PHYSICAL REVIEW D 106, 052010 (2022) - First study of the two-body scattering involving charm hadrons
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PHYSICAL REVIEW D 106, 052010 (2022)
First study of the two-body scattering involving charm hadrons
S. Acharya et al.*
(ALICE Collaboration)
(Received 27 January 2022; revised 3 May 2022; accepted 31 August 2022; published 23 September 2022)
This article presents the first measurement of the interaction between charm hadrons and nucleons. The
two-particle momentum correlations of pD− and p̄Dþ pairs are measured by the ALICE Collaboration in
pffiffiffi
high-multiplicity pp collisions at s ¼ 13 TeV. The data are compatible with the Coulomb-only
interaction hypothesis within ð1.1–1.5Þσ. The level of agreement slightly improves if an attractive nucleon
ðNÞD̄ strong interaction is considered, in contrast to most model predictions which suggest an overall
repulsive interaction. This measurement allows for the first time an estimation of the 68% confidence level
interval for the isospin I ¼ 0 inverse scattering length of the ND̄ state f−1 −1
0;I¼0 ∈ ½−0.4; 0.9 fm , assuming
negligible interaction for the isospin I ¼ 1 channel.
DOI: 10.1103/PhysRevD.106.052010
I. INTRODUCTION the scattering parameters of systems involving D and/or D
mesons are pivotal to advance in the interpretation of the
The study of the residual strong interaction among
many observed states. The first step in this direction is the
hadrons is a very active field within nuclear physics.
investigation of the interaction between the p(uud) D− ðc̄dÞ
This interaction can lead to the formation of bound states,
pair and its charge conjugate. This interaction does not
such as nuclei, or molecular states as, for example, the
couple to the lower energy meson-baryon channels since no
Λð1405Þ, which is considered as being generated from the
qq̄ annihilation can occur. A measurement of this interaction
attractive forces in the nucleon (N) K̄–Σπ channels [1–4].
is also an essential reference for the study of the in-medium
One of the most fervent discussions in this context is
D- and D -meson properties [20]. Similarly to kaons and
nowadays revolving around systems involving charm mes-
antikaons, it is theoretically predicted that possible mod-
ons (D, D ). Studies of their interaction are motivated by the
ifications of the charm-meson spectral function at large
observation of several new states with hidden charm and/or
baryonic densities can be connected to a decrease of the
beauty (so-called XYZ states) [5–9], as well as with open chiral condensate, thus providing sensitivity to chiral-
charm such as the Tcc þ [10,11], and also of pentaquark symmetry restoration [21].
states like Pc ð4380Þ and Pc ð4450Þ [12,13]. These exotic So far, the topic of the strong interaction between hadrons
hadrons can be described as compact multiquark states in containing charm quarks was addressed only from a
the context of the constituent-quark model [14], but are also theoretical point of view [22–25] by employing different
considered as natural candidates for loosely bound molecu- effective models anchored to the successful description of
lar states [5,6]. For example, the structure of the χ c1 ð3872Þ other baryon-meson final states, such as the NK̄ and NK
[formerly X(3872)] has been interpreted as a D̄D =DD̄ systems, while data are missing. Scattering experiments [26]
molecular state or as a tetraquark [15]. Currently, definite and systematic studies of stable and unstable nuclei [27],
conclusions are difficult to draw because of the lack of any accompanied by sophisticated calculations achieved within
direct experimental information on the DD̄ strong inter- effective field theories [28,29], allowed us to reach a solid
action. Strong support for the molecular nature of the comprehension of the interaction among nucleons. When
Λð1405Þ came not least from low-energy NK̄ scattering extending these studies to interactions including strange
data and information on the pK̄ scattering length from hadrons, the average properties of the interactions of some
kaonic hydrogen atoms [16–19]. Hence, a determination of strange nucleon–hadron combinations (pK [30–32], pΛ,
and pΣ0 [33–35]) could be gauged with the help of
*
Full author list given at the end of the article. scattering data and measurements of kaonic atoms [36].
The study of Λ hypernuclei [37] led to the extraction of an
Published by the American Physical Society under the terms of average attractive potential. The situation has drastically
the Creative Commons Attribution 4.0 International license.
Further distribution of this work must maintain attribution to changed in recent years, thanks to the novel employment of
the author(s) and the published article’s title, journal citation, the femtoscopy technique [38] in pp and p-Pb collisions at
and DOI. the LHC applied to almost all combinations of protons and
2470-0010=2022=106(5)=052010(16) 052010-1 © 2022 CERN, for the ALICE CollaborationS. ACHARYA et al. PHYS. REV. D 106, 052010 (2022)
strange hadrons [39]. The ALICE Collaboration could III. DATA ANALYSIS
precisely study the following interactions: pp, pK , pΛ, A. Selection of proton and D -meson candidates
pΛ̄, pΣ0 , ΛΛ, ΛΛ̄, pΞ− , pΩ− , and pϕ [39–47]. Since
conventional scattering experiments cannot be performed The proton candidates are selected according to the
with D mesons and charm nuclei [48] have not been methods described in [39]. Charged-particle tracks recon-
structed with the TPC are required to have transverse
discovered yet (searches for charm nuclear states are
momentum 0.5 < pT < 4.05 GeV=c and pseudorapidity
included in the scientific program of the Japan Proton
jηj < 0.8. Particle identification (PID) is conducted by
Accelerator Research Complex [49]), the femtoscopy tech-
measuring the specific energy loss and the time of flight
nique can be employed to study the ND and ND̄ inter-
with the TPC and TOF detectors, respectively. The selec-
actions. In this article, the first measurement of the strong
tion is based on the deviation nσ between the measured and
interaction between a D− meson and a proton is reported. expected values for protons, normalized by the detector
This pioneering analysis employs D− instead of the more resolution σ. For proton candidates with a momentum
abundantly produced D̄0 mesons because of the smaller p < 0.75 GeV=c, only the TPC is used by requiring
contribution from decays of excited charm states and the jnTPC
σ j < 3, while for larger momenta the PID information
possibility to separate particles and antiparticles without of TPC and TOFp are combined and tracks are accepted only
ambiguity. ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ffi
2 TOF 2
if the condition ðnTPC σ Þ þ ðn σ Þ < 3 is fulfilled. With
these selection criteria, the purity of the proton sample
II. EXPERIMENTAL APPARATUS averaged over pT is Pp ¼ 98% [39]. The contribution of
AND DATA SAMPLES secondary protons originating from weak decays or inter-
actions with the detector material is assessed by using MC
The analysis was performed pffiffiffiusing a sample of high- template fits to the measured distribution of the distance of
multiplicity pp collisions at s ¼ 13 TeV collected by
closest approach of the track to the primary vertex. The
ALICE [50,51] during the LHC run 2 (2016–2018). The
estimated average fraction of primary protons is 86% [39].
main detectors used for this analysis to reconstruct and
The D mesons are reconstructed via their hadronic
identify the protons and the D-meson decay products are
decay channel D → K∓ π π , having a branching ratio
the inner tracking system (ITS) [52], the time projection
BR ¼ ð9.38 0.15Þ% [60]. D-meson candidates are
chamber (TPC) [53], and the time-of-flight (TOF) detector
defined combining triplets of tracks reconstructed in the
[54]. They are located inside a large solenoidal magnet TPC and ITS detectors with the proper charge signs,
providing a uniform magnetic field of 0.5 T parallel to the jηj < 0.8, pT > 0.3 GeV=c, and a minimum of two (out
LHC beam direction and cover the pseudorapidity interval of six) hits in the ITS, with at least one in either of the two
jηj < 0.9. The events were recorded with a high-multiplic- innermost layers to ensure a good pointing resolution. To
ity trigger relying on the measured signal amplitudes in the reduce the large combinatorial background and the con-
V0 detector, which consists of two scintillator arrays tribution of D mesons originating from beauty-hadron
covering the pseudorapidity intervals −3.7 < η < −1.7 decays (nonprompt), a machine-learning multiclass classi-
and 2.8 < η < 5.1 [55]. The collected data sample corre- fication algorithm based on boosted decision trees (BDTs)
sponds to the 0.17% highest-multiplicity events out of all provided by the XGBOOST library [61,62] is employed. The
inelastic collisions with at least one charged particle in the variables utilized for the candidate selection in the BDTs
pseudorapidity range jηj < 1 (denoted as INEL > 0). are based on the displaced decay-vertex topology, exploit-
Events were further selected off-line in order to remove ing the mean proper decay length of D mesons of cτ ≈
machine-induced backgrounds [51]. The events were 312 μm [60], and on the PID of charged pions and kaons.
required to have a reconstructed collision vertex located Before that, a preselection of the D candidates based on
within 10 cm from the center of the detector along the the PID information of the decay products is applied by
beam-line direction to maintain a uniform acceptance. requiring a 3σ compatibility either with the TPC or the TOF
Events with multiple primary vertices (pileup), recon- expected signals of the daughter tracks. Signal samples of
structed from track segments measured with the two prompt (originating from charm-quark hadronization or
innermost ITS layers, were rejected. The remaining unde- decays of excited charm states) and nonprompt D mesons
tected pileup is of the order of 1% and therefore negligible for the BDT training are obtained from MC simulations.
in the analysis. After these selections, the analyzed data The background samples are obtained from the sidebands
sample consists of about 109 events. The Monte Carlo of the candidate invariant mass distributions in data. The
(MC) samples used in this analysis consist of pp collisions BDT outputs are related to the candidate probability to be a
simulated using the PYTHIA 8.243 event generator [56,57] prompt or nonprompt D meson, or combinatorial back-
with the Monash-13 tune [58] and GEANT3 [59] for the ground. D-meson candidates are selected in the pT interval
propagation of the generated particles through the detector. between 1 and 10 GeV=c by requiring a high probability to
052010-2FIRST STUDY OF THE TWO-BODY SCATTERING INVOLVING … PHYS. REV. D 106, 052010 (2022)
be a prompt D meson and a low probability to be a via the corresponding acceptance-times-efficiency
combinatorial-background candidate. factors for prompt [ðAcc × εÞprompt
i ] and nonprompt
A selection on the candidate invariant mass ðMðKππÞÞ is [ðAcc × εÞnonprompt ] D
mesons as follows
i
applied to obtain a high-purity sample of D mesons. To
this end, the MðKππÞ distribution of D candidates is fitted 0 1
ðAcc × εÞprompt ðAcc × εÞnonprompt !
in intervals of pT of 1 GeV width in the range 1 < pT < B
1 1
C N prompt
10 GeV=c with a Gaussian function for the signal and an B .
.. .. C×
@ . A N nonprompt
exponential term for the background. The left panel of
Fig. 1 shows the MðKππÞ distribution for D with ðAcc × εÞprompt
n ðAcc × εÞnonprompt
n
0 1 0 1
2 < pT < 3 GeV=c. The width of the Gaussian function Y1 δ1
used to describe the signal peak, σ D , increases from 6 to B . C B . C
10 MeV=c2 with increasing pT as a consequence of the pT −B C B C
@ .. A ¼ @ .. A: ð1Þ
dependence of the momentum resolution. The D -meson Yn δn
candidates in the invariant mass window jMðKππÞj < 2σ D
are selected to be paired with proton candidates. This
The δi factors represent the residuals that account for the
selection, displayed by the two vertical lines in Fig. 1, leads
equations not holding exactly due to the uncertainty of Y i ,
to a purity that is PD− ¼ ð61.7 0.9ðstatÞ 0.7ðsystÞÞ%
on average. The systematic uncertainty of PD− is evaluated ðAcc × εÞnonprompt
i , and ðAcc × εÞprompt
i . The system of
2
by repeating the invariant mass fits, varying the background equations can be solved via a χ minimization, which
fit function and the invariant mass upper and lower limits. leads to the determination of N prompt and N nonprompt . The
The contributions of prompt and nonprompt D mesons right panel of Fig. 1 shows an example of a raw-yield
are depicted in the left panel of Fig. 1 with the red and distribution as a function of the BDT-based selection used
blue distributions, respectively, They are obtained with a in the minimization procedure for D mesons with
data-driven method based on the sampling of the raw yield 2 < pT < 3 GeV=c. The leftmost data point of the dis-
at different values of the BDT output score related to tribution represents the raw yield corresponding to the
the probability of being a nonprompt D meson [63]. loosest selection on the BDT output related to the
The yields of prompt and nonprompt D mesons can be candidate probability of being a nonprompt D meson,
extracted by solving a system of equations that relate while the rightmost one corresponds to the strictest
the raw yield value Y i (obtained with the ith threshold selection, which is expected to preferentially select non-
on the BDT output score) to the corrected yields of prompt D mesons. The prompt and nonprompt compo-
prompt (N prompt ) and nonprompt (N nonprompt ) D mesons nents, obtained for each BDT-based selection using the
×103 ×103
10
ALICE pp, s = 13 TeV 25 ALICE pp, s = 13 TeV
9
High-mult (0−0.17% INEL > 0) High-mult (0−0.17% INEL > 0)
±
8 D± → K π ± π ±
Counts per 4 MeV/c 2
2 < p < 3 GeV/c 20 2 < p < 3 GeV/c
7 T Data T
Data
S
(2σ) = 0.70 Fit
c→D
+
Raw yield
6 S +B Background +
Tot signal 15 b→D
5 c→D
+ Total signal
+
b→D
4
10
3
2 5
1
1.8 1.85 1.9 1.95 2 4 6 8 10 12 14 16 18 20
M (Kππ) (GeV/ c 2) BDT-based selection
FIG. 1. Left: invariant mass distributions of D candidates in the 2 < pT < 3 GeV=c interval. The green solid line shows the total fit
function and the gray dotted line the combinatorial background. The contributions of D mesons originating from charm hadronization
and beauty-hadron decays are obtained with the method relying on the definition of different selection criteria, as explained in the text.
Right: example of raw-yield distribution as a function of the BDT-based selection employed in the procedure adopted for the
determination of the fraction of D originating from beauty-hadron decays for the 2 < pT < 3 GeV=c interval.
052010-3S. ACHARYA et al. PHYS. REV. D 106, 052010 (2022)
procedure described above, are represented by the red and particle pairs produced in events with similar z position of
blue filled histograms, respectively, while their sum is the primary vertex and similar charged-particle multiplicity.
reported by the magenta histogram. Since the correlation functions for pD− and p̄Dþ are
The obtained corrected yields N prompt and N nonprompt can consistent with each other within statistical uncertainties,
then be used to compute the fraction of nonprompt D they are combined and in the following pD− will represent
mesons f jnonprompt for a given selection j, pD− ⊕ p̄Dþ . The normalization constant N is obtained
from k ∈ ½1500; 2000 MeV=c where the correlation func-
f jnonprompt tion is independent of k , as expected since in this region of
k the pairs of particles are not affected by any interaction.
ðAcc × εÞnonprompt
j × N nonprompt The resulting correlation function Cexp ðk Þ is displayed in
¼ :
ðAcc × εÞnonprompt
j × N nonprompt þ ðAcc × εÞprompt
j × N prompt the left panel of Fig. 2. The data are compatible with unity
for k > 500 MeV=c, while they show a possible hint of
ð2Þ an increase for lower k values. In total 200 pD− and
221 p̄Dþ pairs contribute to N same ðk Þ in the region of
The f nonprompt factor for the selections used to build the k < 200 MeV=c, where model calculations [22–25] pre-
pD− and p̄Dþ pairs is estimated to be ð7.7 0.5ðstatÞ dict a deviation from unity. The systematic uncertainties of
0.2ðsystÞÞ%. The systematic uncertainty of f nonprompt is Cexp ðk Þ are assessed by varying the proton and D− selection
evaluated by repeating the procedure with different sets of criteria.
selection criteria and varying the fitting parameters in the The measured two-particle momentum correlation func-
raw-yield extraction. In addition, since the efficiency tion can be related to the source function and the two-
depends on the charged-particle multiplicity, the multiplic- particle wave function via the Koonin-Pratt equation
ity distribution in the MC sample used for the efficiency R
Cðk Þ ¼ d3 r Sðr ÞjΨðk ; r Þj2 [65], where Sðr Þ is the
computation was weighted in order to reproduce the one source function, Ψðk ; r Þ is the two-particle wave func-
in data. tion, and r refers to the relative distance between the two
Differently from the component originating from beauty- particles. The source function for the pD− pairs is
hadron weak decays, D mesons originating from excited estimated by employing the hypothesis of a common
charm-meson strong decays cannot be experimentally source for all hadrons in high-multiplicity pp collisions
resolved from promptly produced D mesons due to their at the LHC corrected for strong decays of extremely short-
short lifetime. The two largest sources are the D → D π 0 lived resonances (cτ ≲ 5 fm) feeding into the particle pairs
and D → D γ decays, having BR ¼ ð30.7 0.5Þ% and [66]. This is the case for resonances strongly decaying into
BR ¼ ð1.6 0.4Þ% [60], respectively. Their contribution is protons. In contrast, both beauty-hadron and D decays
þ þ
estimated from the production cross sectionspof ffiffiffi D and D occur at larger distances than the typical range for the
mesons measured in pp collisions at s ¼ 5.02 TeV strong interaction [60]. This implies that the correlation
[63,64] and employing the PYTHIA 8 decayer for the function for D− mesons originating from these decays will
description of the D → D X decay kinematics. The only carry the imprint of the interaction of the parent
fraction of D mesons in 1 < pT < 10 GeV=c originating particle with the proton without impacting the size of the
from D decays is estimated to be f D− ¼ ð27.6 1.3ðstatÞ emitting source. The core source determined in [66]
2.4ðsystÞÞ%, where statistical and systematic uncertainties features a dependence on the transverse mass mT of the
are propagated from the measurements of the Dþ and Dþ particle pair, which can be attributed to a collective
production cross sections. expansion of the system [65,67–69]. The collective behav-
ior has been studied in high-multiplicity pp collisions by
B. The correlation function the CMS Collaboration and found to be comparable for
light-flavor and charm hadrons [70]. Hence, the core
The proton and D− candidates are then combined and source of pD− pairs with k < 200 MeV=c is estimated
their relative momentum k is evaluated as k ¼ 12 × by parametrizing the measured mT dependence of the
jpp − pD j, where pp;D are the momenta of the two particles source radius extracted from pp correlations in [66] and
in the pair rest frame. The k distribution of pD− pairs, evaluating it at the hmT i ¼ 2.7 GeV=c2 of the pD− pairs.
N same ðk Þ, is then divided by the one obtained combining Since the production mechanism of charm mesons might
proton and D− candidates from different events, N mixed ðk Þ, not be identical to that of light-flavor baryons, the emission
to compute the two-particle momentum correlation function, of the pp and pD− pairs is studied by simulating pp
which is defined as Cexp ðk Þ ¼ N × N same ðk Þ=N mixed ðk Þ collisions with PYTHIA 8.301 [57] and computing their
[65]. The latter provides a correction for the acceptance of relative distance in the pair rest frame, r , considering only
the detector and the normalization for the phase space of the D− mesons originating directly from charm-quark hadro-
particle pairs. To ensure the same geometrical acceptance as nization. These studies indicate that the core source of pD−
for N same, the mixing procedure is conducted only between at the pertinent hmT i is smaller by about 25% compared to
052010-4FIRST STUDY OF THE TWO-BODY SCATTERING INVOLVING … PHYS. REV. D 106, 052010 (2022)
ALICE pp s = 13 TeV ALICE pp s = 13 TeV
High-mult. (0 − 0.17% INEL > 0) High-mult. (0 − 0.17% INEL > 0)
2.0
pD− ⊕ pD+ C exp(k *), pD− ⊕ pD+
Total background
(λpD* = 0.144, λp(K π π ) = 0.383)
1.5 pD*− → pD−
C exp(k* )
(λpD* = 1)
C (k* )
1.5 p(K+π−π−)
(λp(K π π ) = 1)
1.0
1.0
0 500 1000 1500 2000 0 200 400 600 800
k* (MeV/c ) k* (MeV/c )
FIG. 2. Left: experimental pD− correlation function in the range 0 < k < 2 GeV=c. Statistical (bars) and systematic uncertainties
(shaded boxes) are shown separately. The open boxes represent the bin width. Right: experimental pD− correlation function in a reduced
k range together with the contributions from pðKþ π − π − Þ (green band) and pD− (red band), and the total background model (purple
band). The pðKþ π − π − Þ and pD− contributions are not scaled by the respective λ parameter. The width of the dark (light) shaded bands
depicts the statistical (total) uncertainty of the parametrized background contributions.
that of pp pairs. This is included in the systematic 200 MeV=c; MD− ðpT Þ − 5 × σ D− ðpT Þ and [M D− ðpT Þþ
uncertainty of the source radius. The resulting overall 5 × σ D− ðpT Þ; MD− ðpT Þ þ 200 MeV=c] for the left and
source is parametrized by a Gaussian profile characterized right sidebands, respectively. The contamination from
by an effective radius Reff ¼ 0.89þ0.08
−0.22 fm, where the D− → D̄0 π − → Kþ π − π − decays in the right sideband is
uncertainty includes both the one arising from the mT - suppressed by a 2.5σ D− rejection around the mean value of
dependent parametrization and the PYTHIA 8 study. the D− invariant mass peak. The resulting correlation
The correlation function due to the genuine pD− inter- function is parametrized by a third-order polynomial in
action can be extracted from the measured Cexp ðk Þ by k ∈ ½0; 1.5 GeV=c and is displayed by the green curve
estimating and subtracting the contributions of D− mesons reported in the right panel of Fig. 2. The observed behavior
originating from beauty-hadron and D− decays, protons is determined by meson-meson and baryon-meson minijets
originating from strange-hadron decays, as well as mis- and residual two-body interactions among the quadruplet,
identified protons and combinatorial-background D-meson as obtained from previous studies [42,46].
candidates. The experimental correlation function is The residual pD− correlation function is computed
decomposed as employing the Koonin-Pratt formalism using the CATS
framework [71] to obtain a two-particle wave function
Cexp ðk Þ ¼ λp D− × Cp D− ðk Þ þ λpðKþ π− π− Þ × CpðKþ π− π− Þ ðk Þ Ψðk ; r Þ considering only the Coulomb interaction and
assuming that the source radius is the same as for pD− pairs.
þ λpD− × CpD− ðk Þ þ λflat × Cflat : ð3Þ The obtained pD− correlation function is transformed to
the momentum basis of the pD− relative momentum by
The combinatorial (Kþ π − π − ) background below the considering the kinematics of the D− → D− X decay [72].
D− peak and the final-state interaction among protons
The resulting correlation function is shown in the right panel
and D− from D− decays play a significant role. All other
of Fig. 2 as a red band. The purple band in the same figure
contributions are assumed to be characterized by a Cðk Þ
represents the total background that includes all contribu-
compatible with unity and are therefore included in the Cflat
tions with their corresponding weights. Finally, the genuine
contribution. The relative weights, λi , are evaluated consid-
pD− correlation function is obtained by solving Eq. (3) for
ering the contributions to D− candidates described above
CpD− ðk Þ and is shown in Fig. 3.
and following the procedure explained in [39] for the
protons. They are about 33.9% for CpD− ðk Þ and 38.8%, The systematic uncertainties of the genuine pD− corre-
14.4%, and 13.4% for the pðKþ π − π − Þ, pD− , and flat lation function, CpD− ðk Þ, include (i) the uncertainties of
contributions, respectively. Cexp ðk Þ, (ii) the uncertainties of the λi weights, and (iii) the
The correlation function CpðKþ π− π− Þ is extracted from uncertainties related to the parametrization of the back-
the sidebands of the D− candidates, chosen as ½MD− ðpT Þ − ground sources, CpðKþ π − π− Þ ðk Þ and CpD− ðk Þ. In particular,
052010-5S. ACHARYA et al. PHYS. REV. D 106, 052010 (2022)
IV. RESULTS
ALICE pp s = 13 TeV
4 High-mult. (0 − 0.17% INEL > 0) The resulting genuine CpD− ðk Þ correlation function can
−
pD ⊕ pD + be employed to study the pD− strong interaction that is
Coulomb characterized by two isospin configurations and is coupled
3 C. Fontoura et al. to the nD̄0 channel. First of all, in order to assess the effect
of the strong interaction on the correlation function, a
C pD−(k* )
Y. Yamaguchi et al.
J. Hofmann and M. Lutz
reference calculation including only the Coulomb interac-
tion is considered. The corresponding correlation function is
2 J. Haidenbauer et al. (g 2σ/4 π = 2.25)
obtained using CATS [71]. Second, various theoretical
approaches to describe the strong interaction are bench-
marked, including meson exchange (J. Haidenbauer et al.
1 [22]), meson exchange based on heavy quark symmetry
(Y. Yamaguchi et al. [25]), an SU(4) contact interaction
(J. Hoffmann and M. Lutz [23]), and a chiral quark model
0 100 200 300 400 (C. Fontoura et al. [24]). The relative wave functions for the
k* (MeV/c )
model of J. Haidenbauer et al. [22] are provided directly,
while for the other models [23–25] they are evaluated by
FIG. 3. Genuine pD− correlation function compared with employing a Gaussian potential whose strength is adjusted
different theoretical models (see text for details). The null to describe the corresponding published I ¼ 0 and I ¼ 1
hypothesis is represented by the curve corresponding to the scattering lengths listed in Table I. The pD− correlation
Coulomb interaction only. function is computed within the Koonin-Pratt formalism,
taking into account explicitly the coupling between the pD−
as previously mentioned, the systematic uncertainty on and nD̄0 channels [73] and including the Coulomb inter-
Cexp ðk Þ is estimated by varying the proton and D− - action [74]. The finite experimental momentum resolution is
candidate selection criteria and ranges between 0.5% and considered in the modeling of the correlation functions [39].
3% as a function of k . The uncertainties of the λi weights The outcome of these models is compared in Fig. 3 with
are derived from the systematic uncertainties on the proton the measured genuine pD− correlation function. The degree
and D− purities (Pp and PD− ), f D− , and f nonprompt reported of consistency between data and models is quantified by the
in Sec. III A. The systematic uncertainties of CpðKþ π − π− Þ ðk Þ p-value computed in the range k < 200 MeV=c. It is
expressed by the number of standard deviations nσ reported
are estimated following the same procedure adopted for
in Table I, where the nσ range accounts, at one standard
Cexp ðk Þ and, in addition, by varying the range of the fit of
deviation level, for the total uncertainties of the data points
the correlation function parametrized from the sidebands and the models. The values of the scattering lengths f 0 for
regions of the invariant mass distribution. Additional the different models are also reported in Table I. Here, the
checks are performed by varying the invariant mass interval high-energy physics convention on the scattering-length
used to define the sidebands region of up to 100 MeV=c2 . sign is adopted: a negative value corresponds to either a
The resulting systematic uncertainty ranges from 1% to repulsive interaction or to an attractive one with presence of
5%. The systematic uncertainty of CpD− ðk Þ is due to the a bound state, while a positive value corresponds to an
uncertainty on the emitting source. Considering the small attractive interaction. The data are compatible with the
λpD− ðk Þ this uncertainty results to be negligible compared Coulomb-only hypothesis within ð1.1–1.5Þ σ. Nevertheless,
to the other sources of uncertainty. The overall relative the level of agreement slightly improves in case of the
Systematic uncertainty on CpD− ðk Þ resulting from the models by J. Haidenbauer et al. (employing g2σ =4π ¼ 2.25)
different sources ranges between 3% and 10% and is which predicts an attractive interaction, and by Y.
maximum in the lowest k interval. Yamaguchi et al. which foresees the formation of a ND̄
TABLE I. Scattering parameters of the different theoretical models for the ND̄ interaction [22–25] and degree of
consistency with the experimental data computed in the range k < 200 MeV=c.
Model f0 ðI ¼ 0Þ f0 ðI ¼ 1Þ nσ
Coulomb (1.1–1.5)
Haidenbauer et al. [22] (g2σ =4π ¼ 2.25) 0.67 0.04 (0.8–1.3)
Hofmann and Lutz [23] −0.16 −0.26 (1.3–1.6)
Yamaguchi et al. [25] −4.38 −0.07 (0.6–1.1)
Fontoura et al. [24] 0.16 −0.25 (1.1–1.5)
052010-6FIRST STUDY OF THE TWO-BODY SCATTERING INVOLVING … PHYS. REV. D 106, 052010 (2022)
6 6
ALICE pp s = 13 TeV ALICE pp s = 13 TeV
High-mult. (0 − 0.17 % INEL > 0) High-mult. (0 − 0.17 % INEL > 0)
5 5
4 4
χ2
χ2
3 3
2 2
1 1
3
0 0 ×10
−1 −0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 −2 −1.8 −1.6 −1.4 −1.2 −1 −0.8 −0.6
f 0,−1I=0 (fm−1) V I=0 (MeV)
FIG. 4. χ 2 distributions obtained by comparing the measured CpD− ðk Þ for k < 200 MeV=c with the correlation function calculated
with an interaction modeled by a Gaussian potential with an interaction range given by ρ-meson exchanges as a function of the inverse
scattering length (left panel) and the interaction potential (right panel) for I ¼ 0. The blue dotted lines represent the value of f −1
0;I¼0 and
2
V I ¼ 0 for which the χ is minimum and for the 1σ confidence interval.
bound state with a mass of 2804 MeV=c2 in the I ¼ 0 confidence interval as a function of the emitting source
channel. radius. Figure 5 shows the confidence interval as a function
Finally, the scattering parameters can be constrained by of the source radius varied within 1σ of its uncertainty. The
comparing the data with the outcome of calculations carried dashed interval corresponds to the radius uncertainty due to
out varying the strength of the potential and the source only the mT dependence while the full-shaded interval shows
radius. In this case the interaction potential is parametrized the total radius uncertainty. The most probable value
by a Gaussian-type functional form with the range of ρ- reported in Fig. 5 with the star symbol corresponds to an
meson exchange. In this estimation, it is assumed that the
interaction in the I ¼ 1 channel is negligible for simplicity.
1.0
The correlation function CpD− ðk Þ is computed including
ALICE pp s = 13 TeV
also the Coulomb interaction and the coupled channel. This
High-mult. (0 − 0.17% INEL > 0)
procedure is repeated for different values of the interaction
potential for the I ¼ 0 channel (V I ¼ 0). For all the
correlation functions corresponding to the different inter- 0.5
Best fit
68% C.L.
f 0,−1I=0 (fm−1)
action potentials, the agreement with the data is evaluated
by computing the χ 2 using a bootstrap procedure. Both mT dependence unc. on R eff
total R eff unc.
the statistical and systematic uncertainties of the data are
considered in the bootstrap procedure, as well as the
uncertainty on the emitting source radius (Reff ) in the 0.0
computed CpD− ðk Þ, which is varied within 1σ of its
uncertainty. The resulting overall χ 2 distributions are shown
in Fig. 4 as a function of f −1
0;I¼0 and V I ¼ 0 in the left and
right panels, respectively. The data are found to be consistent
−0.5
with a potential strength of V I¼0 ∈ ½−1450; −1050 MeV 0.7 0.8 0.9 1.0
within 1σ. This corresponds to an inverse scattering-length R eff (fm)
interval of f −1 −1
0;I¼0 ∈ ½−0.4; 0.9 fm . Since the determined
potential strength is always attractive, the positive values of FIG. 5. Regions of 68% confidence intervals for the inverse
the scattering length imply an attractive interaction without scattering length f−1
0;I¼0 as a function of the source radius varied
within one standard deviation considering only the mT depend-
bound states, while the negative values are consistent with ence on Reff and the total uncertainty (see text for details) under
the presence of a ND̄ bound state. The same procedure was the assumption of negligible interaction for I ¼ 1. The most
repeated for fixed values of Reff in order to obtain the 1σ probable value is reported by the star symbol.
052010-7S. ACHARYA et al. PHYS. REV. D 106, 052010 (2022)
attractive interaction with the formation of a bound state. Foundation, Croatia; Centro de Aplicaciones Tecnológicas
Given that most models predict a repulsive I ¼ 1 interaction, y Desarrollo Nuclear (CEADEN), Cubaenergía, Cuba;
in reality the I ¼ 0 interaction might have to be even more Ministry of Education, Youth and Sports of the Czech
attractive. The herewith presented limits provide valuable Republic, Czech Republic; The Danish Council for
guidance for further theoretical studies advancing the under- Independent Research | Natural Sciences, the VILLUM
standing of the strong interaction in the charm sector. FONDEN and Danish National Research Foundation
(DNRF), Denmark; Helsinki Institute of Physics (HIP),
V. SUMMARY Finland; Commissariat à l’Energie Atomique (CEA) and
Institut National de Physique Nucléaire et de Physique des
In conclusion, this article presents the first measurement
Particules (IN2P3) and Centre National de la Recherche
of correlation functions involving charm hadrons, which
Scientifique (CNRS), France; Bundesministerium für
allows one to access to the strong interaction between a
Bildung und Forschung (BMBF) and GSI
proton and a charm meson. The genuine pD− correlation
Helmholtzzentrum für Schwerionenforschung GmbH,
function reflects the pattern of an overall attractive inter-
Germany; General Secretariat for Research and
action. The data are compatible within ð1.1–1.5Þσ with the
Technology, Ministry of Education, Research and
correlation function obtained from the hypothesis of a
Religions, Greece; National Research, Development and
Coulomb-only interaction. The degree of consistency
Innovation Office, Hungary; Department of Atomic Energy
improves when considering, in addition, state-of-the-art
Government of India (DAE), Department of Science and
models that predict an attractive strong ND̄ interaction
Technology, Government of India (DST), University
with or without a bound state. Finally, assuming no
Grants Commission, Government of India (UGC) and
interaction for the I ¼ 1 channel, the scattering length
Council of Scientific and Industrial Research (CSIR),
of the ND̄ system in the isospin I ¼ 0 channel is estimated India; Indonesian Institute of Science, Indonesia; Istituto
as f −1 −1
0;I¼0 ∈ ½−0.4; 0.9 fm . This exploratory study paves Nazionale di Fisica Nucleare (INFN), Italy; Japanese
the way for precision studies of the strong interactions Ministry of Education, Culture, Sports, Science and
involving charm hadrons, facilitated by about one order of Technology (MEXT) and Japan Society for the
magnitude larger pp data samples expected to be collected Promotion of Science (JSPS) KAKENHI, Japan;
in the next years during the LHC runs 3 and 4 [75]. Consejo Nacional de Ciencia (CONACYT) y
Tecnología, through Fondo de Cooperación Internacional
ACKNOWLEDGMENTS en Ciencia y Tecnología (FONCICYT) and Dirección
The ALICE Collaboration would like to thank all its General de Asuntos del Personal Academico (DGAPA),
engineers and technicians for their invaluable contributions Mexico; Nederlandse Organisatie voor Wetenschappelijk
to the construction of the experiment and the CERN Onderzoek (NWO), Netherlands; The Research Council of
accelerator teams for the outstanding performance of the Norway, Norway; Commission on Science and Technology
LHC complex. The ALICE Collaboration gratefully for Sustainable Development in the South (COMSATS),
acknowledges the resources and support provided by all Pakistan; Pontificia Universidad Católica del Perú, Peru;
Grid centres and the Worldwide LHC Computing Grid Ministry of Education and Science, National Science
(WLCG) collaboration. The ALICE Collaboration Centre and WUT ID-UB, Poland; Korea Institute of
acknowledges the following funding agencies for their Science and Technology Information and National
support in building and running the ALICE detector: A. I. Research Foundation of Korea (NRF), Republic of
Alikhanyan National Science Laboratory (Yerevan Physics Korea; Ministry of Education and Scientific Research,
Institute) Foundation (ANSL), State Committee of Science Institute of Atomic Physics, Ministry of Research and
and World Federation of Scientists (WFS), Armenia; Innovation and Institute of Atomic Physics and University
Austrian Academy of Sciences, Austrian Science Fund Politehnica of Bucharest, Romania; Joint Institute for
(FWF): [M 2467-N36] and Nationalstiftung für Forschung, Nuclear Research (JINR), Ministry of Education and
Technologie und Entwicklung, Austria; Ministry of Science of the Russian Federation, National Research
Communications and High Technologies, National Centre Kurchatov Institute, Russian Science Foundation
Nuclear Research Center, Azerbaijan; Conselho Nacional and Russian Foundation for Basic Research, Russia;
de Desenvolvimento Científico e Tecnológico (CNPq), Ministry of Education, Science, Research and Sport of
Financiadora de Estudos e Projetos (Finep), Fundação de the Slovak Republic, Slovakia; National Research
Amparo à Pesquisa do Estado de São Paulo (FAPESP) and Foundation of South Africa, South Africa; Swedish
Universidade Federal do Rio Grande do Sul (UFRGS), Research Council (VR) and Knut & Alice Wallenberg
Brazil; Ministry of Education of China (MOEC), Ministry Foundation (KAW), Sweden; European Organization for
of Science and Technology of China (MSTC) and National Nuclear Research, Switzerland; Suranaree University of
Natural Science Foundation of China (NSFC), China; Technology (SUT), National Science and Technology
Ministry of Science and Education and Croatian Science Development Agency (NSDTA), Suranaree University of
052010-8FIRST STUDY OF THE TWO-BODY SCATTERING INVOLVING … PHYS. REV. D 106, 052010 (2022)
Technology (SUT), Thailand Science Research and Ukraine; Science and Technology Facilities Council
Innovation (TSRI) and National Science, Research and (STFC), United Kingdom; National Science Foundation
Innovation Fund (NSRF), Thailand; Turkish Energy, of the United States of America (NSF) and United States
Nuclear and Mineral Research Agency (TENMAK), Department of Energy, Office of Nuclear Physics (DOE
Turkey; National Academy of Sciences of Ukraine, NP), United States of America.
[1] T. Hyodo and D. Jido, The nature of the Λð1405Þ resonance [18] Y. Ikeda, T. Hyodo, and W. Weise, Improved constraints on
in chiral dynamics, Prog. Part. Nucl. Phys. 67, 55 chiral SU(3) dynamics from kaonic hydrogen, Phys. Lett. B
(2012). 706, 63 (2011).
[2] U.-G. Meißner, Two-pole structures in QCD: Facts, not [19] Y. Ikeda, T. Hyodo, and W. Weise, Chiral SU(3) theory of
fantasy!, Symmetry 12, 981 (2020). antikaon-nucleon interactions with improved threshold con-
[3] M. Mai, Review of the Λð1405Þ a curious case of a straints, Nucl. Phys. A881, 98 (2012).
strangeness resonance, Eur. Phys. J. Spec. Top. 230, [20] M. He, R. J. Fries, and R. Rapp, Thermal relaxation of
1593 (2021). charm in hadronic matter, Phys. Lett. B 701, 445 (2011).
[4] T. Hyodo and M. Niiyama, QCD and the strange baryon [21] L. Tolós, C. García-Recio, and J. Nieves, The properties of
spectrum, Prog. Part. Nucl. Phys. 120, 103868 (2021). D and D* mesons in the nuclear medium, Phys. Rev. C 80,
[5] E. S. Swanson, The new heavy mesons: A status report, 065202 (2009).
Phys. Rep. 429, 243 (2006). [22] J. Haidenbauer, G. Krein, U.-G. Meißner, and A. Sibirtsev,
[6] F.-K. Guo, C. Hanhart, U.-G. Meißner, Q. Wang, Q. Zhao, D̄N interaction from meson-exchange and quark-gluon
and B.-S. Zou, Hadronic molecules, Rev. Mod. Phys. 90, dynamics, Eur. Phys. J. A 33, 107 (2007).
015004 (2018). [23] J. Hofmann and M. F. M. Lutz, Coupled-channel study of
[7] A. Hosaka, T. Iijima, K. Miyabayashi, Y. Sakai, and S. crypto-exotic baryons with charm, Nucl. Phys. A763, 90
Yasui, Exotic hadrons with heavy flavors: X, Y, Z, and (2005).
related states, Prog. Theor. Exp. Phys. 2016, 062C01 [24] C. E. Fontoura, G. Krein, and V. E. Vizcarra, D̄N interaction
(2016). in a color-confining chiral quark model, Phys. Rev. C 87,
[8] N. Brambilla, S. Eidelman, C. Hanhart, A. Nefediev, C.-P. 025206 (2013).
Shen, C. E. Thomas, A. Vairo, and C.-Z. Yuan, The XYZ [25] Y. Yamaguchi, S. Ohkoda, S. Yasui, and A. Hosaka, Exotic
states: Experimental and theoretical status and perspectives, baryons from a heavy meson and a nucleon—Negative
Phys. Rep. 873, 1 (2020). parity states–, Phys. Rev. D 84, 014032 (2011).
[9] R. Aaij et al. (LHCb Collaboration), Near-threshold DD̄ [26] Stoks, Klomp, Rentmeester, and J. deSwart, Partial-wave
spectroscopy and observation of a new charmonium state, J. analysis of all nucleon-nucleon scattering data below
High Energy Phys. 07 (2019) 035. 350 MeV, Phys. Rev. C 48, 792 (1993).
[10] R. Aaij et al. (LHCb Collaboration), Observation of an [27] F. Nowacki, A. Obertelli, and A. Poves, The neutron-rich
exotic narrow doubly charmed tetraquark, Nat. Phys. 18, edge of the nuclear landscape: Experiment and theory, Prog.
751 (2022). Part. Nucl. Phys. 120, 103866 (2021).
[11] R. Aaij et al. (LHCb Collaboration), Study of the doubly [28] K. Hebeler, J. D. Holt, J. Menendez, and A. Schwenk,
charmed tetraquark T þcc , Nat. Commun. 13, 3351 (2022). Nuclear forces and their impact on neutron-rich nuclei and
[12] R. Aaij et al. (LHCb Collaboration), Observation of J=ψp neutron-rich matter, Annu. Rev. Nucl. Part. Sci. 65, 457
Resonances Consistent with Pentaquark States in Λ0b → (2015).
J=ψK − p Decays, Phys. Rev. Lett. 115, 072001 (2015). [29] E. Gebrerufael, K. Vobig, H. Hergert, and R. Roth, Ab Initio
[13] R. Aaij et al. (LHCb Collaboration), Observation of a Description of Open-Shell Nuclei: Merging No-Core Shell
Narrow Pentaquark State, Pc ð4312Þþ , and of Two-Peak Model and In-Medium Similarity Renormalization Group,
Structure of the Pc ð4450Þþ , Phys. Rev. Lett. 122, 222001 Phys. Rev. Lett. 118, 152503 (2017).
(2019). [30] G. S. Abrams and B. Sechi-Zorn, Charge-exchange scatter-
[14] M. Gell-Mann, A schematic model of baryons and mesons, ing of low-energy K- mesons in hydrogen, Phys. Rev. 139,
Phys. Lett. 8, 214 (1964). B454 (1965).
[15] H.-X. Chen, W. Chen, X. Liu, and S.-L. Zhu, The hidden- [31] J. S. Hyslop, R. A. Arndt, L. D. Roper, and R. L. Workman,
charm pentaquark and tetraquark states, Phys. Rep. 639, 1 Partial wave analysis of K þ nucleon scattering, Phys. Rev. D
(2016). 46, 961 (1992).
[16] B. Borasoy, R. Nissler, and W. Weise, Kaonic Hydrogen and [32] A. Olin and T. S. Park, Kaon nucleon scattering and
K- p Scattering, Phys. Rev. Lett. 94, 213401 (2005). reactions at low energies, Nucl. Phys. A691, 295 (2001).
[17] M. Bazzi et al. (SIDDHARTA Collaboration), A new [33] F. Eisele, H. Filthuth, W. Foehlisch, V. Hepp, and G. Zech,
measurement of kaonic hydrogen x-rays, Phys. Lett. B Elastic Σ p scattering at low energies, Phys. Lett. 37B, 204
704, 113 (2011). (1971).
052010-9S. ACHARYA et al. PHYS. REV. D 106, 052010 (2022)
[34] G. Alexander, U. Karshon, A. Shapira, G. Yekutieli, R. [54] A. Akindinov et al., Performance of the ALICE time-of-
Engelmann, H. Filthuth, and W. Lughofer, Study of the Λ − flight detector at the LHC, Eur. Phys. J. Plus 128, 44 (2013).
N system in low-energy Λ − p elastic scattering, Phys. Rev. [55] E. Abbas et al. (ALICE Collaboration), Performance of the
173, 1452 (1968). ALICE VZERO system, J. Instrum. 8, P10016 (2013).
[35] B. Sechi-Zorn, B. Kehoe, J. Twitty, and R. Burnstein, Low- [56] T. Sjöstrand, S. Mrenna, and P. Z. Skands, PYTHIA 6.4
energy Λ–proton elastic scattering, Phys. Rev. 175, 1735 physics and manual, J. High Energy Phys. 05 (2006) 026.
(1968). [57] T. Sjöstrand, S. Ask, J. R. Christiansen, R. Corke, N. Desai,
[36] J. Hrtánková and J. Mareš, K − - nuclear states: Binding P. Ilten, S. Mrenna, S. Prestel, C. O. Rasmussen, and P. Z.
energies and widths, Phys. Rev. C 96, 015205 (2017). Skands, An introduction to PYTHIA 8.2, Comput. Phys.
[37] A. Feliciello and T. Nagae, Experimental review of hyper- Commun. 191, 159 (2015).
nuclear physics: recent achievements and future perspec- [58] P. Skands, S. Carrazza, and J. Rojo, Tuning PYTHIA 8.1:
tives, Rep. Prog. Phys. 78, 096301 (2015). The Monash 2013 Tune, Eur. Phys. J. C 74, 3024 (2014).
[38] S. Pratt, Pion interferometry of quark-gluon plasma, Phys. [59] R. Brun, F. Bruyant, M. Maire, A. C. McPherson, and P.
Rev. D 33, 1314 (1986). Zanarini, GEANT 3: User’s Guide Geant 3.10, Geant 3.11;
[39] S. Acharya et al. (ALICE Collaboration), p-p, p-Λ and Λ-Λ Rev. Version (CERN, Geneva, 1987).
correlations studied via femtoscopy in pp reactions at [60] P. A. Zyla et al. (Particle Data Group), Review of particle
pffiffiffi
s ¼ 7 TeV, Phys. Rev. C 99, 024001 (2019). physics, Prog. Theor. Exp. Phys. 2020, 083C01 (2020).
[40] S. Acharya et al. (ALICE Collaboration), Scattering Studies [61] T. Chen and C. Guestrin, XGBoost: A scalable tree boosting
with Low-Energy Kaon-Proton Femtoscopy in Proton-Pro- system, in Proceedings of the 22nd ACM SIGKDD
ton Collisions at the LHC, Phys. Rev. Lett. 124, 092301 International Conference on Knowledge Discovery and Data
(2020). Mining (University of Washington, 2016), arXiv:1603.02754.
[41] S. Acharya et al. (ALICE Collaboration), Exploring the [62] L. Barioglio, F. Catalano, M. Concas, P. Fecchio, F. Grosa,
NΛ-NΣ coupled system with high precision correlation F. Mazzaschi, and M. Puccio, hipe4ml/hipe4ml, 10.5281/
techniques at the LHC, Phys. Lett. B 833, 137272 (2022). zenodo.5070132 (2021).
[42] S. Acharya et al. (ALICE Collaboration), Investigation of [63] S. Acharya et al. (ALICE Collaboration), Measurement pffiffiffi of
the p-Σ0 interaction via femtoscopy in pp collisions, Phys. beauty and charm production in pp collisions at s ¼
Lett. B 805, 135419 (2020). 5.02 TeV via non-prompt and prompt D mesons, J. High
[43] S. Acharya et al. (ALICE Collaboration), Study of the Λ-Λ Energy Phys. 05 (2021) 220.
interaction with femtoscopy correlations in pp and p–Pb [64] S. Acharya et al. (ALICE Collaboration), Measurement of
pffiffiffi
collisions at the LHC, Phys. Lett. B 797, 134822 (2019). D0 , Dþ , Dþ and Dþ s production in pp collisions at s¼
[44] S. Acharya et al. (ALICE Collaboration), First Observation 5.02 TeV with ALICE, Eur. Phys. J. C 79, 388 (2019).
of an Attractive Interaction between a Proton and a Cascade [65] M. A. Lisa, S. Pratt, R. Soltz, and U. Wiedemann, Femto-
Baryon, Phys. Rev. Lett. 123, 112002 (2019). scopy in relativistic heavy ion collisions, Annu. Rev. Nucl.
[45] S. Acharya et al. (ALICE Collaboration), Unveiling the Part. Sci. 55, 357 (2005).
strong interaction among hadrons at the LHC, Nature [66] S. Acharya et al. (ALICE Collaboration), Search for a
(London) 588, 232 (2020). common baryon source in high-multiplicity pp collisions at
[46] S. Acharya et al. (ALICE Collaboration), Experimental the LHC, Phys. Lett. B 811, 135849 (2020).
Evidence for an Attractive p-ϕ Interaction, Phys. Rev. Lett. [67] I. G. Bearden et al., Space-time evolution of the hadronic
127, 172301 (2021). source in peripheral to central Pb þ Pb collisions, Eur. Phys.
[47] S. Acharya et al. (ALICE Collaboration), Investigating the J. C 18, 317 (2000).
role of strangeness in baryon—antibaryon annihilation at [68] A. Kisiel, M. Gałażyn, and P. Bożek, Pion, kaon, and proton
pffiffiffiffiffiffiffiffi
the LHC, Phys. Lett. B 829, 137060 (2022). femtoscopy in Pb–Pb collisions at sNN ¼ 2.76 TeV mod-
[48] A. Hosaka, T. Hyodo, K. Sudoh, Y. Yamaguchi, and S. eled in ð3 þ 1ÞD hydrodynamics, Phys. Rev. C 90, 064914
Yasui, Heavy hadrons in nuclear matter, Prog. Part. Nucl. (2014).
Phys. 96, 88 (2017). [69] V. M. Shapoval, P. Braun-Munzinger, I. A. Karpenko, and
[49] H. Noumi, Physics in J-PARC hadron-hall extension, J. Y. M. Sinyukov, Femtoscopy correlations of kaons in Pb þ
Phys. Soc. Jpn. Conf. Proc. 13, 010017 (2017). Pb collisions at LHC within hydrokinetic model, Nucl.
[50] K. Aamodt et al. (ALICE Collaboration), The ALICE Phys. A929, 1 (2014).
experiment at the CERN LHC, J. Instrum. 3, S08002 [70] A. M. Sirunyan et al. (CMS Collaboration), Studies of
(2008). charm and beauty hadron long-range correlations in pp
[51] B. B. Abelev et al. (ALICE Collaboration), Performance of and pPb collisions at LHC energies, Phys. Lett. B 813,
the ALICE experiment at the CERN LHC, Int. J. Mod. Phys. 136036 (2021).
A 29, 1430044 (2014). [71] D. L. Mihaylov, V. Mantovani Sarti, O. W. Arnold, L.
[52] K. Aamodt et al. (ALICE Collaboration), Alignment of the Fabbietti, B. Hohlweger, and A. M. Mathis, A femtoscopic
ALICE inner tracking system with cosmic-ray tracks, J. correlation analysis tool using the Schrödinger equation
Instrum. 5, P03003 (2010). (CATS), Eur. Phys. J. C 78, 394 (2018).
[53] J. Alme et al., The ALICE TPC, a large 3-dimensional [72] A. Kisiel, H. Zbroszczyk, and M. Szymański, Extracting
tracking device with fast readout for ultra-high multiplicity baryon-antibaryon strong interaction potentials from pΛ̄
events, Nucl. Instrum. Methods Phys. Res., Sect. A 622, 316 femtoscopic correlation functions, Phys. Rev. C 89, 054916
(2010). (2014).
052010-10FIRST STUDY OF THE TWO-BODY SCATTERING INVOLVING … PHYS. REV. D 106, 052010 (2022)
[73] R. Lednicky, V. Lyuboshitz, and V. Lyuboshitz, Final-state Collisions and Chiral SU(3) Dynamics, Phys. Rev. Lett.
interactions in multichannel quantum systems and pair 124, 132501 (2020).
correlations of nonidentical and identical particles at low [75] S. Acharya et al. (ALICE Collaboration), Future high-
relative velocities, Phys. At. Nucl. 61, 2050 (1998), https:// energy pp programme with ALICE, Technical Report
inis.iaea.org/search/search.aspx?orig_q=RN:35064786. No. ALICE-PUBLIC-2020-005, CERN, 2020, https://cds
[74] Y. Kamiya, T. Hyodo, K. Morita, A. Ohnishi, and W. Weise, .cern.ch/record/2724925.
K − p Correlation Function from High-Energy Nuclear
S. Acharya,142 D. Adamová,96 A. Adler,74 J. Adolfsson,81 G. Aglieri Rinella,34 M. Agnello,30 N. Agrawal,54
Z. Ahammed,142 S. Ahmad,16 S. U. Ahn,76 I. Ahuja,38 Z. Akbar,51 A. Akindinov,93 M. Al-Turany,108 S. N. Alam,16
D. Aleksandrov,89 B. Alessandro,59 H. M. Alfanda,7 R. Alfaro Molina,71 B. Ali,16 Y. Ali,14 A. Alici,25
N. Alizadehvandchali,125 A. Alkin,34 J. Alme,21 G. Alocco,55 T. Alt,68 I. Altsybeev,113 M. N. Anaam,7 C. Andrei,48
D. Andreou,91 A. Andronic,145 V. Anguelov,105 F. Antinori,57 P. Antonioli,54 C. Anuj,16 N. Apadula,80 L. Aphecetche,115
H. Appelshäuser,68 S. Arcelli,25 R. Arnaldi,59 I. C. Arsene,20 M. Arslandok,147 A. Augustinus,34 R. Averbeck,108 S. Aziz,78
M. D. Azmi,16 A. Badalà,56 Y. W. Baek,41 X. Bai,108,129 R. Bailhache,68 Y. Bailung,50 R. Bala,102 A. Balbino,30
A. Baldisseri,139 B. Balis,2 D. Banerjee,4 Z. Banoo,102 R. Barbera,26 L. Barioglio,106 M. Barlou,85 G. G. Barnaföldi,146
L. S. Barnby,95 V. Barret,136 C. Bartels,128 K. Barth,34 E. Bartsch,68 F. Baruffaldi,27 N. Bastid,136 S. Basu,81 G. Batigne,115
D. Battistini,106 B. Batyunya,75 D. Bauri,49 J. L. Bazo Alba,112 I. G. Bearden,90 C. Beattie,147 P. Becht,108 I. Belikov,138
A. D. C. Bell Hechavarria,145 F. Bellini,25 R. Bellwied,125 S. Belokurova,113 V. Belyaev,94 G. Bencedi,69,146 S. Beole,24
A. Bercuci,48 Y. Berdnikov,99 A. Berdnikova,105 L. Bergmann,105 M. G. Besoiu,67 L. Betev,34 P. P. Bhaduri,142 A. Bhasin,102
I. R. Bhat,102 M. A. Bhat,4 B. Bhattacharjee,42 P. Bhattacharya,22 L. Bianchi,24 N. Bianchi,52 J. Bielčík,37 J. Bielčíková,96
J. Biernat,118 A. Bilandzic,106 G. Biro,146 S. Biswas,4 J. T. Blair,119 D. Blau,82,89 M. B. Blidaru,108 C. Blume,68 G. Boca,28,58
F. Bock,97 A. Bogdanov,94 S. Boi,22 J. Bok,61 L. Boldizsár,146 A. Bolozdynya,94 M. Bombara,38 P. M. Bond,34
G. Bonomi,58,141 H. Borel,139 A. Borissov,82 H. Bossi,147 E. Botta,24 L. Bratrud,68 P. Braun-Munzinger,108 M. Bregant,121
M. Broz,37 G. E. Bruno,33,107 M. D. Buckland,23,128 D. Budnikov,109 H. Buesching,68 S. Bufalino,30 O. Bugnon,115
P. Buhler,114 Z. Buthelezi,72,132 J. B. Butt,14 A. Bylinkin,127 S. A. Bysiak,118 M. Cai,7,27 H. Caines,147 A. Caliva,108
E. Calvo Villar,112 J. M. M. Camacho,120 R. S. Camacho,45 P. Camerini,23 F. D. M. Canedo,121 M. Carabas,135
F. Carnesecchi,25,34 R. Caron,137,139 J. Castillo Castellanos,139 E. A. R. Casula,22 F. Catalano,30 C. Ceballos Sanchez,75
I. Chakaberia,80 P. Chakraborty,49 S. Chandra,142 S. Chapeland,34 M. Chartier,128 S. Chattopadhyay,142 S. Chattopadhyay,110
T. G. Chavez,45 T. Cheng,7 C. Cheshkov,137 B. Cheynis,137 V. Chibante Barroso,34 D. D. Chinellato,122 S. Cho,61
P. Chochula,34 P. Christakoglou,91 C. H. Christensen,90 P. Christiansen,81 T. Chujo,134 C. Cicalo,55 L. Cifarelli,25
F. Cindolo,54 M. R. Ciupek,108 G. Clai,54,‡ J. Cleymans,124,† F. Colamaria,53 J. S. Colburn,111 D. Colella,33,53,107 A. Collu,80
M. Colocci,25,34 M. Concas,59,§ G. Conesa Balbastre,79 Z. Conesa del Valle,78 G. Contin,23 J. G. Contreras,37
M. L. Coquet,139 T. M. Cormier,97 P. Cortese,31 M. R. Cosentino,123 F. Costa,34 S. Costanza,28,58 P. Crochet,136
R. Cruz-Torres,80 E. Cuautle,69 P. Cui,7 L. Cunqueiro,97 A. Dainese,57 M. C. Danisch,105 A. Danu,67 P. Das,87 P. Das,4
S. Das,4 S. Dash,49 A. De Caro,29 G. de Cataldo,53 L. De Cilladi,24 J. de Cuveland,39 A. De Falco,22 D. De Gruttola,29
N. De Marco,59 C. De Martin,23 S. De Pasquale,29 S. Deb,50 H. F. Degenhardt,121 K. R. Deja,143 R. Del Grande,106
L. Dello Stritto,29 W. Deng,7 P. Dhankher,19 D. Di Bari,33 A. Di Mauro,34 R. A. Diaz,8 T. Dietel,124 Y. Ding,7,137 R. Divià,34
D. U. Dixit,19 Ø. Djuvsland,21 U. Dmitrieva,63 J. Do,61 A. Dobrin,67 B. Dönigus,68 A. K. Dubey,142 A. Dubla,91,108
S. Dudi,101 P. Dupieux,136 M. Durkac,117 N. Dzalaiova,13 T. M. Eder,145 R. J. Ehlers,97 V. N. Eikeland,21 F. Eisenhut,68
D. Elia,53 B. Erazmus,115 F. Ercolessi,25 F. Erhardt,100 A. Erokhin,113 M. R. Ersdal,21 B. Espagnon,78 G. Eulisse,34
D. Evans,111 S. Evdokimov,92 L. Fabbietti,106 M. Faggin,27 J. Faivre,79 F. Fan,7 W. Fan,80 A. Fantoni,52 M. Fasel,97
P. Fecchio,30 A. Feliciello,59 G. Feofilov,113 A. Fernández Téllez,45 A. Ferrero,139 A. Ferretti,24 V. J. G. Feuillard,105
J. Figiel,118 V. Filova,37 D. Finogeev,63 F. M. Fionda,55 G. Fiorenza,34 F. Flor,125 A. N. Flores,119 S. Foertsch,72 S. Fokin,89
E. Fragiacomo,60 E. Frajna,146 A. Francisco,136 U. Fuchs,34 N. Funicello,29 C. Furget,79 A. Furs,63 J. J. Gaardhøje,90
M. Gagliardi,24 A. M. Gago,112 A. Gal,138 C. D. Galvan,120 P. Ganoti,85 C. Garabatos,108 J. R. A. Garcia,45 E. Garcia-Solis,10
K. Garg,115 C. Gargiulo,34 A. Garibli,88 K. Garner,145 P. Gasik,108 E. F. Gauger,119 A. Gautam,127 M. B. Gay Ducati,70
M. Germain,115 S. K. Ghosh,4 M. Giacalone,25 P. Gianotti,52 P. Giubellino,59,108 P. Giubilato,27 A. M. C. Glaenzer,139
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