General balance functions of identified charged hadron pairs of (π,K,p) in Pb–Pb collisions at √sNN = 2.76 TeV

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/ General balance functions of identified charged hadron pairs of (π,K,p) in Pb–Pb collisions at √sNN = 2.76 TeV © 2022 European Organization for Nuclear Research, ALICE. Published by Elsevier B.V. Published version ALICE Collaboration ALICE Collaboration. (2022). General balance functions of identified charged hadron pairs of (π,K,p) in Pb–Pb collisions at √sNN = 2.76 TeV. Physics Letters B, 833, Article 137338. https://doi.org/10.1016/j.physletb.2022.137338 2022 Physics Letters B 833 (2022) 137338 Contents lists available at ScienceDirect Physics Letters B www.elsevier.com/locate/physletb General balance functions of identified charged hadron pairs of (π, K, p)in Pb–Pb collisions at √sNN =2.76 TeV .ALICE Collaboration a r t i c l e i n f o a b s t r a c t Article history: Received 28 October 2021 Received in revised form 9 May 2022 Accepted 18 July 2022 Available online 21 July 2022 Editor: M. Pierini First measurements of balance functions (BFs) of all combinations of identified charged hadron (π, K, p) pairs in Pb–Pb collisions at √sNN =2.76 TeV recorded by the ALICE detector are presented. The BF measurements are carried out as two-dimensional differential correlators versus the relative rapidity (y) and azimuthal angle (ϕ) of hadron pairs, and studied as a function of collision centrality. The ϕ dependence of BFs is expected to be sensitive to the light quark diffusivity in the quark–gluon plasma. While the BF azimuthal widths of all pairs substantially decrease from peripheral to central collisions, the longitudinal widths exhibit mixed behaviors: BFs of ππ and cross-species pairs narrow significantly in more central collisions, whereas those of KK and pp are found to be independent of collision centrality. This dichotomy is qualitatively consistent with the presence of strong radial flow effects and the existence of two stages of quark production in relativistic heavy-ion collisions. Finally, the first measurements of the collision centrality evolution of BF integrals are presented, with the observation that charge balancing fractions are nearly independent of collision centrality in Pb–Pb collisions. Overall, the results presented provide new and challenging constraints for theoretical models of hadron production and transport in relativistic heavy-ion collisions. ©2022 European Organization for Nuclear Research, ALICE. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP3. Convincing evidence for the production of strongly interacting quark–gluon plasma (QGP) in heavy-ion (AA) collisions has been reported from a variety of measurements at the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC) [1–4], including observations of strong elliptic flow [5–7], suppression of high transverse momentum (pT) hadron production [8–13], suppression of quarkonium states [14–19], as well as dihadron correlation functions [20,21]. Many of these findings are quantitatively explained by hydrodynamic calculations in which the QGP matter undergoes radial and azimuthally anisotropic collective motion. The existence of the latter is well established based on measurements of flow coefficients with finite pseudorapidity (η) gap and multi-particle cumulants, whereas the presence of the former is inferred in part from the increase of average transverse momenta with the mass of hadrons [22], the centrality dependence of eventby-event pTfluctuations [23,24], as well as the observed narrowing of the near-side peak of balance functions (BFs) in central collisions relative to that observed in peripheral collisions [25–30]. Balance functions essentially amount to differences of correlation functions of like-sign and unlike-sign charges. They are measured, typically, as functions of particle pair separation in azimuth angle and rapidity. They indicate the degree to which the production of a positive charge is accompanied by the production of a neg- E-mail address: alice -publications @cern .ch. ative charge somewhere in phase space. As such, BFs probe the balancing of charge distributions in momentum space and theoretical studies show they are sensitive to the details of the time (i.e., whether particles are produced early or late), production mechanisms, and transport of balancing charges. Measurements of BFs were originally proposed as a tool to investigate the delayed hadronization and two stages of quark production in the QGP formed in AA collisions [31]. These terms refer to the notion that quark production occurs in two distinct stages, the first at the onset, and the second at the very end (just before hadronization and freeze-out) of AA collisions. The two stages are posited to be separated by a period of isentropic expansion whose duration depends on the multiplicity of produced quarks and gluons and thus the collision impact parameter. Hadron pairs produced at the onset of collisions feature large longitudinal separation (i.e., rapidity differences y) whereas pairs produced after the expansion have smaller yseparations determined by the smaller temperature of the system at that time. AA collisions with smaller impact parameters are expected to produce larger systems with a longer isentropic stage in which late particle production dominates. The longitudinal and azimuthal widths of BFs are thus expected to progressively decrease from peripheral to central collisions as the fraction of late particle production increases. BFs could also provide a precise probe of balancing particle production [32–35], the hadrochemistry of particle production [34,36], as well as the collision dynamics [37,38]. Recent studies also indicate https://doi.org/10.1016/j.physletb.2022.137338 0370-2693/©2022 European Organization for Nuclear Research, ALICE. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP3. ALICE Collaboration Physics Letters B 833 (2022) 137338 that the BF dependence on pair separation in azimuth is sensitive to the diffusivity of light quarks, a measure of the diffusion and scattering of quarks within the QGP, which has thus far received only limited attention [36,39]. Finally, BFs also provide a tool to calibrate measurements of the Chiral Magnetic Effect [40,41] and net charge/baryon fluctuations deemed essential for the determination of QGP susceptibilities [42,43]. Few measurements of BFs of identified hadrons have been reported to date. At RHIC, these include BF measurements of charged hadrons, pion pairs, kaon pairs, as well as proton/antiproton pairs [25–27], whereas at the LHC, only charged hadron BFs have been reported [28,29]. Of these, only the results published by ALICE were fully corrected for detector acceptance and particle losses (efficiency). Integrals of measured BFs have not been considered and no cross-species BFs have been published. Theoretical analyses of measured BFs have consequently focused mainly on the interpretation of the narrowing with collision centrality of charged hadron BFs. The full potential of BFs as a probe of the evolution dynamics and chemistry of the QGP has thus so far been underexploited. In this paper, general balance functions of identified charged hadron species (π, K, p)are reported for the first time. These general BFs are corrected for efficiency and non uniform acceptance effects and it becomes possible to study the effects of two-stage quark production, light quark diffusivity, and relative balancing fractions using BFs of nine distinct identified pairs of charged hadron species. The BF of a species of interest, α, and an associated species, β, was originally defined in terms of conditional densities [31]but it is convenient to compute BFs in terms of normalized cumulants R2according to Bαβ( pα, pβ) =1 2ρβ− 1( pβ−)Rα+β− 2( pα+, pβ−)−Rα−β− 2( pα−, pβ−) +ρβ+ 1( pβ+)Rα−β+ 2( pα−, pβ+)−Rα+β+ 2( pα+, pβ+),(1) with Rαβ 2( pα, pβ)≡ραβ 2( pα, pβ) ρα 1( pα)ρβ 1( pβ)−1(2) where ρα 1( pα) ≡dN/d pαand ραβ 2( pα,  pβ) ≡dNpair/d pαd pβare singleand particle-pair densities of species αand βmeasured at momenta  pαand  pβ, respectively, while labels +and −stand for positive and negative charges. Normalized cumulants R2are robust observables, i.e., independent to first order of measurement efficiencies. They are sensitive to the strength of correlation between species αand β. Their properties were described in several publications [44–47]. The combination of R2correlation functions, normalized by single particle densities, as per Eq. (1), is strictly equivalent to the balance function introduced in Ref. [31,32] and measures the correlation between positive and negative particles of species αand βconstrained by charge conservation. Integrals of inclusive charge balance functions, I+− B() ≡B+−dη, are expected to lie within the range 0 <I+− B() ≤1for limited acceptances . However, they converge to unity for full acceptance coverage. Furthermore, fractions Iαβ B()/Iα B()are determined by the hadrochemistry of the QGP and transport properties of the medium. In the full acceptance coverage limit, the denominator of this fraction must satisfy Iα B() ≡βIαβ B() →1[43]. In this paper, the identified particle BFs of nine pairs of charged hadrons (π±, K±and p/p) ⊗(π±, K±, and p/p) are reported as joint functions of the relative rapidity (y) and azimuthal angle (ϕ) and studied as a function of collision centrality. Measurements of Rαβ 2( pα,  pβ)are carried out in terms of the rapidity and azimuthal angle yα, ϕα, yβ, and ϕβfor fixed pTranges, and averaged across the pair acceptance to yield correlation functions Rαβ 2(y, ϕ)with y =yα−yβand ϕ=ϕα−ϕβfollowing the procedure used in Ref. [44]. The densities of associated particles, ρβ 1, used in Eq. (1), are integrated from pT-dependent densities reported in prior ALICE measurements [22]to match the pT ranges used in measurements of the normalized cumulants R2. The correlators Rαβ 2and densities ρβ 1are corrected for pT-dependent particle losses and non uniform acceptance. Densities ρβ 1were additionally corrected for minor contamination effects as per the procedure described in [22]. The measured BFs thus feature absolute normalization which enables meaningful determination of their integrals and collision centrality dependence. As already mentioned, the shape of the BFs vs. yand ϕis sensitive to the timescales at which particles are produced during the system evolution. Early emission occurs at large effective collisional energy √sand is thus expected to yield broad BFs in yand ϕ, whereas late emission, at collisional energy commensurate with the system temperature, is expected to produce much narrower near side peak correlations vs. yand ϕ[31]. Additionally, the integral of the BFs shall also provide increased sensitivity to the hadrochemistry of the collisions. Indeed whereas contributions to single-particle spectra from hadronic resonance decays must be inferred from models, integrals of the BFs are directly sensitive to the magnitude of (hadronic) feeddown contributions. For instance, by comparing the integrals of π+π−and π±K∓BFs, sensitivity to the relative strengths of processes that lead to such correlated pairs of particles is acquired. It becomes possible to better probe the role of hadronic resonance decay contributions and increased sensitivity to the hadrochemistry of the QGP and its susceptibilities is gained [36]. The BFs presented are based on 1 ×107minimum bias (MB) Pb–Pb collisions at √sNN = 2.76 TeV collected in 2010 by the ALICE collaboration. Descriptions of the ALICE detector and its performance have been reported elsewhere [48,49]. The minimum bias trigger required a combination of hits in the V0 detectors and layers of the SPD detector. The V0 detectors, which cover the full azimuth and the pseudorapidity ranges −3.7 <η<−1.7 and 2.8 <η<5.1, also provided a measurement of the charged particle multiplicity used to classify collisions into centrality classes corresponding to 0–5% (most central) to 80–90% (most peripheral) of the Pb–Pb hadronic cross section [50]. Some centrality classes have been combined to optimize the statistical accuracy of the BFs reported. Particle momenta were determined based on Kalman fits of charged particle tracks reconstructed in the Time Projection Chamber (TPC). The particle identification (PID) of charged hadrons was performed based on specific energy loss (dE/dx) measured in the TPC and particle velocities measured in the Time-of-Flight detector (TOF). Track quality criteria based on the number of space points, the distance of closest approach to the collision primary vertex, and the χ2of the Kalman fits were used to restrict the measurements to primary particles produced by the Pb–Pb collisions and suppress contamination from tracks resulting from weak decays and interactions of particles with the apparatus. Additionally, PID selection criteria based on deviations of dE/dxand TOF from their respective expectation values, at a given momentum, and for each species of interest, were used to optimize the species purity. These and other selection criteria are reported in detail below in the context of a discussion of systematic uncertainties. The analysis focused on the low pTrange, commonly known as the “bulk” physics regime. Slightly different pTranges were used for each species to optimize yields and species purity. Charged pions and kaons were selected in the range 0.2 ≤pT≤2.0GeV/c, whereas (anti-)protons are within 0.5 ≤pT≤2.5GeV/c. The selected rapidity range, largely determined by the TOF coverage, was 2 ALICE Collaboration Physics Letters B 833 (2022) 137338 Fig. 1. Balance functions Bαβ(y,ϕ)of pairs αβ=ππ (left), KK (center), and pp (right) measured in semicentral Pb–Pb collisions at √sNN =2.76 TeV. set to |yπ| ≤0.8 and |yp| ≤0.6for measurements of Bππ and Bpp, respectively, and set to |y| ≤0.7for all other BFs reported. Track reconstruction efficiencies and PID purity were studied with Monte Carlo simulations of Pb–Pb collisions produced with the HIJING generator [51] and propagated through a model of the ALICE detector with GEANT3 [52]. Selected track quality and PID criteria yield purities of 97%, 95%, and 94% for π±, K±, and p/p, respectively, thereby minimizing species contamination and its impact on correlation functions. Corrections for track losses were carried out using a weighting technique [46]. Weights are calculated independently for positive and negative tracks of each species considered, for each centrality range, both magnetic field polarities used in the measurements, versus y, ϕ, pT, as well as the longitudinal position of the primary vertex (PV) of each event, zvtx. Various selection criteria were applied to minimize residual instrumental effects while optimizing particle yields. The PV is required to be in the range |zvtx| ≤6cm of the nominal interaction point. Tracks are required to have a minimum of 70 reconstructed TPC space points (hits), out of a maximum of 159, and a track fit with χ2value per degree of freedom smaller than 2.0 to ensure good track quality. Contamination of BFs by secondary particles (i.e., weak decays or particles scattered within the detector) is suppressed by requiring distances of closest approach (DCA) to PV chosen as DCAz≤2.0cm in the longitudinal direction and DCAxy ≤0.04, 0.04, 2.0cm in the transverse plane for π±, p/p, and K±, respectively. Contamination by e+e−pairs from photon conversion is suppressed by removing tracks closer than 1σdE/dx to the TPC Bethe-Bloch median, at a given momentum, for electrons. Systematic uncertainties on the amplitudes of Bα,β and their integrals were calculated as quadratic sums of systematic uncertainties of the correlation function Rα,β 2and the systematic uncertainties on the published single particle densities [22]used in the computation of the BFs. Uncertainties on Rα,β 2were assessed based on variations of conditions and selection parameters employed in the analysis. A statistical test [53]was used to identify potential biases introduced by those variations and determine their statistical significance. Systematic uncertainties, corresponding to a relative deviation at the maximum of Bα,β associated with operation with two solenoidal magnetic field polarities, are smaller than 4%. Potential biases associated with track selection criteria are up to 3%, whereas the presence of misidentified and secondary particles contribute up to 4%, while kinematic dependencies of the detection efficiency are estimated to be 1%. Systematic uncertainties on the single particle densities [22]are species and collision centrality dependent and typically range from 5 to 10%. In order to obtain BF for all nine combinations of π±, K±, and p/pspecies pairs, Rαβ 2(y, ϕ)correlators were first measured, in each centrality class, for all 36 αβpermutations of positive and negative π, K, and p. These correlators were then combined according to Eq. (1) and multiplied by the single particle densities ρβ 1 in the |y| ≤0.5 rapidity range [22]. Fig. 1shows the Bαβ(y, ϕ) of ππ, KK, and pp pairs in semicentral collisions for illustrative purposes. The nine measured BFs exhibit common features, including prominent near-side peaks centered at (y, ϕ) =(0, 0) and relatively flat and featureless away-sides. The flat away-side arises from the fact that positive and negative particles of a given species feature essentially equal azimuthal anisotropy relative to the collision symmetry plane. It is also an indicator of the fast radial flow profile of the emitting sources, which manifests as strong focusing on the near-side peak [37], although the various species pairs demonstrate different centrality-dependent near-side peak shapes, widths, and magnitudes that indicate that they are subject to different charge balancing pair production and transport mechanisms, as well as final state effects. For instance, Bππ exhibits a deep and narrow dip at (y, ϕ) =(0, 0), within the near-side correlation peak, resulting in part from the Hanbury Brown–Twiss (HBT) effect, with a depth and width that vary with the source size and thus the centrality [32]. BKK exhibits much weaker HBT effects, whereas Bpp also features a narrow dip centered at (y, ϕ) =(0, 0)within a somewhat elongated near-side peak that may reflect the annihilation of pppairs. Pairs of protons and antiprotons emitted at small relative ηand ϕ(as well as small relative pT) are more likely to interact, and thus annihilate, than pairs produced at large separation, thereby leading to a depletion of pairs near y =0 and ϕ=0. The evolution with collision centrality of Bαβ, for all nine combinations α, β=π, K, p, is examined by considering their projections onto the yand ϕaxes in Figs. 2and 3, respectively. The shape and amplitude of Bππ projections onto yexhibit the strongest centrality dependence, whereas those of BπK, Bπp, BKπ and Bpπdisplay significantly smaller dependence on centrality. Uncertainties on the rest of the yprojections do not make it possible to claim any centrality dependence albeit some hints are visible in the cases of BKK and Bpp. The evolution with collision centrality of the measured BFs is further characterized in terms of their longitudinal and azimuthal standard deviation (σ) widths, noted σyand σϕ, respectively, as well as their integral, Iαβ B, as shown in Fig. 4. In the longitudinal direction, the widths σyof all species pairs, except those of KK and pp pairs, exhibit a significant narrowing from peripheral to central collisions. In contrast, BKK is essentially independent in both shape and width σywith changing collision centrality, whereas the width σyof Bpp features little centrality dependence even though this balance function exhibits some shape dependence on centrality. Differences in the evolution of the longitudinal σof pions and kaons BFs were already observed in Au–Au collisions at RHIC [26] and were then interpreted as resulting in part from strong radial 3 ALICE Collaboration Physics Letters B 833 (2022) 137338 Fig. 2. Balance function of species pairs (π, K, p) ⊗(π, K, p)projected onto the yaxis for particle pairs within the full range |ϕ| ≤π. Vertical bars and open boxes represent statistical and systematic uncertainties, respectively. Fig. 3. Balance function projections of species pairs (π, K, p) ⊗(π, K, p)onto the ϕaxis for the different particle pairs. Vertical bars and open boxes represent statistical and systematic uncertainties, respectively. 4 ALICE Collaboration Physics Letters B 833 (2022) 137338 Fig. 4. Longitudinal (y) σwidths (left), azimuthal (ϕ) σwidths (center), and integrals (right) of balance functions of the full species matrix of π±, K±, and p/pwith centrality. For yand ϕwidths, Kπ, pπ, and pK have the same values with πK, πp, and Kp, respectively. For the longitudinal widths, the relative azimuthal angle range for all the species pairs is the full azimuth range |ϕ| ≤π. For the azimuthal widths, the relative rapidity range used for all species pairs is |y| ≤1.2, with the exception of |y| ≤1.4for ππ and |y| ≤1.0for pp. Vertical bars represent statistical uncertainties while systematic uncertainties are displayed as dash line bands. flow profiles and two-stage emission [31,32]. The independence of the width σyof the BKK relative to the narrowing BFs of all other pairs observed in this work suggests two-stage quark production might also be at play at the TeV collision scale. Indeed, pions might be predominantly formed from the light u, ¯ u, d, and ¯ d quarks most abundantly produced in the second quark production stage, whereas kaon production would largely result from s¯ spairs predominantly created during the early stages of collisions [31,32]. Several distinct models have had success in describing the yield of produced hadrons, and more specifically baryons. Such models invoke a range of production mechanisms including parton fragmentation, effective mostly at high-pT, as well as parton coalescence and recombination, playing a predominant role at low and intermediate pT[54–56]. Statistical thermal models and production models involving color transparency [57] and baryon junctions [58]have also had a good measure of success. Single particle spectra of baryons thus do not provide sufficiently discriminating constraints to fully identify baryon production mechanisms. The added information provided by cross-species BFs shall thus contribute by adding new constraints for models of particle production and transport. In particular, given that neutrons, protons, and their excited states are composed of light u and d quarks, believed to be copiously produced in late stage emission (within the context of the two-stage quark production model), it is conceivable that these baryons are predominantly produced by coalescence (recombination) of light quarks in the late stage of the collisions. However, baryons (B) and antibaryons (B) have a relatively large mass and carry a conserved baryonic charge. The question then arises as to whether BB correlated pairs might originate before the formation of thermalized QGP, during the early stages of AA collisions. Late BBproduction is expected to be characterized by narrow longitudinal BFs while early stage emissions would produce pairs with a much wider yrange [31,32]. It is clear from Fig. 2that Bpp must extend beyond the acceptance of the measurement reported in this paper. This suggests that pp pairs have rather wide balance functions that might result from early BBpair separation. Detailed models of BBproduction and transport that account for (strong) decays from resonant states are required, evidently, to firmly establish this conclusion. Fig. 4shows that the σϕwidths of the nine BFs exhibit narrowing trends from peripheral to central collisions. The widths σϕfeature a wide spread of values at a given collision centrality, with those of KK pairs being the largest and those of πK the smallest. The widths also exhibit similar reductions with increasing collision centrality. These observations are in agreement with azimuthal BFs already reported from observations at RHIC for unidentified charged particle and identified ππ, KK pairs [25,26], as well as unidentified charged particle BFs in collisions at the LHC [28,29]. This narrowing can be qualitatively understood as resulting from the larger estimated transverse expansion velocity present in more central AA collisions [59]. It competes with an opposing trend associated with light quark diffusivity, expected to broaden and smear out the long range tails of the ϕBFs for systems featuring increasingly large lifespans [39]. Given the radial boost profile and contributions from resonance decays can be largely calibrated based on the shape of single particle pTspectra, the BF projections presented in Fig. 2, 3and the evolution of their widths σyand σϕ, shown in Fig. 4, then provide the first comprehensive set of azimuthal BFs to estimate the diffusivity of light quarks at the LHC [36,39]. The above discussion neglects possible contributions from the fragmentation of jets but these are anticipated to be small in the pTrange of this measurement. Quantitative estimates of such contributions would need to be accounted for in theoretical modeling of balance functions reported in this work for the purpose of determining the diffusivity of light quarks. Contributions of φ→K++K−decays to BKK were studied using simulated events from the HIJING generator [51]. The amplitude of the near-side peak of BKK is reduced by about 30% when contributions from φ-meson decays are explicitly excluded, while the correlator yand ϕwidths increase by about 7–8%. Effects associated with radial flow, not present in HIJING, could reduce this broadening effect and possibly induce a narrowing of the y width of BKK in more central collisions. However, no such narrowing is observed thereby signaling a more intricate production and transport evolution with competing contributions from φproduced at hadronization of the QGP and by coalescence of kaons within a hadron phase. The evolution with the collision centrality of the integrals Iαβ B of the nine species-pairs Bαβ(y, ϕ)shown in the right panel of Fig. 4is also of considerable interest. By definition, a balance function Bαβ(y, ϕ, pT)measures the “likelihood” of finding a charge balancing particle of a type β, e.g., π+, with a pair separation y, ϕ, pTaway from a reference particle of type α, e.g., π−. But charge balancing can be accomplished, on average, by distinct species, e.g., p, K+, and more rarely produced heavier particles, in additions to π+. The integral, Iαβ B(4π), of Bαβ(y, ϕ, pT)over the full phase space is thus proportional to the average fraction (and probability in the full phase space limit) of balancing partners of species β. Indeed, neglecting contributions from species other than pions, kaons, and protons, one expects the sum, Iα B(4π) ≡Iαπ B(4π) +IαK B(4π) +Iαp B(4π)to converge to unity, Iα B(4π) ≈1, in the full acceptance limit [43]. Integrals Iαβ B(4π)thus amount to probabilities Iαβ B(4π)/Iα B(4π)of having charge balancing of a species αby a species of type βand are indicators of the hadronization chemistry of the QGP, that is, what fraction of species αare accompanied (balanced), on aver5 ALICE Collaboration Physics Letters B 833 (2022) 137338 age, by a species β[43]. However, when measured in a limited acceptance, integrals Iαβ B( <4π)cannot, strictly speaking, be considered charge balancing probabilities. They nonetheless provide useful indicators of the hadrochemistry as well as the flavor and baryon number transport in AA collisions. As such, integrals Iαβ Bshown in Fig. 4as a function of collision centrality are surprising on two accounts. First, they show that the balance fractions are all, but one, approximately independent of collision centrality. The notable exception is the ππ integral which increases by about 20% from peripheral to central collisions. Second, close examination of these pairing fractions shows they are rather different than inclusive probabilities of observing π, K, and p/pin Pb–Pb collisions. For instance, IKπ Bis not larger than IKK Bby the π/K ∼6.7ratio of inclusive single particle yields and Ipp Bis larger than IpK Balso in contrast to observed K/p∼3yield ratios [22]. Hadron species charge balancing pairing fractions are thus indeed very different than the relative probabilities of single hadrons, and as such, provide new and useful information to further probe the hadronization of the QGP. This difference arises because the set of processes P2that lead to a specific balancing pair αβ(e.g., P2:→α±+β∓+X) is, by construction, far smaller than the set of processes P1leading to a given particle species αor β(e.g., P1:→ α±+Xor P1:→ β∓+Y). It is remarkable, nonetheless, that the pairing fractions Iαβ Bexhibit essentially no collision centrality dependence while single particle yield ratios are known to exhibit a weak dependence on collision centrality [9,60]. Note that the observed rise of Iππ Bin more central collisions may artificially result from increased kinematic focusing of pions with centrality in the pTand yacceptance of this measurement. The higher velocity flow fields encountered in more central Pb–Pb collisions could indeed shift and focus the yield of associated pions. Why such a shift is not as important for other charge balancing pairs remains to be elucidated with a comprehensive model accounting for the flow velocity profile and appropriate sets of charge conserving processes yielding balancing charges in the final state of collisions. Recent deployments of hydrodynamic models feature the former but lack the latter [61–63]. Further theoretical work is thus required to interpret the observed collision centrality dependence of the pairing probabilities displayed in Fig. 4. As such calculations become available, the data reported in this work, and specifically the integral Iαβ Bshown in Fig. 4, shall provide increased sensitivity to the hadrochemistry of the QGP and its susceptibilities. In summary, this paper presents the first measurements of the collision centrality evolution of same and cross-species balance functions of identified π±, K±and p/pat the LHC. Measured as functions of particle pair separation in rapidity (y) and azimuth (ϕ), the BFs exhibit prominent near-side peaks centered at (y, ϕ) =(0, 0)which feature different shapes, amplitudes, and widths, and varied dependencies on collision centrality. The BFs of species-pairs measured in this work feature narrowing ϕwidths in more central collisions, owing to the strong radial flow field present in central Pb–Pb collisions. Theoretical studies beyond the scope of this work shall use this data to put upper limits on the diffusivity coefficients of light quarks. In the longitudinal direction, the σwidths of BFs of all species pairs decrease with centrality except for those of KK and pp pairs. The shape and width of KK BFs are independent of collision centrality, while the pp BFs peak shapes depend only minimally on centrality. The observed centrality independence of the KK and narrowing σof other species in the longitudinal direction are qualitatively consistent with effects associated with radial flow and the two-stage quark production scenario, which posits that quark production occurs predominantly in early and late stages separated by a period of isentropic expansion. Integrals Iαβ Bconstitute an important finding of this study as they indicate that pairing fractions Iαβ Bare nearly independent of collision centrality, and provide a valuable quantitative characterization of the hadronization of the QGP. 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. 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), Fundac¸ão de Amparo à Pesquisa do Estado de São Paulo (FAPESP) and Universidade Federal do Rio Grande do Sul (UFRGS), Brazil; Ministry of Education of China (MOEC), Ministry of Science & Technology of China (MSTC) and National Natural Science Foundation of China (NSFC), China; Ministry of Science and Education and Croatian Science Foundation, Croatia; Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN), Cubaenergía, Cuba; Ministry of Education, Youth and Sports of the Czech Republic, Czech Republic; The Danish Council for Independent Research | Natural Sciences, the Villum Fonden and Danish National Research Foundation (DNRF), Denmark; Helsinki Institute of Physics (HIP), Finland; Commissariat à l’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; Indonesian Institute of Science, Indonesia; Istituto Nazionale di Fisica Nucleare (INFN), Italy; Japanese Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan Society for the Promotion of Science (JSPS) KAKENHI and Japanese Ministry of Education, Culture, Sports, Science and Technology (MEXT)of Applied Science (IIST), 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 IDUB, Poland; Korea Institute of Science and Technology Information and National Research Foundation of Korea (NRF), Republic 6 ALICE Collaboration Physics Letters B 833 (2022) 137338 of Korea; Ministry of Education and Scientific Research, Institute of Atomic Physics and Ministry of Research and Innovation and Institute of Atomic Physics, Romania; Joint Institute for Nuclear Research (JINR), Ministry of Education and Science of the Russian Federation, National Research Centre Kurchatov Institute, Russian Science Foundation and Russian Foundation for Basic Research, Russia; Ministry of Education, Science, Research and Sport of the Slovak Republic, Slovakia; National Research Foundation of South Africa, South Africa; Swedish Research Council (VR) and Knut & Alice Wallenberg Foundation (KAW), Sweden; European Organization for Nuclear Research, Switzerland; Suranaree University of Technology (SUT), National Science and Technology Development Agency (NSDTA) and Office of the Higher Education Commission under NRU project of Thailand, Thailand; Turkish Energy, Nuclear and Mineral Research Agency (TENMAK), Turkey; National Academy of Sciences of Ukraine, Ukraine; Science and Technology Facilities Council (STFC), United Kingdom; National Science Foundation of the United States of America (NSF) and United States Department of Energy, Office of Nuclear Physics (DOE NP), United States of America. 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