Studying the interaction between charm and light-flavor mesons

This is a self-archived version of an original article. This version may differ from the original in pagination and typographic details. Author(s): Title: Year: Version: Copyright: Rights: Rights url: Please cite the original version: CC BY 4.0 https://creativecommons.org/licenses/by/4.0/ Studying the interaction between charm and light-flavor mesons © 2024 CERN Published version ALICE Collaboration ALICE Collaboration. (2024). Studying the interaction between charm and light-flavor mesons. Physical Review D, 110(3), Article 032004. https://doi.org/10.1103/physrevd.110.032004 2024 Studying the interaction between charm and light-flavor mesons S. Acharya et al.* (ALICE Collaboration) (Received 1 March 2024; accepted 18 June 2024; published 5 August 2024) The two-particle momentum correlation functions between charm mesons (D and D) and charged light-flavor mesons (πand K) in all charge combinations are measured for the first time by the ALICE Collaboration in high-multiplicity proton–proton collisions at a center-of-mass energy of ffiffiffi s p¼13 TeV. For DK and DK pairs, the experimental results are in agreement with theoretical predictions of the residual strong interaction based on quantum chromodynamics calculations on the lattice and chiral effective field theory. In the case of Dπand Dπpairs, tension between the calculations including strong interactions and the measurement is observed. For all particle pairs, the data can be adequately described by Coulomb interaction only, indicating a shallow interaction between charm and light-flavor mesons. Finally, the scattering lengths governing the residual strong interaction of the Dπand Dπsystems are determined by fitting the experimental correlation functions with a model that employs a Gaussian potential. The extracted values are small and compatible with zero. DOI: 10.1103/PhysRevD.110.032004 I. INTRODUCTION The exploration of the strong interaction within hadrons remains a pivotal question in particle physics. Quantum chromodynamics (QCD) has been well tested at distances significantly shorter than the nucleon’s size, and many high-energy phenomena can be effectively explained through perturbative QCD at the quark level. However, when the distance between quarks reaches the nucleon size, the QCD becomes a strongly coupled theory and the lowenergy processes between hadrons are not yet well described. From the experimental point of view, the residual strong interaction between hadrons has been studied in the past using scattering experiments at low energies with both stable and unstable beams. Numerous results have been achieved for nucleon–nucleon interactions with this method [1,2], however, due to the experimental challenge in realizing scattering experiments with unstable particles, only a reduced set of measurements could have been performed in the strange sector and none in the charm sector. In order to overcome these experimental limitations, the femtoscopy technique has emerged as an interesting tool to study reactions among hadrons [3]. This method is based on the measurement of the correlation function of pairs of hadrons in momentum space, which encodes the information of the interaction between the two hadrons convoluted with the emitting source distribution. The ALICE Collaboration measured the residual strong interaction between several light and strange hadrons using the femtoscopy technique in high-multiplicity proton– proton (pp) collisions, including pp, pK,pΛ,p ¯ Λ,pΣ0, ΛΛ,Λ¯ Λ,pΞ−,pΩ−,pϕ, and ΛK interactions [4–14]. The study of hadronic interactions involving charm mesons (D, D) has gained significant interest after the observation of the charm-strange meson D s0ð2317Þ[15–17], whose mass lies significantly below the quark model [18] predictions (mexperiment −mquark model ≈100 MeV=c2), preventing its accommodation in simple constituent quark models [19]. The puzzle of the D s0ð2317Þlow mass has led to a range of theories, such as those based on the concepts of conventional charm-strange mesons with coupled-channel impacts [20–26],orofD ðÞKmolecule[27–31],orofa tetraquark state composed of cq¯ s¯ q (anti)quarks [32–34]. Models basedon a mixture of tetraquark and molecular states were also proposed [35,36]. In recent years, several exotic hadrons with charm-quark content have been discovered, such as the χc1ð3872Þ[37],T þ cc [38,39],P cð4312Þ,P cð4440Þ, and Pcð4457Þ[21,40,41] states. Similarly to the D s0ð2317Þ, these states can be interpreted as D ¯ D,DD ,orΣc¯ D, Σc¯ D molecular states, or compact multiquark states [42–45].The observation of potential molecular states is, however, not the only measurement that challenges the charm-hadron spectrum in terms of the conventional quark model. In fact, the masses of the nonstrange D 0ð2300Þand D1ð2430Þcharm mesons [46–48] are very similar to the corresponding states in the charm-strange spectrum, D s0ð2317Þand Ds1ð2460Þ [15,17,21], while they are expected to be smaller. When *Full author list given at the end of the article. Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Open access publication funded by CERN. PHYSICAL REVIEW D 110, 032004 (2024) 2470-0010=2024=110(3)=032004(26) 032004-1 © 2024 CERN, for the ALICE Collaboration combining chiral effective field theory with quantum chromodynamics calculations on the lattice, all low-energy open heavy-flavor mesonic states with positive parity can be classified as hadronic molecules. In this framework, pions, kaons, and ηmesons arise as Goldstone bosons and, by computing the Dπ,Dη,andD s¯ K coupled-channel scatterings, a bound state with a large coupling to the Dπchannel is obtained at a mass that corresponds to the D 0ð2300Þstate [49–53]. Nevertheless, their structures remain uncertain owing to the lack of direct experimental information on the residual strong interaction between charm and light hadrons. These measurements are particularly challenging because conventional scattering experiments with charm hadrons are restricted by their short lifetime. Only recently, the residual strong final state interaction involving charm hadrons became experimentally accessible thanks to the femtoscopy technique. The first study of the strong interaction between charm mesons and nucleons (pD−)was published by the ALICE Collaboration in Ref. [54], proving the feasibility of applying the femtoscopy technique to the charm sector. The knowledge of interactions between charm particles and light-flavor hadrons is also essential for the study of ultrarelativistic heavy-ion collisions. In these collisions, a color-deconfined state of matter, called quark-gluon plasma (QGP), is formed [55–59]. Due to the early production, charm quarks are recognized as ideal probes of the QGP, and measurements of the yields and angular anisotropies of charm hadrons can be used to infer information about the QGP properties [60,61]. However, during the hadronic phase following the deconfined state of the system, the charm hadrons can interact with the other particles produced in the collision, which are mainly light-flavor hadrons, via elastic and inelastic processes. These interactions modify the momentum and angular distributions of heavy-flavor hadrons in heavy-ion collisions. Therefore, the scattering parameters of the charm hadrons with lightflavor hadrons, in particular, pions and kaons, must be determined to disentangle this effect from those related to the QGP formation [62]. In this article, the first measurement of the residual strong interaction between nonstrange charm and lightflavor mesons via the femtoscopy technique is presented. This method relies on the fact that particles with similar momentum, hence small relative momentum, can interact with each other strongly, if they are emitted at small relative distance. The momentum correlation functions of the charm mesons Dþand Dþ with charged pions and kaons, also simply referred to as light-flavor mesons in the following, are measured for all charge combinations in pp collisions at ffiffiffi s p¼13 TeV. Section II contains the description of the experimental apparatus, the selection of charm and light-flavor mesons, as well as the singleparticle properties (e.g., purity), which are later needed to extract the final results from the raw experimental data. The measurement of the correlation functions is described in Sec. III, while the evaluation of the systematic uncertainties is discussed in Sec. IV. Finally, the results are presented and compared to model calculations in Sec. V. II. EVENT AND PARTICLE SELECTION This analysis is performed on a data sample of pp collisions at ffiffiffi s p¼13 TeV collected with the ALICE [13] experiment during the LHC Run 2 data-taking period. The events are selected employing a high-multiplicity (HM) trigger. The multiplicity is estimated using the V0 detector, which consists of an array of scintillators located at forward (2.8<η<5.1) and backward (−3.7<η<−1.7) pseudorapidity [63]. The multiplicity estimator is the V0 amplitude, which is related to the energy deposited by ionizing particles in the V0 detector. The triggered events correspond to the 0–0.17% percentile of the inelastic events with the highest V0 amplitude and with at least one charged track in the range jηj<1(INEL >0). The resulting HM dataset consists of approximately 1.0×109inelastic pp collisions with, on average, 30 charged particles per event in the pseudorapidity interval jηj<0.5[10]. Chargedparticle tracks are reconstructed using both the inner tracking system (ITS) [64] and the time projection chamber (TPC) [65], which are embedded in a uniform magnetic field of 0.5 T along the beam direction. They cover the full azimuthal angle and the pseudorapidity interval jηj<0.9. The position of the primary vertex is obtained from the reconstructed tracks, and the particle identification (PID) is performed employing both the TPC and the time-of-flight (TOF) [66] detectors. The PYTHIA 8.243 event generator [67] is used in the Monte Carlo (MC) simulations. The generated particles are transported through a simulation of the ALICE apparatus using G eant 3 [68]. Events and tracks are reconstructed employing the same algorithms as used for real collision data [69], and a selection on large charged-particle multiplicities is applied to mimic the effect of the HM trigger. A. Light-meson selection The Kþand πþcandidates are identified using PID information provided by the TPC and TOF, via the specific energy loss dE=dxand time-of-flight, respectively. For each track, the deviation of the measured quantity with respect to the expected value for a particular particle-species hypothesis in terms of units of the detector resolution is computed and denoted as nTPC=TOF σ. Pion candidates with transverse momentum pT<0.5GeV=c are identified using only the TPC dE=dxsignal via a selection of jnTPC σðπÞj <3.For larger pTthe PID information of TPC and TOF is combined into ncomb σ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðnTPC σÞ2þðnTOF σÞ2 pand a selection of ncomb σ<3is applied. Tracks with pT>0.5GeV=c which do not have a TOF signal are discarded. The PID selection of the kaon candidates is performed similarly with an S. ACHARYA et al. PHYS. REV. D 110, 032004 (2024) 032004-2 additional more complex set of selections on nTPC σand ncomb σ, not only for kaons but also for electrons and pions, in order to suppress possible contamination to the kaon sample in specific momentum regions [14]. The pion and kaon candidates are selected in the pT ranges [0.14, 4.0] and ½0.15;2.15GeV=c, respectively. The lower limit is imposed to suppress the light-meson candidates stemming from interactions with the detector material. The tracks are required to be reconstructed from more than 80 clusters in the TPC to assure a good quality of the track, good pTresolution at large momenta, as well as to remove fake tracks from the sample. In addition, the candidates are selected within a pseudorapidity range of jηj<0.8. To suppress the contribution of particles coming from weak decays or interactions with the detector material, a selection on the distance of closest approach (DCA) to the primary vertex in the transverse plane xy and along the beam axis direction zis applied. For kaons, DCAK xy < 0.1cm and DCAK z<0.2cm are required, while for pions DCAπ xy;z <0.3cm. The purity of the pion and kaon samples, defined as the ratio of the correctly identified particles over the total number of candidates, is computed as a function of pT using MC simulations and is reweighted by the pT distribution of the pion or kaon candidates that form a pair with DðÞþ mesons at low relative momentum. It is found to be 99% for pions and 98% for kaons. The particles can be classified according to their origin: the ones that do not come from interactions with the material of the detector are classified as primary or secondary, according to the ALICE definition [70]. The fraction of each contribution is estimated with a template fit to the DCA distribution. The templates for the DCA distributions of primary particles, secondaries from weak decays, and secondaries from interactions in the material are obtained from MC simulations. The primary fractions are found to be 99.5% and 99.8% for pions and kaons, respectively. A portion of identified primary light-flavor mesons comes, however, from the strong decay of longlived resonances (cτ>5fm). As the fractions of this contribution cannot be determined via DCA template fits, they are estimated with the T hermal F ist statistical hadronization model [71]. The resonances that contribute the most to the pion yield are the ηand ωmesons, while in the case of kaons it is the ϕmeson. The resulting primary fractions of pions and kaons, subtracted of the contribution of such long-lived resonances, are found to be about 88% and 94%, respectively. These values are used in the following analysis as primary fractions. B. Charm-meson selection The Dþ,D þ, and D0candidates are reconstructed via the hadronic decay channels Dþ→K−πþπþ,D þ →D0πþ, followed by D0→K−πþ, and their charge conjugates. The branching ratios (BR) of the considered Dþ,D þ, and D0 decays are BR ¼ð9.38 0.16Þ%,BR¼ð67.70.5Þ%, and BR ¼ð3.947 0.030Þ%, respectively [72]. The tracks fulfilling a set of standard quality selections [54] are combined with the correct charge signs to build Dþand Dþ -meson candidates. The obtained sample of charmmeson candidates consists of three different classes: candidates that result from the combination of uncorrelated pions and kaons form the combinatorial background, charm mesons that come from the hadronization of a charm quark or the decay of excited open-charm or charmonium states, which are referred to as prompt, and DðÞþ mesons that come from the decay of beauty hadrons, which are referred to as nonprompt. To separate the prompt, nonprompt, and combinatorial background contributions, the decay-vertex topology, in combination with the PID information is used. The mean proper decay length of Dand D0mesons is about 312 μm and 123 μm, respectively, while for beauty hadrons it is close to 500 μm[72]. Topological variables, such as the DCA of the charm meson candidate, the Dþ(D0) decay length, and the cosine of the pointing angle, namely the angle between the Dþ(D0) momentum and the line that passes through the primary and secondary vertices, are exploited by a multiclass machine learning (ML) algorithm based on boosted decision trees (BDT). The ML model, provided by the XGB oost library [73,74], is trained using labeled examples of candidates of each class. The samples of prompt and nonprompt Dþand Dþ mesons are obtained from a PYTHIA 8simulation with enhanced production of heavy-flavor hadrons, where only events that contain a c¯ c or b¯ b pair are selected, and the charm mesons are forced to decay in the hadronic decay channels of interest for the analysis. The background sample for Dþis obtained from the data by selecting the sidebands of the candidate invariant-mass distribution. For Dþ mesons, the right sideband of the invariant-mass difference ΔM¼ MðKππÞ−MðKπÞis used. To prepare the sample for the training, loose selections on the PID and decay-vertex topology are applied. The training is performed in several pTintervals. Then, the model is applied to the data, assigning scores to each candidate, which are related to the probabilities that the candidate belongs to each of the three classes. To suppress the combinatorial background and enhance the prompt contribution in the sample, candidates with a low background-score and high prompt-score are selected; the selections are chosen such that they maximize the expected significance and purity. The fraction of nonprompt candidates present in the sample is estimated with a data-driven procedure that relies on the fact that the prompt selection efficiencies change differently to the nonprompt ones when the selection on the ML scores is changed. For each selection ion the ML scores, the raw yield Yiof charm-meson candidates is extracted via a fit to the invariant-mass distribution of the STUDYING THE INTERACTION BETWEEN CHARM AND LIGHT- …PHYS. REV. D 110, 032004 (2024) 032004-3 charm-meson candidates. The fit function is the sum of a Gaussian, for the description of the signal, and an exponential or an exponential multiplied by a power law for the description of the background in the case of Dþand Dþ mesons, respectively. The left panel of Fig. 1shows an example of fit to the ΔMdistribution of Dþ candidates with 2.2<p T<2.4GeV=c. The raw yield is related to the corrected yields of prompt (Nprompt) and nonprompt (Nnonprompt) mesons via δi¼Yi−ðAcc × ϵÞprompt;i ×Nprompt −ðAcc × ϵÞnonprompt;i ×Nnonprompt;ð1Þ where ðAcc × ϵÞprompt=nonprompt is the product of acceptance and efficiency for each selection, and δiare the residuals that account for the equation not holding exactly because of the uncertainties. The definition of multiple sets of selections leads to an overdetermined system of equations, out of which the corrected yields can be extracted via a χ2 minimization. Further details are provided in Ref. [75]. An example of a raw-yield distribution as a function of the BDT-based selection used in the minimization procedure for Dþ mesons with 2.2<p T<2.4GeV=c is shown in the right panel of Fig. 1. The leftmost data point of the distribution represents the raw yield corresponding to the loosest selection on the BDToutput related to the candidate probability of being a nonprompt Dþ meson, while the rightmost one corresponds to the strictest selection, which is expected to preferentially select nonprompt Dþ mesons. The prompt and nonprompt components obtained from the minimization procedure are represented by the red and blue filled histograms, respectively. The nonprompt fraction extracted in pTintervals is reweighted with the pT distribution of the DðÞþ mesons that form pairs at low k. The extracted nonprompt fractions are ð7.20.2Þ%for Dπand DK, and ð7.71.3Þ%for Dπand DK. The prompt component of the Dþ-meson sample also includes mesons that come from the decay of excited charm states. The main contribution comes from the decay of the Dþ mesons, via the D →Dþπ0and D →Dþγ decays, that have a branching ratio of ð30.70.5Þ%and ð1.60.4Þ%, respectively [72]. Since the strong final-state interaction (FSI) is only accessible via the study of the primary particles, the Dþmesons that result from the decay of charm resonances represent a source of background. Unlike the contribution of Dþmesons from beauty-hadron decays, it is not possible to experimentally separate it with the procedure described above, due to the short lifetime of the Dþ resonances (cτ≈2400 fm) [72]. The fraction of Dþmesons originating from Dþ decays is estimated in Ref. [54], employing the production cross sections of Dþ and Dþ mesons in pp collisions at ffiffiffi s p¼5.02 TeV [75,76] and a simulation with PYTHIA 8.2 for the description of the D →DþX decay kinematics. It is estimated to be ð27.61.3ðstatÞ2.4ðsystÞÞ%. To obtain a high-purity sample of DðÞþ -meson candidates, the following procedure is used. The distribution of the invariant mass of the Dþ-meson candidates and invariant-mass difference of the Dþ-meson candidates is fitted in several pTintervals, from 1 to 10 GeV=c. FIG. 1. Left: distribution of invariant-mass difference for Dþ candidates in the 2.2<p T<2.4GeV=c interval. The green solid line shows the total fit function and the gray dotted line the combinatorial background. The contributions of Dþ 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 for the 2.2<p T<2.4GeV=c interval, employed in the procedure adopted for the determination of the fraction of Dþ originating from beauty-hadron decays. S. ACHARYA et al. PHYS. REV. D 110, 032004 (2024) 032004-4 The sample of DðÞþ mesons used for the analysis is obtained by applying a selection to the invariant mass of the candidates, which is defined by a 2σwindow around the nominal mass, MD¼1869.66 0.05 MeV=c2and MD ¼2010.26 0.05 MeV=c2[72], where σis the width of the fitted Gaussian. This selection range is represented by the vertical dashed lines in Fig. 1. The purity is computed as the ratio of the signal candidates over the total number of candidates in this invariant-mass range, where the number of signal candidates is extracted with a fit to the invariant-mass distribution. This results in a pTintegrated purity of around 71% for Dþmesons and 67% for Dþ mesons. III. THE CORRELATION FUNCTION In this analysis, the interaction between the charm mesons DðÞ and the light-flavor mesons πand K is investigated employing the correlation function [77], defined as CðkÞ¼N×NsameðkÞ NmixedðkÞ;ð2Þ where k¼1 2×jp 1−p 2jis the relative momentum of two particles with momentum p1and p2in the pair rest frame, denoted by the asterisk, Nis a normalization constant, and Nsame ðmixedÞðkÞis the kdistribution of the pairs measured in the same (mixed) events. The mixed-event distribution, which does not contain any effect of the strong FSI, reflects the phase space of the underlying event. Therefore, it serves as a reference to which the same-event distribution can be compared in order to extract information on the strong FSI of a specific system. To ensure a good quality of the reference sample, Nmixed, the mixing is performed only between events with similar multiplicity and primaryvertex position [5,7,10]. As the same (mixed) event distributions of the pairs are found to be compatible with the ones of the respective charge conjugates, they are combined in order to enhance the statistical precision. In the following, same-charge DðÞX refers to DðÞþXþ⊕DðÞ−X− pairs, while opposite-charge DðÞX refers to DðÞþX−⊕ DðÞ−Xþpairs, where X is either K or π. The normalization constant Nis chosen such that the mean value of the correlation function equals unity in a given range at large k, where the particles are not close enough in momentum space to experience FSI. The number of pairs and the normalization range for the different channels are reported in Table I. The latter are chosen according to the shape of the same (mixed) event distributions, which decreases and flattens out at different kregions depending on the involved light-flavor meson. The experimental correlation functions are computed in kintervals of 50 MeV=c, and the horizontal position of each data point is the average of the kdistribution of the mixed event in the corresponding kinterval. The effect of the finite momentum resolution of the ALICE detector on data is found to be negligible. The experimental correlation functions involving Dþand light-flavor mesons, obtained from Eq. (2), are shown in the left panels of Figs. 2and 3. They are raw quantities, which can be decomposed as CrawðkÞ¼CfemtoðkÞ×CnonfemtoðkÞ;ð3Þ where CfemtoðkÞ¼Pi;jλi;j×Ci;jðkÞ, with Ci;jðkÞarising from the FSI between the ith and jth components of the two particle species involved in the analysis, namely primary, secondary, and misidentified particles. Each of these contributions is weighted according to so-called λparameters, which are computed as λij ¼pipjfifjwhere pi;jand fi;jare, respectively, the purities and primary (secondary) fractions of the ith and jth contributions to the particle samples, discussed in Sec. II A. The contribution to CfemtoðkÞ, that only includes primary signal particles, is also referred to as genuine correlation function CgenðkÞ and is used to extract the relevant physics information about the strong FSI for the pair of interest. A detailed discussion TABLE I. Number of pairs with small relative momenta, where final-state effects become relevant and in the full krange, as well as the normalization range for the individual particle pair combinations under investigation. Pair Number of pairs in NsameðkÞ Normalization rangeTotal k<200 MeV=c Dþπþ⊕D−π−3.0×1062.0×105k∈½1.0;1.5GeV=c Dþπ−⊕D−πþ2.9×1062.1×105 DþKþ⊕D−K−1.7×1051.9×103k∈½1.5;2.0GeV=c DþK−⊕D−Kþ1.6×1052.2×103 Dþπþ⊕D−π−4.7×1053.3×104k∈½1.5;2.0GeV=c Dþπ−⊕D−πþ4.8×1053.4×104 DþKþ⊕D−K−4.9×104479 k∈½1.5;2.0GeV=c DþK−⊕DþK−4.8×104477 STUDYING THE INTERACTION BETWEEN CHARM AND LIGHT- …PHYS. REV. D 110, 032004 (2024) 032004-5 on the different contributions to CfemtoðkÞcan be found in Sec. III A. The remaining residual backgrounds, not related to FSI, are included in the term CnonfemtoðkÞ, which is discussed in Sec. III B. A. Contributions related to FSI There are several contributions to CfemtoðkÞin Eq. (3) in the case of DðÞþ and light-flavor mesons. When it is not possible to constrain them experimentally, these contributions can be modeled using the Koonin-Pratt equation [77], CðkÞ¼Zd3rSðrÞjψðr;kÞj2;ð4Þ where the so-called source function SðrÞcontains the distribution of the relative distance in the pair rest frame, and ψðr;kÞdenotes the two-particle wave function, which contains the interaction. Together they determine the shape of the correlation function, which is sensitive to the strong FSI at small k<200 MeV=c, also denoted as femtoscopic region. The source is constrained from the core-resonance model [78], which is based on the hypothesis of a common FIG. 2. Experimental Dπraw correlation functions [CrawðkÞ] with statistical (bars) and systematic uncertainties (boxes) (left column) and background contributions to the experimental correlation functions (right column). The width of the bands corresponds to the total uncertainty σtot ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi σ2 stat þσ2 syst q. The violet band describes the total background, fitted to the data, and used to extract the genuine correlation function from the raw signal. This band consists of several contributions, which are also shown individually in the figure, scaled by the appropriate λparameter. The results are shown for opposite-charge (first row) and same-charge (second row) pairs. S. ACHARYA et al. PHYS. REV. D 110, 032004 (2024) 032004-6 emission source of all hadrons [79] and is anchored to p−pcorrelation data in pp collisions. The model is characterized by a mT-dependent Gaussian core of width rcore, from which all primordial particles, which are created directly during the hadronization process, and do not stem from an intermediate decay, are emitted. Therefore, by measuring the mTof the reconstructed particle pairs with small kit is possible to obtain the respective core radius from a parametrization of the p–p data used in the model, following several previous femtoscopic analyses [6,7,10–12,54,80]. The mean mTof DðÞπpairs with k< 200 MeV=c is about 2.55 GeV=c2, while it is approximately 2.66 GeV=c2for DðÞK pairs. This leads to core radii of rDðÞπ core ¼0.82þ0.07 −0.07 fm and rDðÞK core ¼0.81þ0.08 −0.07 fm for DðÞπand DðÞK pairs, respectively. However, also shortlived resonances feeding into the yields of the particles of interest have to be considered, as they lead to an effective enlargement of the source. This is accounted for in the coreresonance model by fixing the yields of the resonances and employing an event generator to model their propagation and relative spatial orientation. At large rthese resonances lead to an exponential tail in the Gaussian-shaped source distributions obtained from the model for both DðÞK and DðÞπ. Therefore, the effective source employed in this analysis is obtained by parametrizing the distributions with two Gaussian sources of width ri eff, which are combined FIG. 3. Experimental DK raw correlation functions [CrawðkÞ] with statistical (bars) and systematic uncertainties (boxes) (left column) and background contributions to the experimental correlation functions (right column). The width of the bands corresponds to the total uncertainty σtot ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi σ2 stat þσ2 syst q. The violet band describes the total background, fitted to the data, and used to extract the genuine correlation function from the raw signal. This band consists of several contributions, which are also shown individually in the figure, scaled by the appropriate λparameter. The results are shown for opposite-charge (first row) and same-charge (second row) pairs. STUDYING THE INTERACTION BETWEEN CHARM AND LIGHT- …PHYS. REV. D 110, 032004 (2024) 032004-7 with the weight w, leading to Seff ðrÞ¼wS1ðrÞþ ð1−wÞS2ðrÞ. The values of the source parameters can be found in Table II. Employing SeffðrÞas source function in Eq. (4) ultimately leads to two properly weighted correlation functions with the respective Gaussian sources, S1ðrÞand S2ðrÞ. The two-particle wave function ψðr;kÞcan be obtained by numerically solving the Schrödinger equation for a given interaction potential, for example by employing CATS [81], a correlation analysis tool using the Schrödinger equation. The relevant contribution to CfemtoðkÞ, needed to extract information of the strong FSI between DðÞπand DðÞK, is the genuine correlation function CgenðkÞ, which is associated to primary light-flavor mesons and signal DðÞþ candidates. As the DðÞþ -meson samples are not pure, the correlation between combinatorial background candidates and lightflavor mesons has to be taken into account, which arises from the interaction between the light-flavor mesons and the particles from which the background DðÞþ-meson candidate is built from [82]. It is estimated using a datadriven approach, where pions or kaons are paired with a pure sample of background DðÞþ mesons, obtained from the sidebands of the invariant-mass intervals outside the DðÞþ-meson signal region. The resulting correlation function is referred to as CSBðkÞ. For the Dþmesons, the sideband intervals start at 5 σD away from the nominal mass and extend for 200 MeV=c2. The σDcorresponds to the width of the Gaussian function describing the signal peak and is determined via a fit to the invariant-mass distribution, considering its pTdependence. For the Dþ mesons, the selection is analogous except that, instead of the invariant mass, the invariant-mass difference MðKππÞ−MðKπÞis used, and only the right sideband is considered. Since a contamination from Dþ -meson is expected in the Dþ-meson sideband sample, due to Dþ →D0πþand subsequent D0→K−πþdecays, the invariant-mass interval ½1.992;2.028MeV=c2is excluded. This corresponds to 2.5σDaround the Dþ mass. The correlation functions obtained from the left and right sidebands are compatible within the uncertainties and combined as a weighted average, considering the relative abundances of background in the left and right half of the Dþ-meson signal region. The correction of the combinatorial Dπcorrelation function requires a different approach with respect to the traditional sideband method. This is due to the presence of an additional source of correlated background that arises from the correlation of a soft pion of a real Dþ decay with a background Dþ candidate formed by the D0meson coming from the same Dþ decay of the soft pion andan unrelated pion. Such a correlation results in a peak in the correlation function at k≈40 MeV=c, which cannot be removed via pairor particle-level selections since the particle’s origin is not known in data. For this reason, the correction for the combinatorial background cannot be carried out via a sideband analysis. Instead, the background-corrected correlation function is directly computed as C0 rawðkÞ¼NpsameðkÞNsameðkÞ pmixedðkÞNmixedðkÞ;ð5Þ where psame=mixedðkÞis the purityof the Dþ -meson sample, calculated in the sameand mixed-events, as a function of k. Since the peak in the correlation function comes from the combinatorial background of the Dþ -meson candidates, a reweighting by the purity removes by construction the artifact at k≈40 MeV=c. The opposite-charge DK correlation function is affected by a similar issue since the D0 meson decays into K−via D0→K−πþ. However, in this case, the peak associated with the correlated background is found to be at k≈600 MeV=c, outside the femtoscopic region. As the correlation function above 200 MeV=c does not carry information about the strong FSI, the traditional sideband method is used to correct for the combinatorial background. As already discussed in Sec. II B, a significant fraction of the Dþmesons is produced from the decays of charmhadron resonances. As this contribution cannot be separated experimentally, it is modeled using the Koonin-Pratt formalism with Coulomb potential, which is found to adequately describe the experimental correlation functions involving Dþ mesons, presented in Sec. V. Subsequently, the so obtained correlation functions are mapped into the ones of (Dþ←Dþ)πand (Dþ←Dþ)K pairs, respectively. The transformation of the momentum basis is performed using GENBOD phase-space simulations [83] of the D →Dπ0decay, as in this case the kinematics are most stringently constrained. Contributions to the Dþmeson yield from decays of other excited charm resonances are considered to be negligible [72]. A flat correlation function is assumed for sources of background that are not expected to lead to correlations, or that can be assumed negligible due to their small λscaling parameter. They include contributions from particle pairs involving nonprimary light-flavor mesons and contamination of the samples, as well as nonprompt DðÞþ mesons. Especially, the correlation of primary light-flavor mesons TABLE II. Parameters of the effective source Seff ðrÞ, which is given by the weighted sum of two Gaussian distributions of width ri eff and used in the modeling of the correlation functions. The difference between the DðÞπand DðÞKsystems is due to the different transverse mass of the systems as well as resonances feeding into the light-flavor mesons. Pair wr 1 eff [fm] r2 eff [fm] DðÞK0.78þ0.02 −0.01 0.86þ0.09 −0.07 2.03þ0.19 −0.12 DðÞπ0.66þ0.03 −0.02 0.97þ0.09 −0.08 2.52þ0.36 −0.20 S. ACHARYA et al. PHYS. REV. D 110, 032004 (2024) 032004-8 uncertainty of the data as well as the predictions. In the case of the I¼3=2channel, the measurements also show a tension with the theoretical predictions, it is, however, smaller than in the I¼1=2channel. In the Dπcase, a deviation of 2–5σis found, depending on the model, while it is around 3–4σfor Dπ. A much larger source size could diminish this discrepancy, as it leads to a less pronounced correlation signal for a given interaction strength. However, there is no obvious motivation for assuming a breaking of the universal mTscaling of the core radius [78,79] in the case of correlation functions involving charm mesons. Especially, it is successfully used in the analysis of the experimental pD−correlation function [54]. In Ref. [95] the hidden gauge formalism, implementing unitarization in coupled channels, is used to study the molecular nature of the lowest-lying D1states [D1ð2420Þand D1ð2430Þ], as well as the scattering amplitudes of some of the members of the meson-baryon basis considered (Dπ,Dρ) and the corresponding correlation functions. In order to better accommodate the D1ð2430Þwithin the experimental observations [46,96], a bare quark-model pole structure is added explicitly, whose parameters dependence allows the authors to consider two plausible scenarios. The one denoted as Model B in their publication provides as a result a scattering length of aI¼1=2 Dπ¼0.1fm, which is a value much closer to the one obtained in the present work. Alternatively, other complex structures, for example, in higher partial waves, not taken into account by the theory models, could modify the predictions. In summary, the measured correlation functions between charm mesons and light-flavor mesons are compatible with the predictions obtained with only Coulomb interaction, suggesting that the residual strong interaction between these pairs of particles is shallow. A significant discrepancy in the I¼1=2channel is found with respect to the predictions for the DðÞπscattering lengths, which is much less pronounced in the I¼3=2channel. This discrepancy could be reconciled with the theory only in the case of a sizeable emitting source, which is not well motivated. The current precision of the DðÞK correlation functions does not allow for the discrimination between the available models and for a firm conclusion on the possible formation of bound states. Finally, the measured interactions suggest that the rescattering probability of charm mesons with light hadrons in the hadronic phase of the system produced in ultrarelativistic collisions is small. Even with values of scattering lengths predicted by theory calculations, which are larger than the measured ones reported in this article, a small impact on the D-meson final momenta is expected [62], given the duration of the hadronic phase of the system created in ultrarelativistic heavy-ion collisions of about Δτhad ≈5–10 fm=c [13,62,97]. FIG. 7. Scattering length of the Dπ(left) and Dπ(right) interaction, for the two isospin channels that characterize the systems. They are extracted from a simultaneous χ2minimization to the experimental correlation functions. The red (orange) areas represent the resulting confidence intervals for a 68% (95%) probability. The dashed lines correspond to Coulomb interaction only, as the scattering lengths of the strong interaction vanish. As comparison, the available theoretical predictions [89–94], listed in Tables IV and V, are shown as well. TABLE VI. The scattering lengths a0of the DðÞπinteraction, extracted from a χ2minimization to the experimental genuine correlation function, using a Gaussian potential to parametrize the strong interaction. Pair Ia 0[fm] Dπ3=20.01 0.02ðstatÞ0.01ðsystÞ 1=20.02 0.03ðstatÞ0.01ðsystÞ Dπ3=20.05 0.04ðstatÞ0.02ðsystÞ 1=2−0.03 0.05ðstatÞ0.02ðsystÞ STUDYING THE INTERACTION BETWEEN CHARM AND LIGHT- …PHYS. REV. D 110, 032004 (2024) 032004-15 VI. CONCLUSION The study of the residual strong interactions of DðÞþ mesons with charged pions and kaons is performed for the first time, using high-multiplicity proton–proton collision data at ffiffiffi s p¼13 TeV collected with the ALICE detector at the LHC. The femtoscopy technique is used to test various theoretical models of the strong interaction by comparing the experimental correlation functions for the different particle pairs with the predictions by theory. As comparison also the Coulomb-only assumption is tested and, within the current uncertainties, all the measured correlation functions can be well described by it. For the same charge Dπ system, a slight tension with the Coulomb-only assumption of nσ¼2.62 is observed. Still, it describes the data better than the model including the strong interaction. A comparison of the DK and DK data to theoretical predictions does not lead to a clear result, as no preference among the different models of the strong interaction or Coulomb-only hypothesis is observed due to the limited statistical precision. In the case of Dπinteraction instead, the experimental data indicates that the theoretical models overestimate the scattering lengths, especially in the opposite-charge Dπcorrelation function, where a strong discrepancy is found. In comparison, Coulomb-only predictions yield a better description of the data. The same can be observed for the correlation functions involving Dþ mesons. Among the experimental correlation functions studied in this work, the ones of the Dπand Dπsystems are the most precise. Therefore, they are used to determine the scattering lengths of the strong interaction, which is modeled using a Gaussian potential. The scattering parameters are found to be small and compatible with zero. Especially, the disagreement between the scattering length of the isospin channel I¼1=2, extracted from the data, and the theoretical predictions is found to be larger than 5σ, challenging the current understanding of the residual strong interaction between D mesons and pions. These findings also provide important information for the interpretation of the measurements of D-meson production and angular anisotropy in heavy-ion collisions [60,61] since they suggest that the effect of the rescattering of DðÞþ mesons with light hadrons during the hadronic phase of the system produced in such collisions is small. The precision of these measurements will improve with the data taken during the LHC Run 3 data-taking period. In fact, the dataset collected by the ALICE Collaboration will benefit from various detector upgrades, which include an improved spatial resolution crucial for the reconstruction of heavy-flavor decay vertices, and a larger luminosity thanks to the higher readout rate achievable [98]. Furthermore, with such improvements, the momentum correlation functions of other particle pairs involving charm hadrons will also become accessible. ACKNOWLEDGMENTS 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 centers 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 `a Pesquisa do Estado de São Paulo (FAPESP) and Universidade Federal do Rio Grande do Sul (UFRGS), Brazil; Bulgarian Ministry of Education and Science, within the National Roadmap for Research Infrastructures 2020-2027 (object CERN), Bulgaria; 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 `al’Energie Atomique (CEA) and Institut National de Physique Nucl´eaire 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; National Research and Innovation Agency— BRIN, Indonesia; Istituto Nazionale di Fisica Nucleare (INFN), Italy; Japanese Ministry of Education, Culture, S. ACHARYA et al. PHYS. REV. D 110, 032004 (2024) 032004-16 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, Ministry of Research and Innovation and Institute of Atomic Physics and Universitatea Nationala de Stiinta si Tehnologie Politehnica Bucuresti, Romania; 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 (NSTDA) and National Science, Research and Innovation Fund (NSRF via PMU-B B05F650021), 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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Oyama ,77 Y. Pachmayer ,95 S. Padhan ,48 D. Pagano ,56,136 G. Paić,66 S. Paisano-Guzmán ,45 A. Palasciano ,51 S. Panebianco ,132 H. Park ,127 H. Park ,106 J. E. Parkkila ,33 Y. Patley ,48 B. Paul ,23 M. M. D. M. Paulino ,112 H. Pei ,6T. Peitzmann ,60 X. Peng ,11 M. Pennisi ,25 S. Perciballi ,25 D. Peresunko ,143 G. M. Perez ,7Y. Pestov,143 V. Petrov ,143 M. Petrovici ,46 R. P. Pezzi ,67,105 S. Piano ,58 M. Pikna ,13 P. Pillot ,105 O. Pinazza ,33,52 L. Pinsky,118 C. Pinto ,96 S. Pisano ,50 M. Płoskoń,75 M. Planinic,90 F. Pliquett,65 M. G. Poghosyan ,88 B. Polichtchouk ,143 S. Politano ,30 N. Poljak ,90 A. Pop ,46 S. Porteboeuf-Houssais ,129 V. Pozdniakov ,144,†I. Y. Pozos ,45 K. K. Pradhan ,49 S. K. Prasad ,4 S. Prasad ,49 R. Preghenella ,52 F. Prino ,57 C. A. Pruneau ,139 I. Pshenichnov ,143 M. Puccio ,33 S. Pucillo ,25 S. Qiu ,85 L. Quaglia ,25 S. Ragoni ,15 A. Rai ,140 A. Rakotozafindrabe ,132 L. Ramello ,57,135 F. Rami ,131 M. Rasa ,27 S. S. Räsänen ,44 R. Rath ,52 M. P. Rauch ,21 I. Ravasenga ,33 K. F. Read ,88,124 C. Reckziegel ,114 A. R. Redelbach ,39 K. Redlich ,80,§§ C. A. Reetz ,98 H. D. Regules-Medel,45 A. Rehman,21 F. Reidt ,33 H. A. Reme-Ness ,35 Z. Rescakova,38 K. Reygers ,95 A. Riabov ,143 V. Riabov ,143 R. Ricci ,29 M. Richter ,21 A. A. Riedel ,96 W. Riegler ,33 A. G. Riffero ,25 C. Ripoli,29 C. Ristea ,64 M. V. Rodriguez ,33 M. Rodríguez Cahuantzi ,45 S. A. Rodríguez Ramírez ,45 K. Røed ,20 R. Rogalev ,143 E. Rogochaya ,144 T. S. Rogoschinski ,65 D. Rohr ,33 D. Röhrich ,21 S. Rojas Torres ,36 P. S. Rokita ,138 G. Romanenko ,26 F. Ronchetti ,50 E. D. Rosas,66 K. Roslon ,138 A. Rossi ,55 A. Roy ,49 S. Roy ,48 N. Rubini ,26 D. Ruggiano ,138 R. Rui ,24 P. G. Russek ,2R. Russo ,85 A. Rustamov ,82 E. Ryabinkin ,143 Y. Ryabov ,143 A. Rybicki ,109 J. Ryu ,17 W. Rzesa ,138 O. A. M. Saarimaki ,44 S. Sadhu ,32 S. Sadovsky ,143 J. Saetre ,21 K. Šafaˇ rík ,36 S. K. Saha ,4 S. Saha ,81 B. Sahoo ,49 R. Sahoo ,49 S. Sahoo,62 D. Sahu ,49 P. K. Sahu ,62 J. Saini ,137 K. Sajdakova,38 S. Sakai ,127 M. P. Salvan ,98 S. Sambyal ,92 D. Samitz ,104 I. Sanna ,33,96 T. B. Saramela,112 D. Sarkar ,84 P. Sarma ,42 V. Sarritzu ,23 V. M. Sarti ,96 M. H. P. Sas ,33 S. Sawan ,81 E. Scapparone ,52 J. Schambach ,88 H. S. Scheid ,65 C. Schiaua ,46 R. Schicker ,95 F. Schlepper ,95 A. Schmah,98 C. Schmidt ,98 H. R. Schmidt,94 M. O. Schmidt ,33 M. Schmidt,94 N. V. Schmidt ,88 A. R. Schmier ,124 R. Schotter ,131 A. Schröter ,39 J. Schukraft ,33 K. Schweda ,98 G. Scioli ,26 E. Scomparin ,57 J. E. Seger ,15 Y. Sekiguchi,126 D. Sekihata ,126 M. Selina ,85 I. Selyuzhenkov ,98 S. Senyukov ,131 J. J. Seo ,95 D. Serebryakov ,143 L. Serkin ,66 L. Šerkšnytė,96 A. Sevcenco ,64 T. J. Shaba ,69 A. Shabetai ,105 R. Shahoyan,33 A. Shangaraev ,143 B. Sharma ,92 D. Sharma ,48 H. Sharma ,55 M. Sharma ,92 S. Sharma ,77 S. Sharma ,92 U. Sharma ,92 A. Shatat ,133 O. Sheibani,118 K. Shigaki ,93 M. Shimomura,78 J. Shin,12 S. Shirinkin ,143 Q. Shou ,40 Y. Sibiriak ,143 S. Siddhanta ,53 T. Siemiarczuk ,80 T. F. Silva ,112 D. Silvermyr ,76 T. Simantathammakul,107 R. Simeonov ,37 B. Singh,92 B. Singh ,96 K. Singh ,49 R. Singh ,81 R. Singh ,92 R. Singh ,49,98 S. Singh ,16 V. K. Singh ,137 V. Singhal ,137 T. Sinha ,101 B. Sitar ,13 M. Sitta ,57,135 T. B. Skaali,20 G. Skorodumovs ,95 N. Smirnov ,140 R. J. M. Snellings ,60 E. H. Solheim ,20 J. Song ,17 C. Sonnabend ,33,98 J. M. Sonneveld ,85 F. Soramel ,28 A. B. Soto-hernandez ,89 R. Spijkers ,85 I. Sputowska ,109 J. Staa ,76 J. Stachel ,95 I. Stan ,64 P. J. Steffanic ,124 S. F. Stiefelmaier ,95 D. Stocco ,105 I. Storehaug ,20 N. J. Strangmann ,65 P. Stratmann ,128 S. Strazzi ,26 A. Sturniolo ,31,54 C. P. Stylianidis,85 A. A. P. Suaide ,112 C. Suire ,133 M. Sukhanov ,143 M. Suljic ,33 R. Sultanov ,143 V. Sumberia ,92 S. Sumowidagdo ,83 I. Szarka ,13 M. Szymkowski ,138 S. F. Taghavi ,96 G. Taillepied ,98 J. Takahashi ,113 G. J. Tambave ,81 S. Tang ,6Z. Tang ,122 J. D. Tapia Takaki ,120 N. Tapus,115 L. A. Tarasovicova ,128 M. G. Tarzila ,46 G. F. Tassielli ,32 A. Tauro ,33 A. Tavira García ,133 G. Tejeda Muñoz ,45 A. Telesca ,33 L. Terlizzi ,25 C. Terrevoli ,51 S. Thakur ,4D. Thomas ,110 A. Tikhonov ,143 N. Tiltmann ,33,128 A. R. Timmins ,118 M. Tkacik,108 T. Tkacik ,108 A. Toia ,65 R. Tokumoto,93 S. Tomassini,26 K. Tomohiro,93 N. Topilskaya ,143 M. Toppi ,50 T. Tork ,133 V. V. Torres ,105 A. G. Torres Ramos ,32 A. Trifiró ,31,54 A. S. Triolo ,31,33,54 S. Tripathy ,52 T. Tripathy ,48 V. Trubnikov ,3W. H. Trzaska ,119 T. P. Trzcinski ,138 A. Tumkin ,143 R. Turrisi ,55 T. S. Tveter ,20 K. Ullaland ,21 B. Ulukutlu ,96 A. Uras ,130 M. Urioni ,136 G. L. Usai ,23 M. Vala,38 N. Valle ,56 L. V. R. van Doremalen,60 M. van Leeuwen ,85 C. A. van Veen ,95 R. J. G. van Weelden ,85 S. ACHARYA et al. PHYS. REV. D 110, 032004 (2024) 032004-22 P. Vande Vyvre ,33 D. Varga ,47 Z. Varga ,47 P. Vargas Torres,66 M. Vasileiou ,79 A. Vasiliev ,143 O. Vázquez Doce ,50 O. Vazquez Rueda ,118 V. Vechernin ,143 E. Vercellin ,25 S. Vergara Limón,45 R. Verma,48 L. Vermunt ,98 R. V´ertesi ,47 M. Verweij ,60 L. Vickovic,34 Z. Vilakazi,125 O. Villalobos Baillie ,102 A. Villani ,24 A. Vinogradov ,143 T. Virgili ,29 M. M. O. Virta ,119 V. Vislavicius,76 A. Vodopyanov ,144 B. Volkel ,33 M. A. Völkl ,95 S. A. Voloshin ,139 G. Volpe ,32 B. von Haller ,33 I. Vorobyev ,33 N. Vozniuk ,143 J. Vrláková ,38 J. Wan,40 C. Wang ,40 D. Wang,40 Y. Wang ,40 Y. Wang ,6A. Wegrzynek ,33 F. T. Weiglhofer,39 S. C. Wenzel ,33 J. P. Wessels ,128 J. Wiechula ,65 J. Wikne ,20 G. Wilk ,80 J. Wilkinson ,98 G. A. Willems ,128 B. Windelband ,95 M. Winn ,132 J. R. Wright ,110 W. Wu,40 Y. Wu ,122 Z. Xiong,122 R. Xu ,6A. Yadav ,43 A. K. Yadav ,137 S. Yalcin ,73 Y. Yamaguchi ,93 S. Yang,21 S. Yano ,93 E. R. Yeats,19 Z. Yin ,6I.-K. Yoo ,17 J. H. Yoon ,59 H. Yu,12 S. Yuan,21 A. Yuncu ,95 V. Zaccolo ,24 C. Zampolli ,33 M. Zang,6F. Zanone ,95 N. Zardoshti ,33 A. Zarochentsev ,143 P. Závada ,63 N. Zaviyalov,143 M. Zhalov ,143 B. Zhang ,6C. Zhang ,132 L. Zhang ,40 M. Zhang,6S. Zhang ,40 X. Zhang ,6Y. Zhang,122 Z. Zhang ,6M. Zhao ,10 V. Zherebchevskii ,143 Y. Zhi,10 C. Zhong,40 D. Zhou ,6Y. Zhou ,84 J. Zhu ,6,55 Y. Zhu,6 S. C. Zugravel ,57 and N. Zurlo 56,136 (ALICE Collaboration) 1A.I. Alikhanyan National Science Laboratory (Yerevan Physics Institute) Foundation, Yerevan, Armenia 2AGH University of Krakow, Cracow, Poland 3Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, Kiev, Ukraine 4Bose Institute, Department of Physics and Centre for Astroparticle Physics and Space Science (CAPSS), Kolkata, India 5California Polytechnic State University, San Luis Obispo, California, USA 6Central China Normal University, Wuhan, China 7Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN), Havana, Cuba 8Centro de Investigación y de Estudios Avanzados (CINVESTAV), Mexico City and M´erida, Mexico 9Chicago State University, Chicago, Illinois, USA 10China Institute of Atomic Energy, Beijing, China 11China University of Geosciences, Wuhan, China 12Chungbuk National University, Cheongju, Republic of Korea 13Comenius University Bratislava, Faculty of Mathematics, Physics and Informatics, Bratislava, Slovak Republic 14COMSATS University Islamabad, Islamabad, Pakistan 15Creighton University, Omaha, Nebraska, USA 16Department of Physics, Aligarh Muslim University, Aligarh, India 17Department of Physics, Pusan National University, Pusan, Republic of Korea 18Department of Physics, Sejong University, Seoul, Republic of Korea 19Department of Physics, University of California, Berkeley, California, USA 20Department of Physics, University of Oslo, Oslo, Norway 21Department of Physics and Technology, University of Bergen, Bergen, Norway 22Dipartimento di Fisica, Universit`a di Pavia, Pavia, Italy 23Dipartimento di Fisica dell’Universit`a and Sezione INFN, Cagliari, Italy 24Dipartimento di Fisica dell’Universit`a and Sezione INFN, Trieste, Italy 25Dipartimento di Fisica dell’Universit`a and Sezione INFN, Turin, Italy 26Dipartimento di Fisica e Astronomia dell’Universit`a and Sezione INFN, Bologna, Italy 27Dipartimento di Fisica e Astronomia dell’Universit`a and Sezione INFN, Catania, Italy 28Dipartimento di Fisica e Astronomia dell’Universit`a and Sezione INFN, Padova, Italy 29Dipartimento di Fisica “E.R. Caianiello”dell’Universit`a and Gruppo Collegato INFN, Salerno, Italy 30Dipartimento DISAT del Politecnico and Sezione INFN, Turin, Italy 31Dipartimento di Scienze MIFT, Universit`a di Messina, Messina, Italy 32Dipartimento Interateneo di Fisica “M. Merlin”and Sezione INFN, Bari, Italy 33European Organization for Nuclear Research (CERN), Geneva, Switzerland 34Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, University of Split, Split, Croatia 35Faculty of Engineering and Science, Western Norway University of Applied Sciences, Bergen, Norway 36Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Prague, Czech Republic 37Faculty of Physics, Sofia University, Sofia, Bulgaria STUDYING THE INTERACTION BETWEEN CHARM AND LIGHT- …PHYS. REV. D 110, 032004 (2024) 032004-23 38Faculty of Science, P.J. Šafárik University, Košice, Slovak Republic 39Frankfurt Institute for Advanced Studies, Johann Wolfgang Goethe-Universität Frankfurt, Frankfurt, Germany 40Fudan University, Shanghai, China 41Gangneung-Wonju National University, Gangneung, Republic of Korea 42Gauhati University, Department of Physics, Guwahati, India 43Helmholtz-Institut für Strahlen-und Kernphysik, Rheinische Friedrich-Wilhelms-Universität Bonn, Bonn, Germany 44Helsinki Institute of Physics (HIP), Helsinki, Finland 45High Energy Physics Group, Universidad Autónoma de Puebla, Puebla, Mexico 46Horia Hulubei National Institute of Physics and Nuclear Engineering, Bucharest, Romania 47HUN-REN Wigner Research Centre for Physics, Budapest, Hungary 48Indian Institute of Technology Bombay (IIT), Mumbai, India 49Indian Institute of Technology Indore, Indore, India 50INFN, Laboratori Nazionali di Frascati, Frascati, Italy 51INFN, Sezione di Bari, Bari, Italy 52INFN, Sezione di Bologna, Bologna, Italy 53INFN, Sezione di Cagliari, Cagliari, Italy 54INFN, Sezione di Catania, Catania, Italy 55INFN, Sezione di Padova, Padova, Italy 56INFN, Sezione di Pavia, Pavia, Italy 57INFN, Sezione di Torino, Turin, Italy 58INFN, Sezione di Trieste, Trieste, Italy 59Inha University, Incheon, Republic of Korea 60Institute for Gravitational and Subatomic Physics (GRASP), Utrecht University/Nikhef, Utrecht, Netherlands 61Institute of Experimental Physics, Slovak Academy of Sciences, Košice, Slovak Republic 62Institute of Physics, Homi Bhabha National Institute, Bhubaneswar, India 63Institute of Physics of the Czech Academy of Sciences, Prague, Czech Republic 64Institute of Space Science (ISS), Bucharest, Romania 65Institut für Kernphysik, Johann Wolfgang Goethe-Universität Frankfurt, Frankfurt, Germany 66Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de M´exico, Mexico City, Mexico 67Instituto de Física, Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, Brazil 68Instituto de Física, Universidad Nacional Autónoma de M´exico, Mexico City, Mexico 69iThemba LABS, National Research Foundation, Somerset West, South Africa 70Jeonbuk National University, Jeonju, Republic of Korea 71Johann-Wolfgang-Goethe Universität Frankfurt Institut für Informatik, Fachbereich Informatik und Mathematik, Frankfurt, Germany 72Korea Institute of Science and Technology Information, Daejeon, Republic of Korea 73KTO Karatay University, Konya, Turkey 74Laboratoire de Physique Subatomique et de Cosmologie, Universit´e Grenoble-Alpes, CNRS-IN2P3, Grenoble, France 75Lawrence Berkeley National Laboratory, Berkeley, California, USA 76Lund University Department of Physics, Division of Particle Physics, Lund, Sweden 77Nagasaki Institute of Applied Science, Nagasaki, Japan 78Nara Women’s University (NWU), Nara, Japan 79National and Kapodistrian University of Athens, School of Science, Department of Physics, Athens, Greece 80National Centre for Nuclear Research, Warsaw, Poland 81National Institute of Science Education and Research, Homi Bhabha National Institute, Jatni, India 82National Nuclear Research Center, Baku, Azerbaijan 83National Research and Innovation Agency—BRIN, Jakarta, Indonesia 84Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark 85Nikhef, National institute for subatomic physics, Amsterdam, Netherlands 86Nuclear Physics Group, STFC Daresbury Laboratory, Daresbury, United Kingdom 87Nuclear Physics Institute of the Czech Academy of Sciences, Husinecˇ Rež, Czech Republic 88Oak Ridge National Laboratory, Oak Ridge, Tennessee, USA 89Ohio State University, Columbus, Ohio, USA 90Physics Department, Faculty of Science, University of Zagreb, Zagreb, Croatia 91Physics Department, Panjab University, Chandigarh, India S. ACHARYA et al. PHYS. REV. D 110, 032004 (2024) 032004-24