Investigating the nature of the K∗0(700) state with π±K0S correlations at the LHC

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/ Investigating the nature of the K0(700) state with π±K0S correlations at the LHC © 2024 The Author(s). Published by Elsevier B.V. Funded by SCOAP³. Published version ALICE Collaboration ALICE Collaboration. (2024). Investigating the nature of the K0(700) state with π±K0S correlations at the LHC. Physics Letters B, 856, Article 138915. https://doi.org/10.1016/j.physletb.2024.138915 2024 Phys. Lett. B 856 (2024) 138915 Available online 30 July 2024 0370-2693/© 2024 The Author(s). Published by Elsevier B.V. Funded by SCOAP³. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Contents lists available at ScienceDirect Physics Letters B journal homepage: www.elsevier.com/locate/physletb Letter Investigating the composition of the K∗ 0(700) state with 𝜋±K0 Scorrelations at the LHC .ALICE Collaboration⋆ A R T I C L E I N F O A B S T R A C T Editor: M. Doser Dataset link: https:// www .hepdata .net /record /ins2739149 The first measurements of femtoscopic correlations with the particle pair combinations 𝜋±K0 Sin pp collisions at √𝑠=13TeV at the Large Hadron Collider (LHC) are reported by the ALICE experiment. Using the femtoscopic approach, it is shown that it is possible to study the elusive K∗ 0(700) particle that has been considered a tetraquark candidate for over forty years. Source and final-state interaction parameters are extracted by fitting a model assuming a Gaussian source to the experimentally measured two-particle correlation functions. The final-state interaction in the 𝜋±K0 Ssystem is modeled through a resonant scattering amplitude, defined in terms of a mass and a coupling parameter, The extracted mass and Breit–Wigner width, derived from the coupling parameter, of the final-state interaction are found to be consistent with previous measurements of the K∗ 0(700). The small value and increase of the correlation strength with increasing source size support the hypothesis that the K∗ 0(700) is a four-quark state, i.e. a tetraquark state of the form (q1, q2, q3, q3)in which q1, q2and q3indicate the flavor of the valence quarks of the 𝜋and K0 S. This latter trend is also confirmed via a simple geometric model that assumes a tetraquark structure of the K∗ 0(700) resonance. 1. Introduction Femtoscopy with identical charged pions has been a useful tool for many years to experimentally probe the geometry of the space-time structure of the freeze-out probability distribution in high-energy pp and heavy-ion collisions [1]. Identical-kaon femtoscopic measurements have also been carried out to complement the identical pion studies, examples of which are measurements in Au–Au collisions at center-of-mass energy per nucleon pair √𝑠NN = 200 GeV at the Relativistic Heavy-Ion Collider by the STAR Collaboration [2](K 0 SK0 S) and PHENIX Collaboration [3](K ±K±), and for pp collisions at √𝑠=5.02, 7, and 13 TeV and Pb–Pb collisions at √𝑠NN =2.76 TeV at the CERN LHC by the ALICE Collaboration [4–7](K 0 SK0 Sand K±K±). In the femtoscopic method, the momentum correlations of pairs of particles when interactions with the other particles in the collision system cease, i.e. during “freeze out” [8], can be utilized to get insight into the strength of the pair interaction, i.e. the final-state interaction (FSI), at low relative momentum. The homogeneity region size, the strength, and even the nature of the FSI at freeze out can be determined by fitting the experimental two-particle correlation function to a model based on the FSI. Results on non-identical kaon femtoscopy with K0 SK±pairs were published by ALICE in pp collisions at √𝑠=5.02, 7, and 13 TeV and Pb– Pb collisions at √𝑠NN =2.76 TeV [7,9,10]. Although the general goals ⋆E-mail address: alice -publications @cern .ch. of non-identical kaon femtoscopy studies overlap with those for identical kaon femtoscopy, e.g. to extract information about the space–time geometry of the collision region and determine the pair-wise interaction strength, the latter is different in each case. For the identical kaon cases, in which pair-wise quantum statistical correlations are present, the interactions are the following: K±K±– Coulomb interaction, and K0 SK0 S– strong FSI through the f0(980)/a0(980) resonances. For the K0 SK±pairs, there are no quantum statistical correlations and the only interaction present is the strong FSI through the a0(980) resonance. K0 SK±femtoscopy should thus be sensitive to the properties of the a0(980) resonance. It has been suggested in many papers in the literature that the a0(980) could be a four-quark or tetraquark state [11]. It was first proposed in 1977 that experimentally-observed low-lying mesons, such as the a0(980) and K∗ 0(700), are part of a SU(3) tetraquark nonet using the MIT Bag model [12], which was later followed up with lattice QCD calculations [13]. There have been a number of QCD studies of these mesons that can be categorized as QCD-inspired models, see for example Refs. [11,14–16], and lattice QCD calculations, see for example Refs. [17–19]. Indeed, the results of the ALICE K0 SK±studies mentioned above suggested that the a0(980) is a tetraquark state. This suggestion is based on comparing the extracted pair-wise interaction strength of K0 SK±between pp and Pb–Pb collisions as well as with the K0 SK0 Sstudies [4,6,7,9,10]. https://doi.org/10.1016/j.physletb.2024.138915 Received 6 January 2024; Received in revised form 21 June 2024; Accepted 25 July 2024 Physics Letters B 856 (2024) 138915 2 ALICE Collaboration From a geometric picture, since a tetraquark version of the a0(980) contains a strange – anti-strange quark pair, a FSI through it should be suppressed for a small system as in pp collisions due to an increased annihilation probability, whereas for a large Pb–Pb collision this suppression should not be present. Thus, a strong FSI would be expected from Pb–Pb collisions and weak FSI from pp collisions, and this is what was observed in experiments. It would also be expected that a strong pair-wise correlation would be seen for K0 SK0 Sstudies since quantum statistics is dominant over FSI effects. This exception is corroborated by experimental findings [4,6,7]. The success of the ALICE K0 SK±studies on the nature of the a0(980) resonance motivated the first femtoscopic study ever of 𝜋±K0 Scorrelations in √𝑠=13 TeV pp collisions. Another resonance that is a tetraquark candidate is the K∗ 0(700) that decays with a branching ratio of ∼ 100% into 𝜋K pairs [12]. The K∗ 0(700) is listed in the Review of Particle Physics [20]as a strange meson with spin 0 and isospin 1 2, the quark content of the K∗ 0(700)+state being us. Its mass is listed as 845 ±17 MeV/𝑐2and it is a very broad resonance with Breit–Wigner width of 468 ±30MeV/𝑐2. The mass of the K∗ 0(700) is above the 𝜋±K0 Sthreshold, that is of about 637.18 MeV/𝑐2, and its width is seen to encompass this threshold and below. The tetraquark version of the K∗ 0(700)+would have quark content usddand would decay by direct quark transfer into a 𝜋+K0pair [12]. Thus by measuring 𝜋±K0 Scorrelations it should be possible to study the quark nature of the K∗ 0(700) using similar methods as mentioned above for the a0(980) studies, i.e. measuring the strength of the FSI, assuming that the 𝜋±K0 SFSI goes solely through the K∗ 0(700). This scenario will be studied by extracting the mass and width parameters of the FSI and comparing them with previous measurements of the K∗ 0(700) [21]. In the present Letter, a study of femtoscopic correlations with the non-identical pair combination 𝜋±K0 Sin pp collisions at √𝑠=13TeV is presented for the first time to study the nature of the K∗ 0(700) resonance. The choice of using pp collisions for this work responds to the necessity of studying the FSI in a small system in which the strength of the FSI is expected to be more sensitive to the system size and thus to the quark nature of the resonance [7]. Due to the shortrange nature of the strong interaction which might produce the resonant state, measurements in pp collisions are more suited since interparticle distances of a few fm are obtained [8]. Moreover, it has already been observed that the presence of resonances in the correlation function is enhanced for measurements in small colliding systems, since the signalto-background for the considered state scales as 1∕multiplicity [8]. The results presented in this Letter are obtained using data collected by the ALICE Collaboration [22,23]during the 2015–2018 pp LHC run. The Letter is organized into seven sections: Introduction, Data Analysis, Correlation Function, Fitting, Systematic uncertainties, Results and Discussion, and Summary. The Data Analysis section gives details on how the data were taken and how the 𝜋±and K0 Swere reconstructed and identified. The Correlation Function section describes how the 𝜋±K0 S pairs were used to construct the correlation functions for this analysis. The Fitting section describes the model used to fit the correlation functions in order to extract the source parameters and FSI parameters. The Systematic uncertainties section discusses how the systematic uncertainties were calculated. The Results and Discussion section presents the results for the extracted parameters and discusses their interpretation. The Summary section summarizes the results of the present work. 2. Data analysis The ALICE detector and its performance are described in detail in Refs. [22,24]. Collision events are selected by using the information from the V0 detectors composed of the V0C and V0A scintillator arrays [25,26], located on both sides of the interaction point, covering the pseudorapidity intervals −3.7 <𝜂<−1.6and 2.8 <𝜂<5.1, respectively. In the analysis 5 ×10 8minimum bias triggered pp collisions at √𝑠=13TeV were used. Charged particle multiplicity classes, given in terms of multiplicity percentile intervals of the visible inelastic pp cross section, were also determined from the V0 detectors [27]. The Time Projection Chamber (TPC) [28]and the Inner Tracking System (ITS) [22]were used for charged particle tracking. These detectors cover the pseudorapidity range of |𝜂| <0.9and are located within a solenoid magnet with a field strength of magnitude 𝐵=0.5T. The momentum (𝑝) determination for charged tracks was made using only the TPC space points. The ITS provided excellent spatial resolution in determining the primary collision vertex. This vertex was used to constrain the tracks reconstructed with the TPC, requiring it to be within ±10 of the center of the ALICE detector. The average momentum resolution typically obtained in this analysis for charged tracks was less than 10 MeV/𝑐[24]. The selections based on the quality of track fitting [24,28,29], in addition to the standard track quality criteria [24], were used to ensure that only well-reconstructed tracks were taken into account in the analysis. The quality of the track was determined by the 𝜒2∕𝑁value for the Kalman fit to the particle trajectory in the TPC, where N is the number of TPC clusters attached to the track [24]. The track was rejected if the value was larger than 4.0. Analysis specific event selection criteria were also applied. The event must have one accepted possible 𝜋±K0 Spair. To reduce the effects of mini-jets which tend to produce non-flat structures in the twoparticle correlation functions used in femtoscopy [30], a selection on the event transverse sphericity, calculated from the azimuthal distribution of tracks, was applied by requiring 𝑆T>0.7. 𝑆Tis a scalar quantity that takes values in the range 0 −1characterizing the event shape, i.e. 𝑆T∼0values represent elongated events that are “jet-like” and result from a single hard-scattering of partons, whereas 𝑆T∼1values represent spherical “non-jet-like” events resulting from many soft parton scatterings or several hard parton scatterings. See Ref. [30]for more details. Note that the 𝑆T>0.7selection is estimated to have <10% effect on the multiplicity of tracks entering the femtoscopy analysis since this selection tends to remove single hard-scattering events. Pileup events were rejected using the timing information from the V0 (for out of bunch pile-up) and multiple reconstructed vertices from tracks (or track segments in the Silicon Pixel Detector layers of the ITS) [29,30]. The possible effect due to remaining pile-up events passing the event selection criteria described above was investigated by performing the analysis using only low interaction-rate data-taking periods. No significant difference was found in the results of the analysis compared with the higher interaction-rate runs used. Both sets of runs were combined for the present analysis. Charged particles were identified with the central barrel detectors. Particle Identification (PID) for reconstructed tracks was carried out using both the TPC and Time-Of-Flight (TOF) detectors. For the TPC, the specific ionization energy loss d𝐸∕d𝑥was measured, and for the TOF, the flight time of the particle in the pseudorapidity range |𝜂| <0.9 was measured [29,31]. For the PID signal, a value (𝑁𝜎) was assigned to each track denoting the number of standard deviations between the measured PID signal and the expected values, assuming a mass hypothesis, divided by the detector resolution for both detectors [6,24,29,31]. A parametrized Bethe-Bloch formula [24]was used for the TPC PID to calculate the expected energy loss ⟨d𝐸∕d𝑥⟩in the detector for a particle with a given charge, mass, and momentum. The particle mass was used to calculate the expected time-of-flight as a function of track length and momentum for the TOF PID. The detailed description of the particle identification methods is given in Ref. [32]. For Monte Carlo (MC) calculations, particles from pp collisions simulated by the general-purpose generator PYTHIA8 [33]with the Monash 2013 tune [34]were transported through a GEANT3 [35]model of the ALICE detector. The total number of simulated pp collisions used in this analysis is 5 ×10 8. Physics Letters B 856 (2024) 138915 3 ALICE Collaboration Table 1 𝜋±and K0 Sselection criteria. Neutral kaon selection Value Daughter 𝑝T>0.15 GeV/𝑐 Daughter |𝜂|<0.8 Daughter DCA (3D) to primary vertex >0.4cm Daughter TPC PID [𝑁𝜎]<3 Daughter TOF PID [𝑁𝜎](for𝑝>0.8GeV/𝑐)<3 Kalman fit 𝜒2∕𝑁≤4 |𝜂|<0.8 DCA (3D) between daughters <0.3cm DCA (3D) to primary vertex <0.3cm Decay length (3D, lab frame) <30 cm Decay radius (2D, lab frame) >0.2cm Cosine of pointing angle >0.99 Invariant mass 0.485 <𝑚<0.510 GeV/𝑐2 Primary pion selection Value 𝑝T0.15 <𝑝 T<1.2GeV/𝑐 |𝜂|<0.8 Transverse DCA to primary vertex <2.4cm Longitudinal DCA to primary vertex <3.0cm TOF PID [𝑁𝜎] with valid TOF signal and 𝑝>0.5GeV/𝑐<2 TPC PID [𝑁𝜎] if no TOF signal for all 𝑝<2 Kalman fit 𝜒2∕𝑁≤4 The methods used to select and identify individual K0 Sand 𝜋±particles are similar to those used for the ALICE K±K0 Sanalysis in pp collisions at √𝑠=13TeV [7]. K0 Sare reconstructed from their decay into 𝜋+𝜋−, which has a branching ratio of 69% [20]. The neutral K0 Sdecay vertices and parameters are reconstructed and calculated from pairs of detected 𝜋+𝜋−tracks, and selected based on their invariant mass and the K0 Sdecay topology. The selection criteria for the K0 Sand the daughter pions are shown in Table 1. The selection criteria are based on decay topology, i.e. distance-ofclosest-approach (DCA) between charged pion daughters, DCA of daughter pion to the primary vertex, DCA of reconstructed K0 Sto the primary vertex, cosine of pointing angle, and decay length of K0 S, and were tuned to optimize purity and statistical significance. If two reconstructed K0 S particles share a daughter track, both are removed from the analysis. The MC samples were used to study any bias that might be induced by this procedure, which resulted in rejecting <1% of the K0 Scandidates [6,7]. Reconstructed K0 Scandidates within invariant mass range 0.485 <𝑚(𝜋+𝜋−) <0.510 GeV/𝑐2are used in this analysis which gives 98 ±1%purity of K0 S. The purity here is defined as signal/(signal + background). The signal and background counts are calculated by fitting a fourth-order polynomial to the side-bands of the signal region to estimate the background there and subtracting this from the invariant mass histogram. A Gaussian is used to fit the signal peak in the invariant mass distribution (see Fig. 2 of Ref. [6]). Primary charged pions are selected using the PID information from the TPC and TOF detectors. The TPC is used for PID in the full momentum range, except if a valid TOF signal is available for 𝑝 >0.5GeV/𝑐 then TOF PID is used. For more details, refer to Refs. [5,6]. Table 1 summarizes the criteria used for the charged pion selection. The average charged pion purity is found using MC simulations to be 98.1 ±0.1%, in agreement with the charged pion purity reported in Ref. [6]. Two-track effects, such as the merging of two real tracks into one reconstructed track and the splitting of one real track into two reconstructed tracks, are an important challenge for femtoscopic studies. A selection on the minimum separation distance between the primary pion and a daughter pion from the decay of the K0 Sin the 𝜋±K0 Spair was made from the corresponding TPC tracks using the same method as described in Ref. [7]. The distance between the two tracks was calculated in different positions along their trajectory in the TPC (at radial distances from 85 to 150 cm from the interaction point) and a minimum separation distance of 20 cm was required. 3. Measurement of correlation functions The momentum correlations of 𝜋±K0 Spairs using the two-particle correlation function are studied in this analysis. The correlation function is defined as 𝐶(𝑘∗) =𝐴(𝑘∗)∕𝐵(𝑘∗), where 𝐴(𝑘∗)is the measured distribution of pairs from the same event and 𝐵(𝑘∗)is the reference distribution of pairs from mixed events. The denominator 𝐵(𝑘∗)is formed by mixing particles from one event with particles from 10 different events that satisfy the conditions that the primary vertex positions along the beam direction are within 2 cm of each other, and have similar multiplicity, i.e. events within 2% difference in multiplicity percentile are mixed. Other sizes of the mixed events buffer were also investigated with no significant effect on the results of this work. All events used are required to satisfy the 𝑆T>0.7selection. The 𝑘∗is the magnitude of the momentum of each of the particles in the pair rest frame. In the present case of unequal mass particles in the pair, 𝑚1and 𝑚2, 𝑘∗is given by 𝑘∗=√ √ √ √𝑎2−𝑚2 1𝑚2 2 2𝑎+𝑚2 1+𝑚2 2 (1) where, 𝑎≡(𝑞2 inv +𝑚2 1+𝑚2 2)∕2.(2) For convenience, the square of the invariant momentum difference 𝑞2 inv =|𝑝1−𝑝2|2−|𝐸1−𝐸2|2is evaluated with the momenta and energies of the two particles measured in the laboratory frame. In the case where 𝑚1=𝑚2, 𝑘∗can be expressed as 𝑘∗=𝑞inv∕2. A 𝑘∗bin size of 20 MeV/𝑐 was used in the analyses presented in this Letter. Correlation functions are analyzed for three cases: 1) 0 − 100% multiplicity class and 𝑘𝑇>0GeV/𝑐, 2) 0 − 100% multiplicity class and 𝑘𝑇<0.5GeV/𝑐, and 3) 0 −5%multiplicity class and 𝑘𝑇<0.5GeV/𝑐, where 𝑘T=|𝑝T1 +𝑝T2|∕2, and where 𝑝T1 and 𝑝T2 are the transverse momenta of the particles in the pair. The three cases correspond to the following average 𝑘𝑇and average charged-particle pseudorapidity density (⟨𝑑𝑁∕𝑑𝜂⟩in the |𝜂| <0.8range) values [27]: 1) ⟨𝑘𝑇⟩=0.655 GeV/𝑐, ⟨𝑑𝑁∕𝑑𝜂⟩=6.89, 2) ⟨𝑘𝑇⟩=0.323 GeV/𝑐, ⟨𝑑𝑁∕𝑑𝜂⟩=6.89, and 3) ⟨𝑘𝑇⟩=0.326 GeV/𝑐, ⟨𝑑𝑁∕𝑑𝜂⟩= 21.2. The purpose of analyzing these Physics Letters B 856 (2024) 138915 4 ALICE Collaboration Fig. 1. Top row: 𝜋±K0 Scorrelation functions experimentally measured (blue dots) compared with PYTHIA8+GEANT3 simulations (red squares) obtained in pp collisions at √𝑠=13TeV for 0 − 100% multiplicity class and 𝑘𝑇>0(left), 0 − 100% multiplicity class and 𝑘T<0.5GeV/𝑐(center), and 0–5%multiplicity class and 𝑘T<0.5GeV/𝑐(right). The PYTHIA8+GEANT3 correlation function is normalized to the data at 𝑘∗=0.5GeV/c. Bottom row: Ratio of Data to PYTHIA8+GEANT3 simulations for the three studied cases. Statistical uncertainties are represented by bars. cases is to obtain different femtoscopic source sizes and to study the effect of source size on the FSI. It has been found from femtoscopy measurements in pp collisions that the source size depends on both ⟨𝑘𝑇⟩and ⟨𝑑𝑁∕𝑑𝜂⟩[4,36]. In addition, case 1) was chosen to maximize the sample size and to provide a selection-free case to compare with the other cases having multiplicity and 𝑘𝑇selections. Monte Carlo simulations were used to simulate correlation functions which were compared with experimental data. Fig. 1shows in the top row the correlation functions experimentally measured (blue) along with the simulated ones (red). The MC correlation functions are normalized to the experimental ones at 𝑘∗=0.5GeV/𝑐for the three cases mentioned above. The single-event and mixed-event distributions of the correlation functions are summed over 𝜋+K0 Sand 𝜋−K0 Spairs, since it is found that there is no significant difference between the 𝜋+K0 Sand 𝜋−K0 Scorresponding correlation functions. The decay of the K∗(892) meson is clearly seen at 𝑘∗∼0.3GeV/𝑐for all cases. For 𝑘∗>0.35 GeV/𝑐 a non-flat baseline is also observed in all cases. This non-flat baseline is associated with soft parton fragmentation, or mini-jets, that are not completely suppressed by the transverse sphericity selection [36–38], as well as the presence of momentum conservation effects. Non-flat baselines in two-particle correlation functions obtained in pp collisions are often observed [9,36,37]. In particular, measured correlation functions show a decreasing dependence of the baseline with increasing 𝑘∗for low multiplicity classes, and a reversal of this dependence for higher multiplicity classes, as seen in Fig. 1. This effect in the data is seen to be present as well in the PYTHIA8 simulations. The simulations well reproduce the K∗(892) peak and the background visible at larger 𝑘∗, hence in order to remove these two contributions, the measured correlation function is subsequently divided by the simulated one, defined as 𝐶′(𝑘∗), as shown in the bottom panels of Fig. 1. The statistical uncertainty from the MC correlation function is propagated with the uncertainty from the experimental one in the ratio, which becomes the final correlation function. Finite track momentum resolution can smear the relative momentum correlation functions used in this analysis. This effect is corrected using MC simulations as done in previous works [22,23]. It is found that the effect of the momentum resolution correction is small for the very lowest 𝑘∗bin with the largest statistical error bars and negligible for the rest of the bins, resulting in a <3% effect on the extracted fit parameters. 4. Fitting The momentum resolution corrected ratio of the experimental 𝜋±K0 S correlation function to the MC correlation function was fitted by a model in order to extract information on the size of the source, as well as the strength and nature of the FSI between the particles in the pair. The fit function is given by, 𝐶′(𝑘∗)=𝜅[𝐶Lednicky(𝑘∗)+𝜀𝑑𝑁𝐵𝑊 𝑑𝑚 𝑑𝑚 𝑑𝑘∗](3) where, 𝑑𝑁𝐵𝑊 𝑑𝑚 ∝Γ892 (𝑚−𝑚892)2+Γ 2 892∕4 (4) is the Breit–Wigner resonance distribution. This last term fits out any residual presence of the K∗(892) peak (see below). The quantities 𝜀and 𝜅, where 𝜀is the magnitude of a correction term on the MC modeling of the K∗(892) (see below) and 𝜅is an overall normalization factor, are fit parameters, and Γ892 and 𝑚892 are the fullwidth at half maximum (FWHM) and mass of the K∗(892), respectively, taken from the Review of Particle Physics [20]. The first term in Eq. (3) is a modified version of the Lednicky parametrization [2,39,40] which assumes that the pair interaction is due to strong final-state interaction of a near-threshold resonance. The second term in Eq. (3)is used to fit out the small residual bump in the ratio that results from a slight overcompensation of the MC in modeling the K∗(892) peak in the data that can be seen in Fig. 1, located at 𝑘∗∼0.3GeV/𝑐. Fitting out this residual bump results in an improved 𝜒2∕ndf for all of the fits. A Gaussian distribution of the source size in the pair reference frame is assumed in the FSI parameterization. More general forms for this distribution could be used, but using the Gaussian results in the analytic form of the Lednicky equation. Another motivation for staying with the Gaussian is to facilitate comparisons with previous published results that also used the Gaussian distribution. Physics Letters B 856 (2024) 138915 5 ALICE Collaboration Fig. 2. Example fit of Eq. (5)to the corrected correlation functions after Eq. (3)has been used to remove the PYTHIA8+GEANT3 overcompensation of the K∗(892), for 𝜋±K0 Sfrom √𝑠=13TeV pp collisions for 0 − 100% multiplicity class and 𝑘𝑇>0(left), 0 − 100% multiplicity class and 𝑘T<0.5GeV/𝑐(center), and 0–5%multiplicity class and 𝑘T<0.5GeV/𝑐(right). Statistical uncertainties are represented as bars. The quantity 𝐶Lednicky(𝑘∗)has the form 𝐶Lednicky(𝑘∗)=1+(𝜆𝛼 2)[|||| 𝑓(𝑘∗) 𝑅|||| 2 +4𝑓(𝑘∗) √𝜋𝑅 𝐹1(2𝑘∗𝑅) −2𝑓(𝑘∗) 𝑅𝐹2(2𝑘∗𝑅)+Δ𝐶](5) and 𝐹1(𝑧)= 𝑧 ∫ 0 𝑑𝑥𝑒𝑥2−𝑧2 𝑧;𝐹2(𝑧)= 1−𝑒−𝑧2 𝑧.(6) 𝛼is the symmetry parameter and is set to 0.5 assuming symmetry in K0and K0production since the K0 Sis a linear combination of these; 𝑅 is the radius parameter of the source; and 𝜆is the correlation strength. The term 𝑓(𝑘∗)is the s-wave 𝜋±K0 Sscattering amplitude whose FSI contribution is the near-threshold resonance. A relativistic Breit–Wigner amplitude is assumed, 𝑓(𝑘∗)= 𝛾 𝑀2 𝑅−𝑠−𝑖𝛾𝑘∗.(7) In Eq. (7), 𝑀𝑅is the mass of the resonance, and 𝛾is the coupling of the resonance to its decay channel, i.e. 𝜋±K0 S. Also, 𝑠 =( √𝑚2 K+𝑘∗2 + √𝑚2 𝜋+𝑘∗2)2is the square of the energy of the pair in its rest frame. A Breit–Wigner form was chosen for 𝑓(𝑘∗)since the fitted 𝑀𝑅and 𝛾to the FSI resonance from the present work will be compared with other measurements that used the Breit–Wigner form in order to identify the resonance [41,42]. The quantity Δ𝐶is a correction to the derivation of Eq. (5), that assumes spherical outgoing waves, to account for the true scattered waves in the inner region of the short-range potential [2,7], and is given by, Δ𝐶=(2 + 𝑚𝜋∕𝑚K+𝑚K∕𝑚𝜋) 2√𝜋𝑅3𝛾|𝑓(𝑘∗)|2.(8) As a test, a p-wave term was added to the s-wave term in the scattering amplitude in deriving the Lednicky equation to study whether there was interference of the K∗(892) with the s-wave FSI. It was found that the p-wave term had a negligible effect on the fits, and was thus ignored. The fitting strategy was to make a six-parameter fit of Eq. (3)to the corrected ratio of the experimental 𝜋±K0 Scorrelation function to the corresponding MC correlation function to extract 𝑅, 𝜆, 𝑀𝑅, 𝛾, 𝜀, and 𝜅. The nominal fit range is 0 <𝑘 ∗<0.76 GeV/𝑐in all cases. The nominal maximum of 0.76 GeV/𝑐of the fit range was set to give the optimal overlap between the experimental and MC correlation functions in the baseline region. Fig. 2shows the correlation functions and fits. The MC overcompensation of the K∗(892) has been removed from the “Data/MC” points by subtracting out the second term in Eq. (3)in order to show how well 𝐶Lednicky(𝑘∗)fits the ratio, and the ratio has been divided by 𝜅. The 𝜒2∕ndf for the fits shown in Fig. 2are 1.6, 1.8, and 0.92, with p-values of 1.7% and 0.36% and 60%, respectively. 5. Systematic uncertainties Table 2shows the total systematic uncertainties on the 𝑅, 𝜆𝑀 𝑅, and 𝛾parameters extracted from the 𝜋±K0 Scorrelation function in pp collisions at √𝑠=13TeV. The “fit systematic uncertainty” column reports the systematic uncertainty due to varying the 𝑘∗fit range. Varying the fit range by 20% resulted in <3% effect on the fit parameters. Fitting uncertainties were calculated including correlations among the fit parameters as done using a MINOS algorithm in order to obtain conservative estimates of the uncertainties [43]. The “selection systematic uncertainty” column reports the systematic uncertainty related to the variation of track and PID selection criteria used in the data analysis. To determine this, the single particle selection criteria shown in Table 1were varied by ±10%, and the value chosen for the minimum separation distance of same-sign tracks was varied by ±20%[7]. The systematic uncertainty related to the sphericity selection of 𝑆T>0.7is also included in this source of systematic uncertainty, where 𝑆Twas varied by ±10% from its nominal selection value. The uncertainty was estimated from the variation of the results with respect to those obtained with the nominal selections. The resulting relative systematic uncertainties are of about 10% for 𝜆, about 5% for 𝑅, and about 2% for the other parameters. The “total systematic uncertainty” column is obtained as the sum in quadrature of the contribution of the two sources described above. The “total uncertainty” column is the sum in quadrature of the statistical uncertainty and the total systematic uncertainty. As seen, the total systematic uncertainties tend to be greater than or comparable to the statistical uncertainties. Table 3shows an approximate breakdown of the relative systematic uncertainties (in percentage) from the different variations considered. See Table 1in Section 2for the nominal values of the selection criteria. Note that “min. sep. var.” refers to the variation of the selection for minimum separation between K0 Sdaughter and primary pions in the TPC, mentioned earlier, and “𝑚(𝜋+𝜋−)and primary vertex variations” refer to the combined effect of varying the invariant mass selection for K0 Sand varying the selection for the primary vertex of the event. As seen, in general the variations have the largest effect on 𝜆 and the smallest effect on 𝑀𝑅and 𝛾, with the 𝑆Tvariation having the largest single-variation effect on all of the parameters. 6. Results and discussion The 𝑅, 𝜆, 𝑀𝑅, and 𝛾parameters extracted from the present analysis of 𝜋±K0 Scorrelation functions in pp collisions at √𝑠=13TeV are reported in Table 2for the three cases mentioned above. The 𝜆parame- Physics Letters B 856 (2024) 138915 6 ALICE Collaboration Table 2 Fit results for R, 𝜆, 𝑀𝑅, and 𝛾showing statistical and systematic uncertainties from the present analysis. Uncertainties are symmetric unless specified otherwise. See the text for the description of the various sources of uncertainties. 𝑅,𝜆,𝑀𝑅,or𝛾fit value statistical uncertainty fit systematic uncertainty selection systematic uncertainty total systematic uncertainty total uncertainty 0 − 100% multiplicity class 𝑘𝑇>0 𝑅(fm) 0.912 0.037 0.011 0.053 0.054 0.065 𝜆0.0783 +0.0096 0.0032 0.0078 0.0084 +0.0127 -0.0086 -0.0121 𝑀𝑅(GeV/𝑐2) 0.833 0.002 0.006 0.013 0.015 0.015 𝛾(GeV) 0.890 0.015 0.012 0.016 0.020 0.025 0 − 100% multiplicity class 𝑘𝑇<0.5GeV/𝑐 𝑅(fm) 1.063 0.058 0.015 0.064 0.066 0.088 𝜆0.111 0.017 0.004 0.013 0.014 0.022 𝑀𝑅(GeV/𝑐2) 0.804 0.003 0.005 0.013 0.014 0.014 𝛾(GeV) 0.801 0.023 0.020 0.014 0.024 0.033 0−5% multiplicity class 𝑘𝑇<0.5GeV/𝑐 𝑅(fm) 1.618 +0.136 0.015 0.089 0.090 +0.163 -0.109 -0.142 𝜆0.274 +0.077 0.001 0.026 0.026 +0.081 -0.053 -0.059 𝑀𝑅(GeV/𝑐2) 0.765 0.004 0.002 0.012 0.013 0.013 𝛾(GeV) 0.714 +0.042 0.005 0.013 0.014 +0.044 -0.037 -0.039 Table 3 Breakdown of the relative systematic uncertainties for R, 𝜆, 𝑀𝑅, and 𝛾from the variation of track, PID and mixedevent selection criteria. The %Δ row is the percentage that the quantity was changed. See the text for the description of the various uncertainties. Quantity changed Fit range Min. sep. var. TOF, TPC 𝑁𝜎 DCA var. 𝑚(𝜋+𝜋−)and primary vertex var. Multiplicity difference for event mixing Decay length 𝑆Tvar. %Δ 20 20 10 10 10 10 10 10 %𝑅11221 1 13 %𝜆35333 2 25 %𝑀𝑅1<1<1<1<1<1<12 %𝛾21 <1<1<1<1<12 ters are corrected for purity by dividing the extracted 𝜆values with the product of the 𝜋±and K0 Spurities (see Section 2). Since the main goal of this measurement is to study the K∗ 0(700) resonance, one must first establish that the FSI of the 𝜋±K0 Spair occurs indeed through this resonance. This can be done by comparing the measured 𝑀𝑅and 𝛾parameters extracted from this analysis with previously measured values of 𝑀𝑅and Γ𝑅for the K∗ 0(700) [41,42], where Γ𝑅is the FWHM of the relativistic Breit–Wigner resonance distribution, whose amplitude is expressed as [44], 𝑓(𝑠)∼ 1 𝑀2 𝑅−𝑠−𝑖𝑀𝑅Γ𝑅 .(9) Comparing this denominator with the denominator of Eq. (7), one can obtain an estimate for Γ𝑅from the present results, Γ𝑅=⟨𝑘∗⟩𝛾 𝑀𝑅 ,(10) where ⟨𝑘∗⟩is the average of 𝑘∗determined by weighting 𝑘∗by the experimental 𝑑𝑁∕𝑑𝑘∗distribution over the fit range used in fitting Eq. (3) to the correlation function. Table 4lists the values of Γ𝑅extracted from the present work using Eq. (10)for the three cases studied. The uncertainties shown for ⟨𝑘∗⟩are estimated by considering different 𝑘∗ranges Table 4 The ⟨𝑘∗⟩and corresponding Γ𝑅extracted from the three cases measured in the present work using Eq. (10). Case ⟨𝑘∗⟩(GeV/𝑐)Γ𝑅(GeV/𝑐2) 0 − 100% multiplicity class, 𝑘𝑇>00.403+0.093 −0.056 0.430+0.088 −0.053 0 − 100% multiplicity class, 𝑘𝑇<0.5GeV/𝑐0.408+0.060 −0.050 0.406+0.050 −0.042 0 – 5% multiplicity class, 𝑘𝑇<0.5GeV/𝑐0.418+0.072 −0.053 0.390+0.068 −0.051 for calculating the average, namely 0 <𝑘 ∗<0.6GeV/𝑐and 0 <𝑘 ∗<2 GeV/𝑐, and taking the differences from the nominal ⟨𝑘∗⟩to obtain conservative estimates of the uncertainties. Fig. 3compares the values of 𝑀𝑅and Γ𝑅extracted in the present work with measurements of these quantities for the K∗ 0(700) from the BES [41]and E791 Collaborations [42]. The BES Collaboration measured the relativistic Breit–Wigner parameters of the K∗ 0(700) through the decay of the J/𝜓meson, whereas the E791 Collaboration measured them through the decay of the D+meson. The total uncertainties defined as the quadratic sum of the statistical and systematic uncertainties are shown on the points for all cases. As seen, the values reported in this work agree within uncertainties with the K∗ 0(700) Breit–Wigner param- Physics Letters B 856 (2024) 138915 7 ALICE Collaboration Fig. 3. The extracted Breit–Wigner parameters from the 𝜋±K0 Sfemtoscopic correlation in pp collisions at √𝑠=13TeV compared with those for K∗ 0(700) from the BES [41]and the E791 [42] experiments. The horizontal and vertical bars represent the total uncertainties. The “ALICE average” value is the weighted average of the three ALICE points. Fig. 4. The 𝜆parameter as a function of source size 𝑅extracted from the 𝜋±K0 S femtoscopy measurement in pp collisions at √𝑠=13TeV. Results are compared with the previous ALICE measurements, obtained from K0 SK0 S[6,7]and 𝜋𝜋 [36] femtoscopy studies in pp and Pb–Pb collisions and the calculations from a toy geometric model (see text). The model calculations for the tetraquark and diquark hypotheses for the K∗ 0(700) are shown as black and light green dashed lines, respectively, the short dashed lines representing the Gaussian 𝜌(𝑟)and the long dashed lines representing the exponential 𝜌(𝑟). eters measured in the other two experiments. It is seen that the present results have smaller uncertainties than the previous measurements. It is also seen that although the three Γ𝑅values from the present work agree within uncertainties, the differences among the three 𝑀𝑅values are outside of their uncertainties. This could be a consequence of using the Breit–Wigner function to fit a resonance where the condition Γ𝑅≪𝑀 𝑅is not fulfilled, which can lead to kinematic dependences on the extracted 𝑀𝑅and Γ𝑅[20,44]. However, these differences in 𝑀𝑅 are small compared with the extracted 𝑀𝑅values, and thus it is judged that these results strongly support the assumption that the resonance responsible for the FSI of the 𝜋±K0 Spairs studied in the present work is the K∗ 0(700) resonance. The extracted 𝑅and 𝜆parameters shown in Table 2can be used to obtain information about the quark configuration of the K∗ 0(700). Fig. 4 compares the values of 𝑅and 𝜆extracted in the present work with published results for these parameters from ALICE measurements in pp and Pb–Pb collisions in which 𝜋𝜋 and K0 SK0 Spairs were analyzed [4,6,7,36]. The 𝜋±K0 Sresults are shown with separate statistical (error bars) and systematic (boxes) uncertainties, whereas for the previous results, the error bars represent the combination of the statistical and systematic uncertainties. For the 𝜋𝜋 femtoscopic measurements in pp collisions at √𝑠=7TeV reported in [36]with average 𝑘Tvalues of ∼0.15 and ∼0.35 GeV/𝑐, the 𝜆values are given as varying in the range 0.42 −0.55, so 𝜆 is plotted as the center of this range with uncertainties extending to the upper and lower limits of the range. For the 𝑅parameter, the values from the present 𝜋±K0 Sanalysis are comparable with the published 𝜋𝜋 and K0 SK0 Smeasurements in pp collisions, i.e. in the range 1–2 fm, as would be expected from pp collisions where the source size is ∼1fm. For the 𝜆parameter, whereas the results from 𝜋𝜋 and K0 SK0 Sare compatible with values of about 0.5or greater, for the present 𝜋±K0 Sanalysis significantly lower values are obtained, ranging from about 0.05 to about 0.25 depending on 𝑅. The expectation is that 𝜆would be the same for 𝜋±K0 Sas for the identical-meson measurements. The 𝜆value of ∼0.5has been shown to be due to the presence of long-lived resonances whose decay into the detected mesons impacts the measurement of the “direct” mesons coming from the source of interest [7,45]. Another significant difference between the present 𝜋±K0 S results and the 𝜋𝜋 and K0 SK0 Sresults is that 𝜆has a strong 𝑅dependence for the former, whereas there is no significant dependence of 𝜆on 𝑅 for the latter, i.e. even extending 𝑅to the value from Pb–Pb collisions shows no significant effect on 𝜆. As discussed in Refs. [7] and [9], a physics effect that could cause this difference in 𝜆values for 𝜋±K0 Spairs is related to the possibility that the K∗ 0(700) resonance, that is assumed to be solely responsible for the FSI in the 𝜋±K0 Spair, is actually a tetraquark state of the form (q1, q2, q3, q3), in which q1, q2and q3indicate the flavor of the valence quarks of the 𝜋and K0 S. In particular, q1and q2can be a u or s quark, while q3is a d quark. For example, the quark content of a tetraquark K∗ 0(700)+ would be usdd, whereas the diquark version would be us. The strength of the FSI through a tetraquark K∗ 0(700)+could be decreased by the small source size of the 𝜋±K0 Ssource, i.e. at 𝑅 ∼1fm as is measured in these collisions. This could occur since d−d annihilation would be enhanced due to the proximity of the 𝜋±and K0 Sat their creation, which would open up a non-resonant channel in the scattering process that would be reflected by reducing 𝜆. For a FSI through a diquark K∗ 0(700)+, with the form us, the small source geometry should not reduce its strength. For the K0 SK0 Sand 𝜋𝜋 cases, 𝜆should not be affected by the source size since the pair correlation is dominated by the effect of quantum statistics, for which in the ideal case 𝜆does not depend on 𝑅, and which is found to be much stronger than the strong FSI present for these identical particle pairs [2]. In order to demonstrate the 𝑅dependence of 𝜆for a tetraquark or a diquark K∗ 0(700) based on the geometric considerations discussed above, a simple toy model is constructed, taking the form of the 𝜆factor for a tetraquark state, 𝜆=𝜆0(1 − 𝑎𝑃 )(11) and for a diquark, 𝜆=𝜆0𝑎𝑃 (12) where, 𝑃≡∫𝜌(𝑟)𝜌(|𝑟 − 𝑅|)𝑑𝑉 ∫|𝜌(𝑟)|2𝑑𝑉 (13) can be considered the “overlap probability” between the 𝜋and K0 Sin the pair as they are emitted from the pp collision. The quantity 𝜌(𝑟)is the meson volume distribution, assumed to be the same for the 𝜋and K0 S, 𝜆0 is the maximum value for 𝜆, and 𝑎is essentially the “d−d annihilation efficiency” that in principle could take any value in the range 0 −1. Assuming 𝜌(𝑟) ∼𝑒−𝑟2∕(2𝜎2)or ∼𝑒−𝑟∕𝑟0, 𝜆0=0.6, the average value for 𝜋𝜋 and K0 SK0 Smeasurements from Refs. [36]and [6,7], and assuming 100% d−d annihilation efficiency for any non-zero overlap, 𝑎 =1, the free parameters of the model, i.e. 𝜎and 𝑟0, are adjusted to give a good fit to the 𝜋±K0 Smeasurements. The results from Eqs. (11) and (12)are shown in Fig. 4, along with the results from 𝜋±K0 Smeasurements of this work and Physics Letters B 856 (2024) 138915 8 ALICE Collaboration published ALICE measurements for K0 SK0 S[6,7]and 𝜋𝜋 pairs [36]from pp and Pb–Pb collisions. The free model parameters are set to 𝜎=1.1fm and 𝑟0=0.85 fm for the Gaussian (short dashed lines) and exponential (long dashed lines) distributions, respectively, which are considered reasonable values since hadronic sizes are expected to be ∼1fm. As seen, using reasonable model parameter values, the tetraquark case, Eq. (11), describes the 𝑅dependence of 𝜆from the present measurements well for both the Gaussian and exponential meson shapes as being a geometric effect. The diquark case is seen to predict an 𝑅dependence that is incompatible with the measured one. Therefore, the present results of 𝜋±K0 Sfemtoscopy in pp collisions at √𝑠=13TeV suggest that the K∗ 0(700) is a tetraquark state. 7. Summary Femtoscopic correlations with the particle pair combination 𝜋±K0 S are studied in pp collisions at √𝑠=13TeV for the first time by the ALICE experiment at the LHC. Source parameters and final-state interaction parameters are extracted by fitting a model based on a Gaussian distribution of the source to the experimental two-particle correlation functions. The model used assumes that solely the final-state interaction through a resonance determines the correlations, and is defined in terms of a mass and the coupling parameter to the decay into a 𝜋±K0 Spair. The extracted mass and width parameters of the FSI are consistent with previous measurements of the K∗ 0(700) resonance, and the smaller value and increasing behavior of the 𝜆parameter with 𝑅compared with identical boson measurements give support that the K∗ 0(700) is a four-quark state, i.e. a tetraquark state [19]. A simple geometric model that assumes a tetraquark FSI describes well the 𝑅dependence of 𝜆extracted from the measured correlation functions. Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Data availability This manuscript has associated data in a HEPData repository at: https://www .hepdata .net /record /ins2739149. Acknowledgements The ALICE Collaboration would like to thank all its engineers and technicians for their invaluable contributions to the construction of the experiment and the CERN accelerator teams for the outstanding performance of the LHC complex. The ALICE Collaboration gratefully acknowledges the resources and support provided by all Grid centres and the Worldwide LHC Computing Grid (WLCG) collaboration. The ALICE Collaboration acknowledges the following funding agencies for their support in building and running the ALICE detector: A. I. Alikhanyan National Science Laboratory (Yerevan Physics Institute) Foundation (ANSL), State Committee of Science and World Federation of Scientists (WFS), Armenia; Austrian Academy of Sciences, Austrian Science Fund (FWF): [M 2467-N36] and Nationalstiftung für Forschung, Technologie und Entwicklung, Austria; Ministry of Communications and High Technologies, National Nuclear Research Center, Azerbaijan; Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Financiadora de Estudos e Projetos (Finep), Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) and Universidade Federal do Rio Grande do Sul (UFRGS), Brazil; Bulgarian Ministry of Education and Science, within the National Roadmap for Research Infrastructures 20202027 (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; The Ministry of Education, Youth and Sports of the Czech Republic, Czech Republic; The Danish Council for Independent Research | Natural Sciences, the Villum Fonden and Danish National Research Foundation (DNRF), Denmark; Helsinki Institute of Physics (HIP), Finland; Commissariat à l’Énergie Atomique (CEA) and Institut National de Physique Nucléaire et de Physique des Particules (IN2P3) and Centre National de la Recherche Scientifique (CNRS), France; Bundesministerium für Bildung und Forschung (BMBF) and GSI Helmholtzzentrum für Schwerionenforschung GmbH, Germany; General Secretariat for Research and Technology, Ministry of Education, Research and Religions, Greece; National Research, Development and Innovation Office, Hungary; Department of Atomic Energy, Government of India (DAE), Department of Science and Technology, Government of India (DST), University Grants Commission, Government of India (UGC) and Council of Scientific and Industrial Research (CSIR), India; National Research and Innovation Agency - BRIN, Indonesia; Istituto Nazionale di Fisica Nucleare (INFN), Italy; Japanese Ministry of Education, Culture, Sports, Science and Technology (MEXT) and Japan Society for the Promotion of Science (JSPS) KAKENHI, Japan; Consejo Nacional de Ciencia (CONACYT) y Tecnología, through Fondo de Cooperación Internacional en Ciencia y Tecnología (FONCICYT) and Dirección General de Asuntos del Personal Académico (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 and 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. In addition, individual groups or members have received support from: Czech Science Foundation (grant no. 23-07499S), Czech Republic; European Research Council, Strong 2020 - Horizon 2020 (grant nos. 950692, 824093), European Union; ICSC -Centro Nazionale di Ricerca in High Performance Computing, Big Data and Quantum Computing, European Union - NextGenerationEU; Academy of Finland (Center of Excellence in Quark Matter) (grant nos. 346327, 346328), Finland. References [1] M.A. Lisa, S. Pratt, R. Soltz, U. Wiedemann, Femtoscopy in relativistic heavy ion collisions, Annu. Rev. Nucl. Part. Sci. 55 (2005) 357–402, arXiv :nucl -ex /0505014 [nucl -ex]. [2] STAR Collaboration, B.I. Abelev, et al., Neutral kaon interferometry in Au+Au collisions at √𝑠NN = 200 GeV, Phys. Rev. C 74 (2006) 054902, arXiv :nucl -ex /0608012 [nucl -ex]. [3] PHENIX Collaboration, A. Adare, et al., Systematic study of charged-pion and kaon femtoscopy in Au + Au collisions at √𝑠𝑁𝑁 =200 GeV, Phys. Rev. C 92 (2015) 034914, arXiv :1504 .05168 [nucl -ex]. [4] ALICE Collaboration, B. Abelev, et al., K0 s−K0 scorrelations in pp collisions at √𝑠=7 TeV from the LHC ALICE experiment, Phys. Lett. B 717 (2012) 151–161, arXiv :1206 . 2056 [hep -ex]. Physics Letters B 856 (2024) 138915 15 ALICE Collaboration 96 Physik Department, Technische Universität München, Munich, Germany 97 Politecnico di Bari and Sezione INFN, Bari, Italy 98 Research Division and ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum für Schwerionenforschung GmbH, Darmstadt, Germany 99 Saga University, Saga, Japan 100 Saha Institute of Nuclear Physics, Homi Bhabha National Institute, Kolkata, India 101 School of Physics and Astronomy, University of Birmingham, Birmingham, United Kingdom 102 Sección Física, Departamento de Ciencias, Pontificia Universidad Católica del Perú, Lima, Peru 103 Stefan Meyer Institut für Subatomare Physik (SMI), Vienna, Austria 104 SUBATECH, IMT Atlantique, Nantes Université, CNRS-IN2P3, Nantes, France 105 Sungkyunkwan University, Suwon City, Republic of Korea 106 Suranaree University of Technology, Nakhon Ratchasima, Thailand 107 Technical University of Košice, Košice, Slovak Republic 108 The Henryk Niewodniczanski Institute of Nuclear Physics, Polish Academy of Sciences, Cracow, Poland 109 The University of Texas at Austin, Austin, TX, United States 110 Universidad Autónoma de Sinaloa, Culiacán, Mexico 111 Universidade de São Paulo (USP), São Paulo, Brazil 112 Universidade Estadual de Campinas (UNICAMP), Campinas, Brazil 113 Universidade Federal do ABC, Santo Andre, Brazil 114 Universitatea Nationala de Stiinta si Tehnologie Politehnica Bucuresti, Bucharest, Romania 115 University of Cape Town, Cape Town, South Africa 116 University of Derby, Derby, United Kingdom 117 University of Houston, Houston, TX, United States 118 University of Jyväskylä, Jyväskylä, Finland 119 University of Kansas, Lawrence, KS, United States 120 University of Liverpool, Liverpool, United Kingdom 121 University of Science and Technology of China, Hefei, China 122 University of South-Eastern Norway, Kongsberg, Norway 123 University of Tennessee, Knoxville, TN, United States 124 University of the Witwatersrand, Johannesburg, South Africa 125 University of Tokyo, Tokyo, Japan 126 University of Tsukuba, Tsukuba, Japan 127 Universität Münster, Institut für Kernphysik, Münster, Germany 128 Université Clermont Auvergne, CNRS/IN2P3, LPC, Clermont-Ferrand, France 129 Université de Lyon, CNRS/IN2P3, Institut de Physique des 2 Infinis de Lyon, Lyon, France 130 Université de Strasbourg, CNRS, IPHC UMR 7178, F-67000 Strasbourg, France 131 Université Paris-Saclay, Centre d’Etudes de Saclay (CEA), IRFU, Départment de Physique Nucléaire (DPhN), Saclay, France 132 Université Paris-Saclay, CNRS/IN2P3, IJCLab, Orsay, France 133 Università degli Studi di Foggia, Foggia, Italy 134 Università del Piemonte Orientale, Vercelli, Italy 135 Università di Brescia, Brescia, Italy 136 Variable Energy Cyclotron Centre, Homi Bhabha National Institute, Kolkata, India 137 Warsaw University of Technology, Warsaw, Poland 138 Wayne State University, Detroit, MI, United States 139 Yale University, New Haven, CT, United States 140 Yonsei University, Seoul, Republic of Korea 141 Zentrum für Technologie und Transfer (ZTT), Worms, Germany 142 Affiliated with an institute covered by a cooperation agreement with CERN 143 Affiliated with an international laboratory covered by a cooperation agreement with CERN IDeceased. II Also at: Max-Planck-Institut fur Physik, Munich, Germany. III Also at: Italian National Agency for New Technologies, Energy and Sustainable Economic Development (ENEA), Bologna, Italy. IV Also at: Dipartimento DET del Politecnico di Torino, Turin, Italy. VAlso at: Yildiz Technical University, Istanbul, Türkiye. VI Also at: Department of Applied Physics, Aligarh Muslim University, Aligarh, India. VII Also at: Institute of Theoretical Physics, University of Wroclaw, Poland. VIII Also at: An institution covered by a cooperation agreement with CERN.