2, M. Vieites Diaz38, X. Vilasis-Cardona37,p, V. Volkov33, A.
Vollhardt41, D. Voong47, A. Vorobyev31, V. Vorobyev35, C. Voß65, J.A. de
Vries42, R. Waldi65, C. Wallace49, R. Wallace13, J. Walsh24, J. Wang60, D.R.
Ward48, N.K. Watson46, D. Websdale54, A. Weiden41, M. Whitehead39, J. Wicht49,
G. Wilkinson56,39, M. Wilkinson60, M. Williams39, M.P. Williams46, M.
Williams57, T. Williams46, F.F. Wilson50, J. Wimberley59, J. Wishahi10, W.
Wislicki29, M. Witek27, G. Wormser7, S.A. Wotton48, K. Wraight52, S. Wright48,
K. Wyllie39, Y. Xie63, Z. Xu40, Z. Yang3, H. Yin63, J. Yu63, X. Yuan35, O.
Yushchenko36, M. Zangoli15, M. Zavertyaev11,c, L. Zhang3, Y. Zhang7, A.
Zhelezov12, Y. Zheng62, A. Zhokhov32, L. Zhong3, V. Zhukov9, S. Zucchelli15.

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
37Universitat 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 Urbino, Urbino, Italy
iUniversità di Modena e Reggio Emilia, Modena, Italy
jUniversità di Genova, Genova, Italy
kUniversità di Milano Bicocca, Milano, Italy
lUniversità di Roma Tor Vergata, Roma, Italy
mUniversità di Roma La Sapienza, Roma, Italy
nUniversità della Basilicata, Potenza, Italy
oAGH - University of Science and Technology, Faculty of Computer Science,
Electronics and Telecommunications, Kraków, Poland
pLIFAELS, La Salle, Universitat Ramon Llull, Barcelona, Spain
qHanoi University of Science, Hanoi, Viet Nam
rUniversità di Padova, Padova, Italy
sUniversità di Pisa, Pisa, Italy
tScuola Normale Superiore, Pisa, Italy
uUniversità degli Studi di Milano, Milano, Italy
†Deceased