2021 081 10 May

Experimental evidence for an attractive $\mathrm{p}$–$\phi$ interaction

ALICE Collaboration††thanks: See Appendix A for the list of collaboration
members ALICE Collaboration

This Letter presents the first experimental evidence of the attractive strong
interaction between a proton and a $\phi$ meson. The result is obtained from
two-particle correlations of combined $\mathrm{p}$–$\phi$ $\oplus$
$\overline{\mathrm{p}}$–$\phi$ pairs measured in high-multiplicity pp
collisions at $\sqrt{s}~{}=~{}13$ TeV by the ALICE collaboration. The spin-
averaged scattering length and effective range of the $\mathrm{p}$–$\phi$
interaction are extracted from the fully corrected correlation function
employing the Lednický–Lyuboshits approach. In particular, the imaginary part
of the scattering length vanishes within uncertainties, indicating that
inelastic processes do not play a prominent role for the $\mathrm{p}$–$\phi$
interaction. These data demonstrate that the interaction is dominated by
elastic $\mathrm{p}$–$\phi$ scattering. Furthermore, an analysis employing
phenomenological Gaussian- and Yukawa-type potentials is conducted. Under the
assumption of the latter, the $\mathrm{N}$–$\phi$ coupling constant is found
to be $g_{\mathrm{N}\mbox{--}\phi}=\nolinebreak 0.14\pm\nolinebreak
0.03\,(\mathrm{stat.})\pm\nolinebreak 0.02\,(\mathrm{syst.})$. This work
provides valuable experimental input to accomplish a self-consistent
description of the $\mathrm{N}$–$\phi$ interaction, which is particularly
relevant for the more fundamental studies on partial restoration of chiral
symmetry in nuclear medium.

Quantum Chromodynamics (QCD) is the theory of the strong interaction, where
the degrees of freedom are represented by colored quarks and gluons. The
observable degrees of freedom at low energies, however, are composite hadrons,
and their mass is dynamically generated by the interplay between spontaneous
and explicit chiral symmetry breaking. The spontaneous breaking arises from
the non-zero vacuum expectation value $\langle
0|\mathrm{\overline{q}}\mathrm{q}|0\rangle$ of the ground state of the QCD
Lagrangian, the quark condensate $\mathrm{\overline{q}}$q. The consideration
of the quark mass term leads to the explicit breaking of chiral symmetry. A
link between the hadron properties and $\langle
0|\mathrm{\overline{q}}\mathrm{q}|0\rangle$ is provided by the QCD sum rule
method [1, 2, 3, 4], with the hadrons being interpreted as excitations of the
$\mathrm{\overline{q}}$q ground state. Chiral symmetry is expected to be
partially restored in a dense and/or hot strongly interacting medium [5].
Consequently, the modification of the $\mathrm{\overline{q}}$q condensate in
the medium is reflected in the spectral shape of its hadronic excitations.
This results in a potentially measurable mass shift and/or width broadening of
the hadrons. From the experimental point of view, the light vector mesons
$\uprho$, $\upomega$ and $\phi$ represent the most suitable hadronic probes
due to the short lifetime [6, 7]. The detection through the dileptonic decay
channels ($\mathrm{e}^{+}\mathrm{e}^{-}$and $\upmu^{+}\upmu^{-}$) allows to
infer on the meson properties at the time of their decay [8, 9, 10, 11, 12].

In this context, the $\phi$ meson represents an experimentally challenging
probe due to the narrow decay width in vacuum, which renders its spectral
shape distinguishable from that of the $\uprho$ and $\upomega$ mesons. The
KEK-PS E325 collaboration measured the $\phi$ spectral function in p–C and
p–Cu reactions and reported a slight mass shift and moderate increase of the
width, which was in a model-dependent manner interpreted as an in-medium
modification [13]. The collected data were, however, limited due to the small
branching ratio (BR $\approx$3\text{\times}{10}^{-4}$$ [14]) of the
$\phi\rightarrow\mathrm{e}^{+}\mathrm{e}^{-}$ decay. Larger data samples were
collected by the Spring8-LEPS collaboration in order to determine the $\phi$
production and absorption cross section in photon-induced reactions by
exploiting the decay to $\mathrm{K}^{+}\mathrm{K}^{-}$ (BR $\approx 50\%$
[14]) [15]. The $\mathrm{N}$–$\phi$ cross section in nuclear matter was found
to be much larger than the vacuum cross section, corresponding to an in-medium
$\phi$ width of about $110\text{~{}}\mathrm{/}^{2}$. A similar conclusion was
reached by other experiments from transparency ratio measurements in photon-
[16] and proton-induced reactions [17].

The interpretation of these results is far from trivial due to the lack of
model-independent information on the $\mathrm{N}$–$\phi$ interaction and its
complex dynamics. Because of the hidden strangeness content
($\mathrm{s}\overline{\mathrm{s}}$) of the $\phi$, the direct coupling to u
and d quarks in the nucleon is expected to be suppressed due to the Okubo-
Zweig-Iizuka (OZI) rule [18, 19, 20]. Indications for a possible OZI rule
violation were reported by the HADES collaboration [10]. In addition, several
scenarios allow for a direct interaction of the $\phi$ meson with the nucleon,
including a coupling to its strangeness content [21]. An alternative is the
QCD Van der Waals interaction [22], mediated by multi-gluon exchange, which
has been identified as relevant for the ($\mathrm{c}\overline{\mathrm{c}}$)–N
system [23]. Using a phenomenological Yukawa-type potential with adjusted
parameters, the QCD Van der Waals force is able to form a $\mathrm{N}$–$\phi$
bound state [24]. However, the direct $\mathrm{N}$–$\phi$ coupling is
typically not considered in theoretical descriptions of the interaction in
vacuum and in medium. OZI-allowed $\mathrm{N}$–$\phi$ processes can also
proceed via the coupling to particle pairs with same quantum numbers, such as
$\mathrm{K\mbox{--}\Uplambda,K\mbox{--}\Upsigma,K^{*}\mbox{--}\Uplambda,K^{*}\mbox{--}\Upsigma}$
[25, 26, 27]. More importantly, the properties of the $\phi$ are defined by
the $\phi-\mathrm{K}\overline{\mathrm{K}}$ coupling [18, 19, 20]. Accordingly,
$\mathrm{K}\overline{\mathrm{K}}$ loops and tadpole diagrams contribute to the
self-energy of the $\phi$ [28, 26, 27], linking the $\phi$ properties to the
complex dynamics of the K–N and $\overline{\mathrm{K}}$–N systems [29]. This
was explored by HADES in $\pi$–nucleus reactions at beam energies of
$1.65\text{~{}}\mathrm{G}\mathrm{e}\mathrm{V}$, demonstrating a constant
$\phi/\mathrm{K}^{-}$ ratio in different collision systems [30]. Since a
strong $\mathrm{K}^{-}$ absorption was observed also a strong $\phi$
absorption is expected. The overall $\mathrm{N}$–$\phi$ interaction is defined
by the interplay of all aforementioned processes. However, the present
theoretical and experimental situation is far from being resolved [31].
Indeed, a consistent description of the available photon- and proton-induced
data [15, 16, 17] is still out of reach [25]. This demonstrates the need for a
direct measurement of the two-body $\mathrm{N}$–$\phi$ interaction in vacuum,
in order to constrain theoretical models and correctly interpret the data from
nuclear collisions.

Recently, detailed measurements of the final-state interaction were conducted
employing two-particle correlations in ultra-relativistic proton–proton (pp)
collisions [32, 33, 34, 35, 36, 37, 38, 39]. In this Letter, these studies are
extended to protons and $\phi$ mesons.

The observable is the two-particle correlation function $C(k^{*})$, defined as
$C(k^{*})=\mathcal{N}\times\frac{N_{\rm{same}}(k^{*})}{N_{\rm{mixed}}(k^{*})}$
[40] where $N_{\rm{same}}$ and $N_{\rm{mixed}}$ are the distributions of the
relative momentum
$k^{*}=\frac{1}{2}\times|\mathbf{p}^{*}_{1}-\mathbf{p}^{*}_{2}|$ between both
particles in the pair rest frame (denoted by the ∗) and a normalization
constant $\mathcal{N}$, evaluated from same and mixed events, respectively.
The Koonin-Pratt equation
$C(k^{*})=\int\mathrm{d}^{3}r^{*}~{}S(r^{*})\mid\Psi(\vec{r^{*}},\vec{k^{*}})\mid^{2}$
[40] relates the observable to the source function $S(r^{*})$ and the two-
particle wave function $\Psi(\vec{r^{*}},\vec{k^{*}})$ incorporating the
final-state interaction, where $r^{*}$ is the relative distance between the
two particles.

The results reported in this Letter are based on the analysis of a data sample
of pp collisions at $\sqrt{s}~{}=~{}13$ TeV recorded by ALICE [41, 42] during
the LHC Run 2 (2015–2018). A high-multiplicity trigger relying on the measured
signal amplitudes in the V0 detectors [43] is employed to select collisions
with on average 30 produced charged particles in the pseudorapidity interval
$\left|\eta\right|<0.5$ [38]. The resulting data sample represents the upper
0.17% of the charged-particle distribution of all inelastic collisions with at
least one charged particle in the range $|\eta|<1$ (referred to as INEL $>$ 0)
[37]. The event selection follows [37, 32]. The reconstructed primary vertex
is required to be located within $\pm$$10\text{~{}}\mathrm{c}\mathrm{m}$ of
the nominal interaction point along the beam direction to assure a uniform
detector coverage. Meson-baryon correlation measurements in pp collisions are
contaminated by a so-called minijet background, induced by jet-like structures
associated with hard parton-parton scatterings [44, 35], which influence the
event shape [45, 46]. Therefore, a selection on the transverse sphericity
$S_{\rm{T}}$ [45, 46, 35], defined as in Ref. [45], is utilized to reduce the
minijet contribution. A total of $5\text{\times}{10}^{8}$ events with
$0.7<S_{\rm{T}}<1.0$ [35] are analyzed. The subsystems employed in the
analysis are the Inner Tracking System (ITS) [41], the Time Projection Chamber
(TPC) [47] and the Time-Of-Flight (TOF) detector [48], covering the full
azimuthal angle and the pseudorapidity interval $\left|\eta\right|<0.9$. The
detectors are immersed in a uniform magnetic field of
$0.5\text{~{}}\mathrm{T}$ along the beam direction.

The proton candidates are selected following the methods used in Ref. [32].
The particle identification (PID) is conducted employing the TPC and TOF
detectors by determining the deviation $n_{\sigma}$ between the signal
hypothesis for a proton and the measurement, normalized by the detector
resolution $\sigma$. Contributions from secondary particles stemming from weak
decays or the interaction of primary particles with the detector material are
extracted using Monte Carlo (MC) template fits to the measured distribution of
the Distance of Closest Approach (DCA) of the track to the primary vertex
[32]. This results in a proton purity of 99%, with a primary fraction of 82%
[33]. The $\phi$ meson is reconstructed from its hadronic decay to charged
kaons $\phi\rightarrow\mathrm{K}^{+}\mathrm{K}^{-}$ as in Refs. [49, 50, 51].
Charged kaons are identified with a transverse momentum of $p_{\rm
T}>$0.15\text{~{}}\mathrm{/}$$ and $\left|\eta\right|<0.8$. For momenta
$p<$0.4\text{~{}}\mathrm{/}$$ the PID selection provided by the TPC is used,
while for larger momenta the information of TPC and TOF is combined. A
selection on the DCA of the track to the primary vertex in both the beam
direction ($|\mathrm{DCA}_{z}|<$0.8\text{~{}}\mathrm{c}\mathrm{m}$$) and
transverse plane ($|\mathrm{DCA}_{xy}|<$0.4\text{~{}}\mathrm{c}\mathrm{m}$$)
is employed to increase the fraction of kaons from $\phi$ decays. The purity
of the kaon sample is $>90\%$ for $p_{\rm T}<$1.25\text{~{}}\mathrm{/}$$. The
$\mathrm{K}^{+}\mathrm{K}^{-}$ invariant mass is calculated combining two
oppositely charged kaons assuming their nominal masses [14]. The $\phi$
candidates are selected within a window of
$\pm$8\text{~{}}\mathrm{/\squared}$$ around the nominal $\phi$ mass, resulting
in a total number of $5.8\text{\times}{10}^{6}$ with a purity of $66\%$.

Figure 1: The experimental $\mathrm{p}$–$\phi$ correlation function
$C_{\mathrm{exp}}(k^{*})$ and various contributions as described in Eq. 1.
Statistical (bars) and systematic uncertainties (boxes) are shown separately.
The width of the dark (light) shaded bands depicts the statistical (total)
uncertainty.

A total of $4.17\text{\times}{10}^{4}$ $\mathrm{p}$–$\phi$ and
$3.61\text{\times}{10}^{4}$ $\overline{\mathrm{p}}$–$\phi$ pairs with
$k^{*}<$200\text{~{}}\mathrm{/}$$ contribute to the $N_{\rm{same}}$
distribution of the respective correlation function. As they are compatible
within uncertainties, both correlation functions are combined. In the
following, $\mathrm{p}$–$\phi$ refers to $\mathrm{p}$–$\phi$ $\oplus$
$\overline{\mathrm{p}}$–$\phi$. The correlation function is normalized within
$k^{*}\in[800,1000]~{}$\mathrm{/}$$, where all the contributions to the
correlation function are expected to be flat. The data are unfolded for the
finite momentum resolution of the detector [52], which modifies the
correlation function by 0.7% at low $k^{*}$. The measured $\mathrm{p}$–$\phi$
correlation function is shown in Fig. 1. The $k^{*}$ value of the data points
is determined by the average $\langle$$k^{*}$ $\rangle$ of the
$N_{\mathrm{same}}$ distribution in the corresponding interval. In the region
$150<k^{*}<$600\text{~{}}\mathrm{/}$$ a rise in the correlation function
attributed to residual minijet background is visible. Therefore, any
conclusion on the genuine $\mathrm{p}$–$\phi$ interaction demands a treatment
of the contributions due to residual correlations from the underlying event
topology (minijets and energy/momentum conservation), weak decays feeding to
the particles of interest (feed-down) and misidentifications [32].

The experimental $\mathrm{p}$–$\phi$ correlation function
$C_{\mathrm{exp}}(k^{*})$ is decomposed as

$C_{\mathrm{exp}}(k^{*})=\mathit{M}\times
C_{\mathrm{bkg}}(k^{*})\times\left[\lambda_{\mathrm{p}\mbox{--}\phi}\times
C_{\mathrm{p}\mbox{--}\phi}(k^{*})+\lambda_{\mathrm{flat}}\times
C_{\mathrm{flat}}(k^{*})\right]+\lambda_{\mathrm{p}\mbox{--}(\mathrm{K}^{+}\mathrm{K}^{-})}\times
C_{\mathrm{p}\mbox{--}(\mathrm{K}^{+}\mathrm{K}^{-})}(k^{*}),$ (1)

where $\mathit{M}$ is a normalization constant, $C_{\mathrm{bkg}}(k^{*})$ is
the non femtoscopic background, $C_{\mathrm{p}\mbox{--}\phi}(k^{*})$ the
genuine $\mathrm{p}$–$\phi$ correlation function,
$C_{\mathrm{flat}}(k^{*})\approx 1$ considers the effect from weak decays and
single particle misidentification and
$C_{\mathrm{p}\mbox{--}(\mathrm{K}^{+}\mathrm{K}^{-})}(k^{*})$ is the
contribution from combinatorial $\mathrm{K}^{+}\mathrm{K}^{-}$ background.
Correlations are summed for independent pairs and multiplied when considering
different effects acting on the same pair. The parameters $\lambda_{i}$,
summarized in Table 1, are obtained in a data-driven way from single-particle
properties [32]. As the purity of the $\phi$ candidates depends on $p_{\rm
T}$, it is evaluated for those entering the correlation function, and found to
be 57%.

The combinatorial $\mathrm{K}^{+}\mathrm{K}^{-}$ background, referred to as
$\mathrm{p}$–($\mathrm{K}^{+}\mathrm{K}^{-}$), significantly contributes to
the measured correlation function. Its shape is extracted from the sidebands
of the $\mathrm{K}^{+}\mathrm{K}^{-}$ invariant mass selection and mainly
driven by p–$\mathrm{K}^{+}$ and p–$\mathrm{K}^{-}$ interactions. The sideband
intervals are chosen as
$0.995-1.011~{}$\mathrm{G}\mathrm{eV}\mathrm{/}\mathrm{\text{$c$}}^{2}$$ and
$1.028-1.044~{}$\mathrm{G}\mathrm{eV}\mathrm{/}\mathrm{\text{$c$}}^{2}$$ to
avoid threshold effects and have comparable kinematic properties as the $\phi$
candidates. The resulting correlation function is parametrized with a double
Gaussian and a quadratic polynomial. Finally, a residual $\phi$ amount of
$8.6\%$ in the sidebands is considered, which arises from the tail of the
$\phi$ resonance extending into the sideband intervals. This results in a
$7\%$ contribution to the experimental
$C_{\mathrm{\mathrm{p}\mbox{--}(\mathrm{K}^{+}\mathrm{K}^{-})}}(k^{*})$, which
is absorbed by a renormalization of the $\lambda$ parameters. Since the
$\mathrm{p}$–($\mathrm{K}^{+}\mathrm{K}^{-}$) contribution is obtained from
data, the corresponding residual minijet background and energy-momentum
conservation effects are accounted for. The resulting
$C_{\mathrm{\mathrm{p}\mbox{--}(\mathrm{K}^{+}\mathrm{K}^{-})}}(k^{*})$ is
depicted by the green band in Fig. 1.

The non femtoscopic background $C_{\mathrm{bkg}}(k^{*})$ in Eq. 1 is
multiplied to the genuine $\mathrm{p}$–$\phi$ and flat contributions.
$C_{\mathrm{bkg}}(k^{*})=C_{\mathrm{baseline}}(k^{*})+C_{\mathrm{minijet}}(k^{*})$
is dominated by residual minijet contributions $C_{\mathrm{minijet}}(k^{*})$
obtained from Pythia 8 [53] generated events, which yield a consistent
description of such background [54, 55]. However, further correlations at
large $k^{*}$ due to energy-momentum conservation effects are not properly
reproduced by Pythia 8 [56]. Therefore, an additional
$C_{\mathrm{baseline}}(k^{*})$ function, described by a second order
polynomial, is considered.

Table 1: Weight parameters of the individual components of the $\mathrm{p}$–$\phi$ correlation function. Pair |  Weight $\mathbf{\lambda}$ (%)
---|---
$\mathrm{p}$–$\phi$ | 46.3
$\mathrm{p}$–($\mathrm{K}^{+}\mathrm{K}^{-}$) | 43.3
Flat | 10.4

The data is then fitted with a background model (Eq. 1 with
$C_{\mathrm{p}\mbox{--}\phi}(k^{*})=1$) within
$k^{*}\in[200,800]~{}$\mathrm{/}$$, which accounts for all contributions
besides the genuine $\mathrm{p}$–$\phi$ interaction. The $\lambda$ parameters
and the shape of the minijet and $\mathrm{p}$–($\mathrm{K}^{+}\mathrm{K}^{-}$)
background are fixed in the fit. Only the normalization constant and baseline
parameters are free. The resulting $C_{\mathrm{bkg}}(k^{*})$ is shown by the
red band in Fig. 1 and the mean value of the normalization constant is
$\mathit{M}=0.96$. Accordingly, the total background is obtained as the blue
band in Fig. 1, which accurately reproduces the enhancement between
$200\text{~{}}\mathrm{/}$ and $1000\text{~{}}\mathrm{/}$.

The genuine $\mathrm{p}$–$\phi$ contribution
$C_{\mathrm{p}\mbox{--}\phi}(k^{*})$, is extracted from Eq. 1 by subtracting
the obtained background contributions from the experimental correlation and is
shown in Fig. 2. For $k^{*}>$200\text{~{}}\mathrm{/}$$, it is flat and
consistent with unity within uncertainties. At low $k^{*}$ a pronounced
enhancement with a significance of $4.7-6.6~{}\sigma$ with respect to the
unity becomes apparent, which evidences the attractive nature of the
$\mathrm{p}$–$\phi$ interaction. The systematic uncertainties of the data and
the background description are assessed by varying simultaneously the
selection criteria of protons and kaons as well as the lower limit of the
sphericity. These variations are chosen such that any combination leads to a
maximum change of $\pm 20\%$ of $N_{\mathrm{same}}$ within
$k^{*}<$200\text{~{}}\mathrm{/}$$ in order to retain the statistical
significance. Systematic uncertainties associated with the background
description are evaluated by varying the fit ranges and the order of the
polynomial assumed for $C_{\mathrm{baseline}}(k^{*})$. Uncertainties related
to the unfolding are accounted for according to Ref. [38]. This results in a
relative systematic uncertainty at low $k^{*}$ of $2.8\%$.

In correlation measurements, the detected pairs are emitted in the final state
of the scattering processes. The correlation function of the sample is then
sensitive to elastic and inelastic channels produced in the collision [57].
Inelastic channels opening below threshold act as an effective increase of the
correlation function. The relevant channels for the $\mathrm{p}$–$\phi$
system, $\Uplambda\mbox{--}\mathrm{K}$ and $\Upsigma\mbox{--}\mathrm{K}$ are
located substantially below threshold. Channels appearing above threshold lead
to a cusp structure in $C(k^{*})$ in the vicinity of the threshold. Because of
the large uncertainties and the broad bin width, no such structures are
observed at the opening of the $\Uplambda\mbox{--}\mathrm{K}^{*}$
($k^{*}=$221.6\text{~{}}\mathrm{/}$$) and $\Upsigma\mbox{--}\mathrm{K}^{*}$
($k^{*}=$357.4\text{~{}}\mathrm{/}$$) thresholds.

In order to interpret the measured genuine $\mathrm{p}$–$\phi$ correlation one
has to consider that the $\mathrm{p}$–$\phi$ interaction features one isospin
and two spin configurations. Since the latter cannot be disentangled, spin-
averaged results are presented. The strong $\mathrm{p}$–$\phi$ interaction is
modeled employing the Lednický–Lyuboshits approach [58]. Coupled channel
effects are incorporated via an imaginary contribution to the scattering
length. For large values of $d_{0}$, the term $\propto d_{0}/r_{0}$ that
corrects the asymptotic wave function for small sources has an impact on the
modeled correlation function [34]. Additionally, in line with studies of
charmonium states [23, 59], phenomenological potentials are employed to model
the $\mathrm{p}$–$\phi$ interaction [24], including Yukawa-type,
$V_{\mathrm{Yukawa}}(r)=-A\times r^{-1}\times e^{-\upalpha\times r}$, and
Gaussian-type $V_{\mathrm{Gaussian}}(r)=-V_{\mathrm{eff}}\times
e^{-\upmu\times r^{2}}$ potentials. The correlation functions based on these
potentials are obtained with The Correlation Analysis Tool using the
Schrödinger Equation (CATS) [60].

The particle-emitting source is extracted from studies of
$\mathrm{p}\mbox{--}\mathrm{p}$ and p–$\Uplambda$ pairs [33], which
demonstrated that by accounting for the effect of strong resonances feeding to
the particle pair of interest, a common source for both pairs is found. The
primordial source depends on the transverse mass $m_{\rm{T}}$ of the particle
pair and is obtained by evaluating the core radius at the $\langle
m_{\rm{T}}\rangle=$1.66\text{~{}}\mathrm{/\squared}$$ of the
$\mathrm{p}$–$\phi$ pairs. The strong decays feeding to protons are explicitly
considered [33], while for the $\phi$ a 100% primordial fraction is assumed
[14]. The resulting source function is parametrized by a Gaussian profile with
$r_{\mathrm{eff}}=(1.08\pm 0.05)~{}$\mathrm{f}\mathrm{m}$$.

Figure 2: The genuine $\mathrm{p}$–$\phi$ correlation function
$C_{\mathrm{p}\mbox{--}\phi}(k^{*})$ with statistical (bars) and systematic
uncertainties (boxes). The red band depicts the results from the fit employing
the Lednický–Lyuboshits approach [58]. The width corresponds to one standard
deviation of the uncertainty of the fit.

The interaction parameters are extracted by fitting the genuine
$\mathrm{p}$–$\phi$ correlation function $C_{\mathrm{p}\mbox{--}\phi}(k^{*})$
with the respective model within $k^{*}<$200\text{~{}}\mathrm{/}$$. The
systematic uncertainties of the procedure are assessed by varying the upper
limit of the fit range by $\pm$30\text{~{}}\mathrm{/}$$ and the source radius
within its uncertainties.

The real and imaginary parts of the scattering length obtained from the
Lednický–Lyuboshits fit are $\Re(f_{0})=\nolinebreak 0.85\pm\nolinebreak
0.34\,(\mathrm{stat.})\pm\nolinebreak
0.14\,(\mathrm{syst.})~{}$\mathrm{f}\mathrm{m}$$ and $\Im(f_{0})=\nolinebreak
0.16\pm\nolinebreak 0.10\,(\mathrm{stat.})\pm\nolinebreak
0.09\,(\mathrm{syst.})~{}$\mathrm{f}\mathrm{m}$$. The resulting effective
range is $d_{0}=\nolinebreak 7.85\pm\nolinebreak
1.54\,(\mathrm{stat.})\pm\nolinebreak
0.26\,(\mathrm{syst.})~{}$\mathrm{f}\mathrm{m}$$. $\Re(f_{0})$ deviates by
$2.3\upsigma$ from zero, indicating the attractiveness of the
$\mathrm{p}$–$\phi$ interaction in the approximate vacuum of pp collisions.
Notably, $\Im(f_{0})$ vanishes within uncertainties, indicating that inelastic
processes do not play a prominent role in the interaction. Instead, the
elastic $\mathrm{p}$–$\phi$ interaction appears to be dominant in vacuum. The
scattering length is larger than values found in literature: a recent analysis
of data recorded with the CLAS experiment reports $|f_{0}|=(0.063\pm 0.010)$
fm [61]; a value of around $f_{0}=$0.15\text{~{}}\mathrm{f}\mathrm{m}$$ is
consistent with LEPS measurements of the $\phi$ cross section [62, 63];
studies of an effective Lagrangian combining chiral SU(3) dynamics with vector
meson dominance obtain $f_{0}=(-0.01+i\,0.08)$ fm [64]; and a QCD sum rule
analysis finds $f_{0}=(-0.15\pm 0.02)$ fm [65]. The obtained scattering
lengths are rather model dependent since the data refer to the properties of
the $\phi$ meson inside a nucleus and not to a two-body system as in this
work. This underlines the importance of direct measurements of the two-body
$\mathrm{N}$–$\phi$ interaction to provide constraints for theoretical models.

Finally, the data are employed to constrain the parameters of phenomenological
Gaussian- and Yukawa-type potentials. As the imaginary contribution of the
scattering length is consistent with zero, only real values are used for the
parameters. The fits yield a comparable degree of consistency as the fit with
the Lednický–Lyuboshits approach. The resulting values for the Gaussian-type
potential are $V_{\mathrm{eff}}=\nolinebreak 2.5\pm\nolinebreak
0.9\,(\mathrm{stat.})\pm\nolinebreak 1.4\,(\mathrm{syst.})~{}$\mathrm{MeV}$$
and $\upmu=\nolinebreak 0.14\pm\nolinebreak
0.06\,(\mathrm{stat.})\pm\nolinebreak
0.09\,(\mathrm{syst.})~{}$\mathrm{f}\mathrm{m}^{-2}$$, indicating a much
shallower strong interaction potential than lattice QCD results for the
N–$\mathrm{J}/\psi$ strong interaction [66]. For the Yukawa-type potential the
fit yields $A=\nolinebreak 0.021\pm\nolinebreak
0.009\,(\mathrm{stat.})\pm\nolinebreak 0.006\,(\mathrm{syst.})$ and
$\upalpha=\nolinebreak 65.9\pm\nolinebreak
38.0\,(\mathrm{stat.})\pm\nolinebreak
17.5\,(\mathrm{syst.})~{}$\mathrm{MeV}$$. Predictions of possible
$\mathrm{N}$–$\phi$ bound states employing the same kind of potential with
modified parameters ($\upalpha=$600\text{~{}}\mathrm{M}\mathrm{e}\mathrm{V}$$
and $A=1.25$) [24] are therefore incompatible with this measurement. The
$\mathrm{N}$–$\phi$ coupling constant under the assumption of a Yukawa-type
potential ($g_{\mathrm{N}\mbox{--}\phi}=\sqrt{A}$) is
$g_{\mathrm{N}\mbox{--}\phi}=\nolinebreak 0.14\pm\nolinebreak
0.03\,(\mathrm{stat.})\pm\nolinebreak 0.02\,(\mathrm{syst.})$.

In conclusion, this Letter presents the first correlation-based measurement of
the $\mathrm{p}$–$\phi$ interaction. The correlation function reflects the
pattern of an attractive interaction. The scattering parameters, extracted
with the Lednický–Lyuboshits approach, are $\Re(f_{0})=\nolinebreak
0.85\pm\nolinebreak 0.34\,(\mathrm{stat.})\pm\nolinebreak
0.14\,(\mathrm{syst.})~{}$\mathrm{f}\mathrm{m}$$,$\Im(f_{0})=\nolinebreak
0.16\pm\nolinebreak 0.10\,(\mathrm{stat.})\pm\nolinebreak
0.09\,(\mathrm{syst.})~{}$\mathrm{f}\mathrm{m}$$, and $d_{0}=\nolinebreak
7.85\pm\nolinebreak 1.54\,(\mathrm{stat.})\pm\nolinebreak
0.26\,(\mathrm{syst.})~{}$\mathrm{f}\mathrm{m}$$. Remarkably, the imaginary
contribution to the scattering length vanishes, indicating that inelastic
processes do not play a prominent role. Instead, the interaction is dominated
by the elastic $\mathrm{p}$–$\phi$ dynamics. Under the assumption of a Yukawa-
type potential for the $\mathrm{N}$–$\phi$ interaction, the value of the
coupling constant is extracted as $g_{\mathrm{N}\mbox{--}\phi}=\nolinebreak
0.14\pm\nolinebreak 0.03\,(\mathrm{stat.})\pm\nolinebreak
0.02\,(\mathrm{syst.})$.
These results seem to contradict the interpretation of the $\phi$ production
off nuclear targets in terms of large absorption cross-sections but more data
are needed to extract the precise value of the imaginary part of the
scattering length and the here reported results should serve as an input for
more advanced modellings in medium. The upcoming Run 3 and Run 4 data taking
at the LHC will allow to significantly improve the precision of the extracted
interaction parameters. This measurement demonstrates for the first time that
the $\mathrm{p}$–$\phi$ interaction in vacuum is attractive and dominated by
elastic scattering. It provides valuable experimental input on the
$\mathrm{N}$–$\phi$ interaction, which is fundamental to reach a self-
consistent description of the interaction as required for the correct
interpretation of data from nuclear collisions.

## Acknowledgements

The ALICE Collaboration is grateful to P. Gubler and N. Kaiser for valuable
discussions.

The ALICE Collaboration would like to thank all its engineers and technicians for their invaluable contributions to the construction of the experiment and the CERN accelerator teams for the outstanding performance of the LHC complex. The ALICE Collaboration gratefully acknowledges the resources and support provided by all Grid centres and the Worldwide LHC Computing Grid (WLCG) collaboration. The ALICE Collaboration acknowledges the following funding agencies for their support in building and running the ALICE detector: A. I. Alikhanyan National Science Laboratory (Yerevan Physics Institute) Foundation (ANSL), State Committee of Science and World Federation of Scientists (WFS), Armenia; Austrian Academy of Sciences, Austrian Science Fund (FWF): [M 2467-N36] and Nationalstiftung für Forschung, Technologie und Entwicklung, Austria; Ministry of Communications and High Technologies, National Nuclear Research Center, Azerbaijan; Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Financiadora de Estudos e Projetos (Finep), Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) and Universidade Federal do Rio Grande do Sul (UFRGS), Brazil; Ministry of Education of China (MOEC) , Ministry of Science & Technology of China (MSTC) and National Natural Science Foundation of China (NSFC), China; Ministry of Science and Education and Croatian Science Foundation, Croatia; Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN), Cubaenergía, Cuba; Ministry of Education, Youth and Sports of the Czech Republic, Czech Republic; The Danish Council for Independent Research | Natural Sciences, the VILLUM FONDEN and Danish National Research Foundation (DNRF), Denmark; Helsinki Institute of Physics (HIP), Finland; Commissariat à l’Energie Atomique (CEA) and Institut National de Physique Nucléaire et de Physique des Particules (IN2P3) and Centre National de la Recherche Scientifique (CNRS), France; Bundesministerium für Bildung und Forschung (BMBF) and GSI Helmholtzzentrum für Schwerionenforschung GmbH, Germany; General Secretariat for Research and Technology, Ministry of Education, Research and Religions, Greece; National Research, Development and Innovation Office, Hungary; Department of Atomic Energy Government of India (DAE), Department of Science and Technology, Government of India (DST), University Grants Commission, Government of India (UGC) and Council of Scientific and Industrial Research (CSIR), India; Indonesian Institute of Science, Indonesia; Istituto Nazionale di Fisica Nucleare (INFN), Italy; Institute for Innovative Science and Technology , Nagasaki Institute of Applied Science (IIST), Japanese Ministry of Education, Culture, Sports, Science and Technology (MEXT) and Japan Society for the Promotion of Science (JSPS) KAKENHI, Japan; Consejo Nacional de Ciencia (CONACYT) y Tecnología, through Fondo de Cooperación Internacional en Ciencia y Tecnología (FONCICYT) and Dirección General de Asuntos del Personal Academico (DGAPA), Mexico; Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO), Netherlands; The Research Council of Norway, Norway; Commission on Science and Technology for Sustainable Development in the South (COMSATS), Pakistan; Pontificia Universidad Católica del Perú, Peru; Ministry of Education and Science, National Science Centre and WUT ID-UB, Poland; Korea Institute of Science and Technology Information and National Research Foundation of Korea (NRF), Republic of Korea; Ministry of Education and Scientific Research, Institute of Atomic Physics and Ministry of Research and Innovation and Institute of Atomic Physics, Romania; Joint Institute for Nuclear Research (JINR), Ministry of Education and Science of the Russian Federation, National Research Centre Kurchatov Institute, Russian Science Foundation and Russian Foundation for Basic Research, Russia; Ministry of Education, Science, Research and Sport of the Slovak Republic, Slovakia; National Research Foundation of South Africa, South Africa; Swedish Research Council (VR) and Knut & Alice Wallenberg Foundation (KAW), Sweden; European Organization for Nuclear Research, Switzerland; Suranaree University of Technology (SUT), National Science and Technology Development Agency (NSDTA) and Office of the Higher Education Commission under NRU project of Thailand, Thailand; Turkish Energy, Nuclear and Mineral Research Agency (TENMAK), Turkey; National Academy of Sciences of Ukraine, Ukraine; Science and Technology Facilities Council (STFC), United Kingdom; National Science Foundation of the United States of America (NSF) and United States Department of Energy, Office of Nuclear Physics (DOE NP), United States of America.

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##  Appendix A The ALICE Collaboration

S. Acharya143, D. Adamová98, A. Adler76, J. Adolfsson83, G. Aglieri Rinella35,
M. Agnello31, N. Agrawal55, Z. Ahammed143, S. Ahmad16, S.U. Ahn78, I. Ahuja39,
Z. Akbar52, A. Akindinov95, M. Al-Turany110, S.N. Alam41, D. Aleksandrov91, B.
Alessandro61, H.M. Alfanda7, R. Alfaro Molina73, B. Ali16, Y. Ali14, A.
Alici26, N. Alizadehvandchali127, A. Alkin35, J. Alme21, T. Alt70, L.
Altenkamper21, I. Altsybeev115, M.N. Anaam7, C. Andrei49, D. Andreou93, A.
Andronic146, M. Angeletti35, V. Anguelov107, F. Antinori58, P. Antonioli55, C.
Anuj16, N. Apadula82, L. Aphecetche117, H. Appelshäuser70, S. Arcelli26, R.
Arnaldi61, I.C. Arsene20, M. Arslandok148,107, A. Augustinus35, R.
Averbeck110, S. Aziz80, M.D. Azmi16, A. Badalà57, Y.W. Baek42, X. Bai131,110,
R. Bailhache70, Y. Bailung51, R. Bala104, A. Balbino31, A. Baldisseri140, B.
Balis2, M. Ball44, D. Banerjee4, R. Barbera27, L. Barioglio108,25, M.
Barlou87, G.G. Barnaföldi147, L.S. Barnby97, V. Barret137, C. Bartels130, K.
Barth35, E. Bartsch70, F. Baruffaldi28, N. Bastid137, S. Basu83, G.
Batigne117, B. Batyunya77, D. Bauri50, J.L. Bazo Alba114, I.G. Bearden92, C.
Beattie148, I. Belikov139, A.D.C. Bell Hechavarria146, F. Bellini26,35, R.
Bellwied127, S. Belokurova115, V. Belyaev96, G. Bencedi71, S. Beole25, A.
Bercuci49, Y. Berdnikov101, A. Berdnikova107, D. Berenyi147, L. Bergmann107,
M.G. Besoiu69, L. Betev35, P.P. Bhaduri143, A. Bhasin104, I.R. Bhat104, M.A.
Bhat4, B. Bhattacharjee43, P. Bhattacharya23, L. Bianchi25, N. Bianchi53, J.
Bielčík38, J. Bielčíková98, J. Biernat120, A. Bilandzic108, G. Biro147, S.
Biswas4, J.T. Blair121, D. Blau91, M.B. Blidaru110, C. Blume70, G. Boca29,59,
F. Bock99, A. Bogdanov96, S. Boi23, J. Bok63, L. Boldizsár147, A.
Bolozdynya96, M. Bombara39, P.M. Bond35, G. Bonomi142,59, H. Borel140, A.
Borissov84, H. Bossi148, E. Botta25, L. Bratrud70, P. Braun-Munzinger110, M.
Bregant123, M. Broz38, G.E. Bruno109,34, M.D. Buckland130, D. Budnikov111, H.
Buesching70, S. Bufalino31, O. Bugnon117, P. Buhler116, Z. Buthelezi74,134,
J.B. Butt14, S.A. Bysiak120, D. Caffarri93, M. Cai28,7, H. Caines148, A.
Caliva110, E. Calvo Villar114, J.M.M. Camacho122, R.S. Camacho46, P.
Camerini24, F.D.M. Canedo123, F. Carnesecchi35,26, R. Caron140, J. Castillo
Castellanos140, E.A.R. Casula23, F. Catalano31, C. Ceballos Sanchez77, P.
Chakraborty50, S. Chandra143, S. Chapeland35, M. Chartier130, S.
Chattopadhyay143, S. Chattopadhyay112, A. Chauvin23, T.G. Chavez46, C.
Cheshkov138, B. Cheynis138, V. Chibante Barroso35, D.D. Chinellato124, E.S.
Chizzali108, S. Cho63, P. Chochula35, P. Christakoglou93, C.H. Christensen92,
P. Christiansen83, T. Chujo136, C. Cicalo56, L. Cifarelli26, F. Cindolo55,
M.R. Ciupek110, G. ClaiII,55, J. CleymansI,126, F. Colamaria54, J.S.
Colburn113, D. Colella109,54,34,147, A. Collu82, M. Colocci35,26, M.
ConcasIII,61, G. Conesa Balbastre81, Z. Conesa del Valle80, G. Contin24, J.G.
Contreras38, M.L. Coquet140, T.M. Cormier99, P. Cortese32, M.R. Cosentino125,
F. Costa35, S. Costanza29,59, P. Crochet137, R. Cruz-Torres82, E. Cuautle71,
P. Cui7, L. Cunqueiro99, A. Dainese58, F.P.A. Damas117,140, M.C. Danisch107,
A. Danu69, I. Das112, P. Das89, P. Das4, S. Das4, S. Dash50, S. De89, A. De
Caro30, G. de Cataldo54, L. De Cilladi25, J. de Cuveland40, A. De Falco23, D.
De Gruttola30, N. De Marco61, C. De Martin24, S. De Pasquale30, S. Deb51, H.F.
Degenhardt123, K.R. Deja144, L. Dello Stritto30, S. Delsanto25, W. Deng7, P.
Dhankher19, D. Di Bari34, A. Di Mauro35, R.A. Diaz8, T. Dietel126, Y.
Ding138,7, R. Divià35, D.U. Dixit19, Ø. Djuvsland21, U. Dmitrieva65, J. Do63,
A. Dobrin69, B. Dönigus70, O. Dordic20, A.K. Dubey143, A. Dubla110,93, S.
Dudi103, M. Dukhishyam89, P. Dupieux137, N. Dzalaiova13, T.M. Eder146, R.J.
Ehlers99, V.N. Eikeland21, F. Eisenhut70, D. Elia54, B. Erazmus117, F.
Ercolessi26, F. Erhardt102, A. Erokhin115, M.R. Ersdal21, B. Espagnon80, G.
Eulisse35, D. Evans113, S. Evdokimov94, L. Fabbietti108, M. Faggin28, J.
Faivre81, F. Fan7, A. Fantoni53, M. Fasel99, P. Fecchio31, A. Feliciello61, G.
Feofilov115, A. Fernández Téllez46, A. Ferrero140, A. Ferretti25, V.J.G.
Feuillard107, J. Figiel120, S. Filchagin111, D. Finogeev65, F.M. Fionda56,21,
G. Fiorenza35,109, F. Flor127, A.N. Flores121, S. Foertsch74, P. Foka110, S.
Fokin91, E. Fragiacomo62, E. Frajna147, U. Fuchs35, N. Funicello30, C.
Furget81, A. Furs65, J.J. Gaardhøje92, M. Gagliardi25, A.M. Gago114, A.
Gal139, C.D. Galvan122, P. Ganoti87, C. Garabatos110, J.R.A. Garcia46, E.
Garcia-Solis10, K. Garg117, C. Gargiulo35, A. Garibli90, K. Garner146, P.
Gasik110, E.F. Gauger121, A. Gautam129, M.B. Gay Ducati72, M. Germain117, J.
Ghosh112, P. Ghosh143, S.K. Ghosh4, M. Giacalone26, P. Gianotti53, P.
Giubellino110,61, P. Giubilato28, A.M.C. Glaenzer140, P. Glässel107, D.J.Q.
Goh85, V. Gonzalez145, L.H. González-Trueba73, S. Gorbunov40, M. Gorgon2, L.
Görlich120, S. Gotovac36, V. Grabski73, L.K. Graczykowski144, R.D. Grande108,
L. Greiner82, A. Grelli64, C. Grigoras35, V. Grigoriev96, A. GrigoryanI,1, S.
Grigoryan77,1, O.S. Groettvik21, F. Grosa35,61, J.F. Grosse-Oetringhaus35, R.
Grosso110, G.G. Guardiano124, R. Guernane81, M. Guilbaud117, K. Gulbrandsen92,
T. Gunji135, A. Gupta104, R. Gupta104, I.B. Guzman46, S.P. Guzman46, L.
Gyulai147, M.K. Habib110, C. Hadjidakis80, G. Halimoglu70, H. Hamagaki85, G.
Hamar147, M. Hamid7, R. Hannigan121, M.R. Haque144,89, A. Harlenderova110,
J.W. Harris148, A. Harton10, J.A. Hasenbichler35, H. Hassan99, D.
Hatzifotiadou55, P. Hauer44, L.B. Havener148, S. Hayashi135, S.T. Heckel108,
E. Hellbär70, H. Helstrup37, T. Herman38, E.G. Hernandez46, G. Herrera
Corral9, F. Herrmann146, K.F. Hetland37, H. Hillemanns35, C. Hills130, B.
Hippolyte139, B. Hofman64, B. Hohlweger93,108, J. Honermann146, G.H. Hong149,
D. Horak38, S. Hornung110, A. Horzyk2, R. Hosokawa15, P. Hristov35, C.
Huang80, C. Hughes133, P. Huhn70, T.J. Humanic100, H. Hushnud112, L.A.
Husova146, A. Hutson127, D. Hutter40, J.P. Iddon35,130, R. Ilkaev111, H.
Ilyas14, M. Inaba136, G.M. Innocenti35, M. Ippolitov91, A. Isakov38,98, M.S.
Islam112, M. Ivanov110, V. Ivanov101, V. Izucheev94, M. Jablonski2, B.
Jacak82, N. Jacazio35, P.M. Jacobs82, S. Jadlovska119, J. Jadlovsky119, S.
Jaelani64, C. Jahnke124,123, M.J. Jakubowska144, M.A. Janik144, T. Janson76,
M. Jercic102, O. Jevons113, F. Jonas99,146, P.G. Jones113, J.M. Jowett 35,110,
J. Jung70, M. Jung70, A. Junique35, A. Jusko113, J. Kaewjai118, P. Kalinak66,
A. Kalweit35, V. Kaplin96, S. Kar7, A. Karasu Uysal79, D. Karatovic102, O.
Karavichev65, T. Karavicheva65, P. Karczmarczyk144, E. Karpechev65, A.
Kazantsev91, U. Kebschull76, R. Keidel48, D.L.D. Keijdener64, M. Keil35, B.
Ketzer44, Z. Khabanova93, A.M. Khan7, S. Khan16, A. Khanzadeev101, Y.
Kharlov94, A. Khatun16, A. Khuntia120, B. Kileng37, B. Kim17,63, D. Kim149,
D.J. Kim128, E.J. Kim75, J. Kim149, J.S. Kim42, J. Kim107, J. Kim149, J.
Kim75, M. Kim107, S. Kim18, T. Kim149, S. Kirsch70, I. Kisel40, S. Kiselev95,
A. Kisiel144, J.P. Kitowski2, J.L. Klay6, J. Klein35, S. Klein82, C. Klein-
Bösing146, M. Kleiner70, T. Klemenz108, A. Kluge35, A.G. Knospe127, C.
Kobdaj118, M.K. Köhler107, T. Kollegger110, A. Kondratyev77, N. Kondratyeva96,
E. Kondratyuk94, J. Konig70, S.A. Konigstorfer108, P.J. Konopka35,2, G.
Kornakov144, S.D. Koryciak2, L. Koska119, A. Kotliarov98, O. Kovalenko88, V.
Kovalenko115, M. Kowalski120, I. Králik66, A. Kravčáková39, L. Kreis110, M.
Krivda113,66, F. Krizek98, K. Krizkova Gajdosova38, M. Kroesen107, M.
Krüger70, E. Kryshen101, M. Krzewicki40, V. Kučera35, C. Kuhn139, P.G.
Kuijer93, T. Kumaoka136, D. Kumar143, L. Kumar103, N. Kumar103, S. Kundu35,89,
P. Kurashvili88, A. Kurepin65, A.B. Kurepin65, A. Kuryakin111, S. Kushpil98,
J. Kvapil113, M.J. Kweon63, J.Y. Kwon63, Y. Kwon149, S.L. La Pointe40, P. La
Rocca27, Y.S. Lai82, A. Lakrathok118, M. Lamanna35, R. Langoy132, K.
Lapidus35, P. Larionov53, E. Laudi35, L. Lautner35,108, R. Lavicka38, T.
Lazareva115, R. Lea142,24,59, J. Lee136, J. Lehrbach40, R.C. Lemmon97, I. León
Monzón122, E.D. Lesser19, M. Lettrich35,108, P. Lévai147, X. Li11, X.L. Li7,
J. Lien132, R. Lietava113, B. Lim17, S.H. Lim17, V. Lindenstruth40, A.
Lindner49, C. Lippmann110, A. Liu19, J. Liu130, I.M. Lofnes21, V. Loginov96,
C. Loizides99, P. Loncar36, J.A. Lopez107, X. Lopez137, E. López Torres8, J.R.
Luhder146, M. Lunardon28, G. Luparello62, Y.G. Ma41, A. Maevskaya65, M.
Mager35, T. Mahmoud44, A. Maire139, M. Malaev101, Q.W. Malik20, L.
MalininaIV,77, D. Mal’Kevich95, N. Mallick51, P. Malzacher110, G.
Mandaglio33,57, V. Manko91, F. Manso137, V. Manzari54, Y. Mao7, J. Mareš68,
G.V. Margagliotti24, A. Margotti55, A. Marín110, C. Markert121, M. Marquard70,
N.A. Martin107, P. Martinengo35, J.L. Martinez127, M.I. Martínez46, G.
Martínez García117, S. Masciocchi110, M. Masera25, A. Masoni56, L.
Massacrier80, A. Mastroserio141,54, A.M. Mathis108, O. Matonoha83, P.F.T.
Matuoka123, A. Matyja120, C. Mayer120, A.L. Mazuecos35, F. Mazzaschi25, M.
Mazzilli35, M.A. Mazzoni60, J.E. Mdhluli134, A.F. Mechler70, F. Meddi22, Y.
Melikyan65, A. Menchaca-Rocha73, E. Meninno116,30, A.S. Menon127, M. Meres13,
S. Mhlanga126,74, Y. Miake136, L. Micheletti61,25, L.C. Migliorin138, D.L.
Mihaylov108, K. Mikhaylov77,95, A.N. Mishra147, D. Miśkowiec110, A. Modak4,
A.P. Mohanty64, B. Mohanty89, M. Mohisin Khan16, Z. Moravcova92, C.
Mordasini108, D.A. Moreira De Godoy146, L.A.P. Moreno46, I. Morozov65, A.
Morsch35, T. Mrnjavac35, V. Muccifora53, E. Mudnic36, D. Mühlheim146, S.
Muhuri143, J.D. Mulligan82, A. Mulliri23, M.G. Munhoz123, R.H. Munzer70, H.
Murakami135, S. Murray126, L. Musa35, J. Musinsky66, C.J. Myers127, J.W.
Myrcha144, B. Naik134,50, R. Nair88, B.K. Nandi50, R. Nania55, E. Nappi54,
M.U. Naru14, A.F. Nassirpour83, A. Nath107, C. Nattrass133, A. Neagu20, L.
Nellen71, S.V. Nesbo37, G. Neskovic40, D. Nesterov115, B.S. Nielsen92, S.
Nikolaev91, S. Nikulin91, V. Nikulin101, F. Noferini55, S. Noh12, P.
Nomokonov77, J. Norman130, N. Novitzky136, P. Nowakowski144, A. Nyanin91, J.
Nystrand21, M. Ogino85, A. Ohlson83, V.A. Okorokov96, J. Oleniacz144, A.C.
Oliveira Da Silva133, M.H. Oliver148, A. Onnerstad128, C. Oppedisano61, A.
Ortiz Velasquez71, T. Osako47, A. Oskarsson83, J. Otwinowski120, K. Oyama85,
Y. Pachmayer107, S. Padhan50, D. Pagano142,59, G. Paić71, A. Palasciano54, J.
Pan145, S. Panebianco140, P. Pareek143, J. Park63, J.E. Parkkila128, S.P.
Pathak127, R.N. Patra104,35, B. Paul23, J. Pazzini142,59, H. Pei7, T.
Peitzmann64, X. Peng7, L.G. Pereira72, H. Pereira Da Costa140, D. Peresunko91,
G.M. Perez8, S. Perrin140, Y. Pestov5, V. Petráček38, M. Petrovici49, R.P.
Pezzi117,72, S. Piano62, M. Pikna13, P. Pillot117, O. Pinazza55,35, L.
Pinsky127, C. Pinto27, S. Pisano53, M. Płoskoń82, M. Planinic102, F.
Pliquett70, M.G. Poghosyan99, B. Polichtchouk94, S. Politano31, N. Poljak102,
A. Pop49, S. Porteboeuf-Houssais137, J. Porter82, V. Pozdniakov77, S.K.
Prasad4, R. Preghenella55, F. Prino61, C.A. Pruneau145, I. Pshenichnov65, M.
Puccio35, S. Qiu93, L. Quaglia25, R.E. Quishpe127, S. Ragoni113, A.
Rakotozafindrabe140, L. Ramello32, F. Rami139, S.A.R. Ramirez46, A.G.T.
Ramos34, T.A. Rancien81, R. Raniwala105, S. Raniwala105, S.S. Räsänen45, R.
Rath51, I. Ravasenga93, K.F. Read99,133, A.R. Redelbach40, K. RedlichV,88, A.
Rehman21, P. Reichelt70, F. Reidt35, H.A. Reme-ness37, R. Renfordt70, Z.
Rescakova39, K. Reygers107, A. Riabov101, V. Riabov101, T. Richert83,92, M.
Richter20, W. Riegler35, F. Riggi27, C. Ristea69, S.P. Rode51, M. Rodríguez
Cahuantzi46, K. Røed20, R. Rogalev94, E. Rogochaya77, T.S. Rogoschinski70, D.
Rohr35, D. Röhrich21, P.F. Rojas46, P.S. Rokita144, F. Ronchetti53, A.
Rosano33,57, E.D. Rosas71, A. Rossi58, A. Rotondi29,59, A. Roy51, P. Roy112,
S. Roy50, N. Rubini26, O.V. Rueda83, R. Rui24, B. Rumyantsev77, P.G. Russek2,
A. Rustamov90, E. Ryabinkin91, Y. Ryabov101, A. Rybicki120, H. Rytkonen128, W.
Rzesa144, O.A.M. Saarimaki45, R. Sadek117, S. Sadovsky94, J. Saetre21, K.
Šafařík38, S.K. Saha143, S. Saha89, B. Sahoo50, P. Sahoo50, R. Sahoo51, S.
Sahoo67, D. Sahu51, P.K. Sahu67, J. Saini143, S. Sakai136, S. Sambyal104, V.
SamsonovI,101,96, D. Sarkar145, N. Sarkar143, P. Sarma43, V.M. Sarti108,
M.H.P. Sas148, J. Schambach99,121, H.S. Scheid70, C. Schiaua49, R.
Schicker107, A. Schmah107, C. Schmidt110, H.R. Schmidt106, M.O. Schmidt107, M.
Schmidt106, N.V. Schmidt99,70, A.R. Schmier133, R. Schotter139, J.
Schukraft35, Y. Schutz139, K. Schwarz110, K. Schweda110, G. Scioli26, E.
Scomparin61, J.E. Seger15, Y. Sekiguchi135, D. Sekihata135, I.
Selyuzhenkov110,96, S. Senyukov139, J.J. Seo63, D. Serebryakov65, L.
Šerkšnytė108, A. Sevcenco69, T.J. Shaba74, A. Shabanov65, A. Shabetai117, R.
Shahoyan35, W. Shaikh112, A. Shangaraev94, A. Sharma103, H. Sharma120, M.
Sharma104, N. Sharma103, S. Sharma104, O. Sheibani127, K. Shigaki47, M.
Shimomura86, S. Shirinkin95, Q. Shou41, Y. Sibiriak91, S. Siddhanta56, T.
Siemiarczuk88, T.F. Silva123, D. Silvermyr83, G. Simonetti35, B. Singh108, R.
Singh89, R. Singh104, R. Singh51, V.K. Singh143, V. Singhal143, T. Sinha112,
B. Sitar13, M. Sitta32, T.B. Skaali20, G. Skorodumovs107, M. Slupecki45, N.
Smirnov148, R.J.M. Snellings64, C. Soncco114, J. Song127, A. Songmoolnak118,
F. Soramel28, S. Sorensen133, I. Sputowska120, J. Stachel107, I. Stan69, P.J.
Steffanic133, S.F. Stiefelmaier107, D. Stocco117, I. Storehaug20, M.M.
Storetvedt37, C.P. Stylianidis93, A.A.P. Suaide123, T. Sugitate47, C. Suire80,
M. Suljic35, R. Sultanov95, M. Šumbera98, V. Sumberia104, S. Sumowidagdo52, S.
Swain67, A. Szabo13, I. Szarka13, U. Tabassam14, S.F. Taghavi108, G.
Taillepied137, J. Takahashi124, G.J. Tambave21, S. Tang137,7, Z. Tang131, M.
Tarhini117, M.G. Tarzila49, A. Tauro35, G. Tejeda Muñoz46, A. Telesca35, L.
Terlizzi25, C. Terrevoli127, G. Tersimonov3, S. Thakur143, D. Thomas121, R.
Tieulent138, A. Tikhonov65, A.R. Timmins127, M. Tkacik119, A. Toia70, N.
Topilskaya65, M. Toppi53, F. Torales-Acosta19, T. Tork80, S.R. Torres38, A.
Trifiró33,57, S. Tripathy55,71, T. Tripathy50, S. Trogolo35,28, G.
Trombetta34, V. Trubnikov3, W.H. Trzaska128, T.P. Trzcinski144, B.A.
Trzeciak38, A. Tumkin111, R. Turrisi58, T.S. Tveter20, K. Ullaland21, A.
Uras138, M. Urioni59,142, G.L. Usai23, M. Vala39, N. Valle59,29, S. Vallero61,
N. van der Kolk64, L.V.R. van Doremalen64, M. van Leeuwen93, P. Vande Vyvre35,
D. Varga147, Z. Varga147, M. Varga-Kofarago147, A. Vargas46, M. Vasileiou87,
A. Vasiliev91, O. Vázquez Doce108, V. Vechernin115, E. Vercellin25, S. Vergara
Limón46, L. Vermunt64, R. Vértesi147, M. Verweij64, L. Vickovic36, Z.
Vilakazi134, O. Villalobos Baillie113, G. Vino54, A. Vinogradov91, T.
Virgili30, V. Vislavicius92, A. Vodopyanov77, B. Volkel35, M.A. Völkl107, K.
Voloshin95, S.A. Voloshin145, G. Volpe34, B. von Haller35, I. Vorobyev108, D.
Voscek119, J. Vrláková39, B. Wagner21, C. Wang41, D. Wang41, M. Weber116,
R.J.G.V. Weelden93, A. Wegrzynek35, S.C. Wenzel35, J.P. Wessels146, J.
Wiechula70, J. Wikne20, G. Wilk88, J. Wilkinson110, G.A. Willems146, E.
Willsher113, B. Windelband107, M. Winn140, W.E. Witt133, J.R. Wright121, W.
Wu41, Y. Wu131, R. Xu7, S. Yalcin79, Y. Yamaguchi47, K. Yamakawa47, S. Yang21,
S. Yano47,140, Z. Yin7, H. Yokoyama64, I.-K. Yoo17, J.H. Yoon63, S. Yuan21, A.
Yuncu107, V. Zaccolo24, A. Zaman14, C. Zampolli35, H.J.C. Zanoli64, N.
Zardoshti35, A. Zarochentsev115, P. Závada68, N. Zaviyalov111, H.
Zbroszczyk144, M. Zhalov101, S. Zhang41, X. Zhang7, Y. Zhang131, V.
Zherebchevskii115, Y. Zhi11, D. Zhou7, Y. Zhou92, J. Zhu7,110, Y. Zhu7, A.
Zichichi26, G. Zinovjev3, N. Zurlo142,59

Affiliation Notes

I Deceased

II Also at: Italian National Agency for New Technologies, Energy and
Sustainable Economic Development (ENEA), Bologna, Italy

III Also at: Dipartimento DET del Politecnico di Torino, Turin, Italy

IV Also at: M.V. Lomonosov Moscow State University, D.V. Skobeltsyn Institute
of Nuclear, Physics, Moscow, Russia

V Also at: Institute of Theoretical Physics, University of Wroclaw, Poland

Collaboration Institutes

1 A.I. Alikhanyan National Science Laboratory (Yerevan Physics Institute)
Foundation, Yerevan, Armenia

2 AGH University of Science and Technology, Cracow, Poland

3 Bogolyubov Institute for Theoretical Physics, National Academy of Sciences
of Ukraine, Kiev, Ukraine

4 Bose Institute, Department of Physics and Centre for Astroparticle Physics
and Space Science (CAPSS), Kolkata, India

5 Budker Institute for Nuclear Physics, Novosibirsk, Russia

6 California Polytechnic State University, San Luis Obispo, California, United
States

7 Central China Normal University, Wuhan, China

8 Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN), Havana,
Cuba

9 Centro de Investigación y de Estudios Avanzados (CINVESTAV), Mexico City and
Mérida, Mexico

10 Chicago State University, Chicago, Illinois, United States

11 China Institute of Atomic Energy, Beijing, China

12 Chungbuk National University, Cheongju, Republic of Korea

13 Comenius University Bratislava, Faculty of Mathematics, Physics and
Informatics, Bratislava, Slovakia

14 COMSATS University Islamabad, Islamabad, Pakistan

15 Creighton University, Omaha, Nebraska, United States

16 Department of Physics, Aligarh Muslim University, Aligarh, India

17 Department of Physics, Pusan National University, Pusan, Republic of Korea

18 Department of Physics, Sejong University, Seoul, Republic of Korea

19 Department of Physics, University of California, Berkeley, California,
United States

20 Department of Physics, University of Oslo, Oslo, Norway

21 Department of Physics and Technology, University of Bergen, Bergen, Norway

22 Dipartimento di Fisica dell’Università ’La Sapienza’ and Sezione INFN,
Rome, Italy

23 Dipartimento di Fisica dell’Università and Sezione INFN, Cagliari, Italy

24 Dipartimento di Fisica dell’Università and Sezione INFN, Trieste, Italy

25 Dipartimento di Fisica dell’Università and Sezione INFN, Turin, Italy

26 Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN,
Bologna, Italy

27 Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN,
Catania, Italy

28 Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN,
Padova, Italy

29 Dipartimento di Fisica e Nucleare e Teorica, Università di Pavia, Pavia,
Italy

30 Dipartimento di Fisica ‘E.R. Caianiello’ dell’Università and Gruppo
Collegato INFN, Salerno, Italy

31 Dipartimento DISAT del Politecnico and Sezione INFN, Turin, Italy

32 Dipartimento di Scienze e Innovazione Tecnologica dell’Università del
Piemonte Orientale and INFN Sezione di Torino, Alessandria, Italy

33 Dipartimento di Scienze MIFT, Università di Messina, Messina, Italy

34 Dipartimento Interateneo di Fisica ‘M. Merlin’ and Sezione INFN, Bari,
Italy

35 European Organization for Nuclear Research (CERN), Geneva, Switzerland

36 Faculty of Electrical Engineering, Mechanical Engineering and Naval
Architecture, University of Split, Split, Croatia

37 Faculty of Engineering and Science, Western Norway University of Applied
Sciences, Bergen, Norway

38 Faculty of Nuclear Sciences and Physical Engineering, Czech Technical
University in Prague, Prague, Czech Republic

39 Faculty of Science, P.J. Šafárik University, Košice, Slovakia

40 Frankfurt Institute for Advanced Studies, Johann Wolfgang Goethe-
Universität Frankfurt, Frankfurt, Germany

41 Fudan University, Shanghai, China

42 Gangneung-Wonju National University, Gangneung, Republic of Korea

43 Gauhati University, Department of Physics, Guwahati, India

44 Helmholtz-Institut für Strahlen- und Kernphysik, Rheinische Friedrich-
Wilhelms-Universität Bonn, Bonn, Germany

45 Helsinki Institute of Physics (HIP), Helsinki, Finland

46 High Energy Physics Group, Universidad Autónoma de Puebla, Puebla, Mexico

47 Hiroshima University, Hiroshima, Japan

48 Hochschule Worms, Zentrum für Technologietransfer und Telekommunikation
(ZTT), Worms, Germany

49 Horia Hulubei National Institute of Physics and Nuclear Engineering,
Bucharest, Romania

50 Indian Institute of Technology Bombay (IIT), Mumbai, India

51 Indian Institute of Technology Indore, Indore, India

52 Indonesian Institute of Sciences, Jakarta, Indonesia

53 INFN, Laboratori Nazionali di Frascati, Frascati, Italy

54 INFN, Sezione di Bari, Bari, Italy

55 INFN, Sezione di Bologna, Bologna, Italy

56 INFN, Sezione di Cagliari, Cagliari, Italy

57 INFN, Sezione di Catania, Catania, Italy

58 INFN, Sezione di Padova, Padova, Italy

59 INFN, Sezione di Pavia, Pavia, Italy

60 INFN, Sezione di Roma, Rome, Italy

61 INFN, Sezione di Torino, Turin, Italy

62 INFN, Sezione di Trieste, Trieste, Italy

63 Inha University, Incheon, Republic of Korea

64 Institute for Gravitational and Subatomic Physics (GRASP), Utrecht
University/Nikhef, Utrecht, Netherlands

65 Institute for Nuclear Research, Academy of Sciences, Moscow, Russia

66 Institute of Experimental Physics, Slovak Academy of Sciences, Košice,
Slovakia

67 Institute of Physics, Homi Bhabha National Institute, Bhubaneswar, India

68 Institute of Physics of the Czech Academy of Sciences, Prague, Czech
Republic

69 Institute of Space Science (ISS), Bucharest, Romania

70 Institut für Kernphysik, Johann Wolfgang Goethe-Universität Frankfurt,
Frankfurt, Germany

71 Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México,
Mexico City, Mexico

72 Instituto de Física, Universidade Federal do Rio Grande do Sul (UFRGS),
Porto Alegre, Brazil

73 Instituto de Física, Universidad Nacional Autónoma de México, Mexico City,
Mexico

74 iThemba LABS, National Research Foundation, Somerset West, South Africa

75 Jeonbuk National University, Jeonju, Republic of Korea

76 Johann-Wolfgang-Goethe Universität Frankfurt Institut für Informatik,
Fachbereich Informatik und Mathematik, Frankfurt, Germany

77 Joint Institute for Nuclear Research (JINR), Dubna, Russia

78 Korea Institute of Science and Technology Information, Daejeon, Republic of
Korea

79 KTO Karatay University, Konya, Turkey

80 Laboratoire de Physique des 2 Infinis, Irène Joliot-Curie, Orsay, France

81 Laboratoire de Physique Subatomique et de Cosmologie, Université Grenoble-
Alpes, CNRS-IN2P3, Grenoble, France

82 Lawrence Berkeley National Laboratory, Berkeley, California, United States

83 Lund University Department of Physics, Division of Particle Physics, Lund,
Sweden

84 Moscow Institute for Physics and Technology, Moscow, Russia

85 Nagasaki Institute of Applied Science, Nagasaki, Japan

86 Nara Women’s University (NWU), Nara, Japan

87 National and Kapodistrian University of Athens, School of Science,
Department of Physics , Athens, Greece

88 National Centre for Nuclear Research, Warsaw, Poland

89 National Institute of Science Education and Research, Homi Bhabha National
Institute, Jatni, India

90 National Nuclear Research Center, Baku, Azerbaijan

91 National Research Centre Kurchatov Institute, Moscow, Russia

92 Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark

93 Nikhef, National institute for subatomic physics, Amsterdam, Netherlands

94 NRC Kurchatov Institute IHEP, Protvino, Russia

95 NRC «Kurchatov»Institute - ITEP, Moscow, Russia

96 NRNU Moscow Engineering Physics Institute, Moscow, Russia

97 Nuclear Physics Group, STFC Daresbury Laboratory, Daresbury, United Kingdom

98 Nuclear Physics Institute of the Czech Academy of Sciences, Řež u Prahy,
Czech Republic

99 Oak Ridge National Laboratory, Oak Ridge, Tennessee, United States

100 Ohio State University, Columbus, Ohio, United States

101 Petersburg Nuclear Physics Institute, Gatchina, Russia

102 Physics department, Faculty of science, University of Zagreb, Zagreb,
Croatia

103 Physics Department, Panjab University, Chandigarh, India

104 Physics Department, University of Jammu, Jammu, India

105 Physics Department, University of Rajasthan, Jaipur, India

106 Physikalisches Institut, Eberhard-Karls-Universität Tübingen, Tübingen,
Germany

107 Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg,
Heidelberg, Germany

108 Physik Department, Technische Universität München, Munich, Germany

109 Politecnico di Bari and Sezione INFN, Bari, Italy

110 Research Division and ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum
für Schwerionenforschung GmbH, Darmstadt, Germany

111 Russian Federal Nuclear Center (VNIIEF), Sarov, Russia

112 Saha Institute of Nuclear Physics, Homi Bhabha National Institute,
Kolkata, India

113 School of Physics and Astronomy, University of Birmingham, Birmingham,
United Kingdom

114 Sección Física, Departamento de Ciencias, Pontificia Universidad Católica
del Perú, Lima, Peru

115 St. Petersburg State University, St. Petersburg, Russia

116 Stefan Meyer Institut für Subatomare Physik (SMI), Vienna, Austria

117 SUBATECH, IMT Atlantique, Université de Nantes, CNRS-IN2P3, Nantes, France

118 Suranaree University of Technology, Nakhon Ratchasima, Thailand

119 Technical University of Košice, Košice, Slovakia

120 The Henryk Niewodniczanski Institute of Nuclear Physics, Polish Academy of
Sciences, Cracow, Poland

121 The University of Texas at Austin, Austin, Texas, United States

122 Universidad Autónoma de Sinaloa, Culiacán, Mexico

123 Universidade de São Paulo (USP), São Paulo, Brazil

124 Universidade Estadual de Campinas (UNICAMP), Campinas, Brazil

125 Universidade Federal do ABC, Santo Andre, Brazil

126 University of Cape Town, Cape Town, South Africa

127 University of Houston, Houston, Texas, United States

128 University of Jyväskylä, Jyväskylä, Finland

129 University of Kansas, Lawrence, Kansas, United States

130 University of Liverpool, Liverpool, United Kingdom

131 University of Science and Technology of China, Hefei, China

132 University of South-Eastern Norway, Tonsberg, Norway

133 University of Tennessee, Knoxville, Tennessee, United States

134 University of the Witwatersrand, Johannesburg, South Africa

135 University of Tokyo, Tokyo, Japan

136 University of Tsukuba, Tsukuba, Japan

137 Université Clermont Auvergne, CNRS/IN2P3, LPC, Clermont-Ferrand, France

138 Université de Lyon, CNRS/IN2P3, Institut de Physique des 2 Infinis de Lyon
, Lyon, France

139 Université de Strasbourg, CNRS, IPHC UMR 7178, F-67000 Strasbourg, France,
Strasbourg, France

140 Université Paris-Saclay Centre d’Etudes de Saclay (CEA), IRFU, Départment
de Physique Nucléaire (DPhN), Saclay, France

141 Università degli Studi di Foggia, Foggia, Italy

142 Università di Brescia, Brescia, Italy

143 Variable Energy Cyclotron Centre, Homi Bhabha National Institute, Kolkata,
India

144 Warsaw University of Technology, Warsaw, Poland

145 Wayne State University, Detroit, Michigan, United States

146 Westfälische Wilhelms-Universität Münster, Institut für Kernphysik,
Münster, Germany

147 Wigner Research Centre for Physics, Budapest, Hungary

148 Yale University, New Haven, Connecticut, United States

149 Yonsei University, Seoul, Republic of Korea