Search for a common baryon source in high-multiplicity pp collisions at the LHC

Published in: Physics Letters B DOI: 10.1016/j.physletb.2020.135849 Publication date: 2020 Document version Publisher's PDF, also known as Version of record Document license: CC BY Citation for published version (APA): Alice Collaboration (2020). Search for a common baryon source in high-multiplicity pp collisions at the LHC. Physics Letters B, 811, [135849]. https://doi.org/10.1016/j.physletb.2020.135849


Introduction
Correlation techniques have been used in particle physics since the 1960s [1]. Significant theoretical progress has been made to relate two-particle correlations at small relative momenta to the study of the space-time properties of the particle-emitting source and the final state interactions between the two particles [2,3]. Eventually, these methods were used to study the source size, also referred to as Hanbury Brown and Twiss (HBT) radius, created in heavy-ion collisions [4][5][6][7][8][9][10][11][12][13][14]. Collective effects such as hydrodynamic flow introduce position-momentum correlations to the particle emission, and hence modify the source radii in heavy-ion collisions at LHC energies [5]. In these systems, the decrease of the measured source radii with increasing pair transverse momentum k T =| p T, 1 + p T, 2 | /2, where p T is the transverse momentum of each of the particles, and the transverse mass m T where m is the average mass of the particle pair, is attributed to the collective expansion of the system created in the collision [5,15]. In this context, there are predictions of a common m T scaling of the radius for different particle pairs, which are based on the assumption of the same flow velocities and freeze-out times for all particle species [16,17]. There also is experimental evidence that a common m T scaling of the source radius is present for protons and kaons in heavy-ion collisions [18]. On the other hand, for pions the scaling seems to be only approximate [18,19], which could be explained by the larger effect of the Lorentz boost for lighter particles [16,18] but could also be influenced by the ef-E-mail address: alice -publications @cern .ch.
fect of feed-down from short-lived resonance decays. The radii obtained for Pb-Pb collisions at the LHC can be compared to the freeze-out volume obtained from statistical hadronization models [20] and are also essential ingredients for coalescence models [21][22][23].
Recent studies of high-multiplicity pp collisions reveal unexpected similarities to heavy-ion reactions when considering variables normally linked to collective effects, angular correlations, and strangeness production [24][25][26][27]. The hadronization in pp collisions is expected to occur on a similar time scale for all particles, and if a common radial velocity for all particles should be present, this would lead to a similar m T scaling of the source size as measured for heavy-ion collisions. Unfortunately, the information regarding the m T dependence of the source size measured in pp collisions is limited to low values of m T , as the existing data are based on analyses carried out with π-π and K-K pairs. These studies point to a variation of the radius as a function of the event multiplicity and of the pair m T [28-32]. However, aside a qualitative consideration of a β T scaling [33], no quantitative description could be determined so far.
It is known that strongly decaying resonances may lead to significant exponential tails of the source distribution, which can influence in particular the measured π-π correlations in heavy-ion collisions [34][35][36][37]. This effect is even more pronounced in small collision systems such as pp and p-Pb [38,39], and can substantially modify the measured source radii, not only for mesons, but for baryons as well. So far a solid modeling of the strong resonance contribution to the source function is still missing.
In this work, we present the first study of the source function with a quantitative evaluation of the effect of strong resonance https://doi.org/10.1016/j.physletb.2020.135849 0370-2693/© 2020 CERN for the benefit of the ALICE Collaboration. 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 SCOAP 3 . decays. The search for a common particle-emitting source is conducted employing data measured in high-multiplicity pp collisions at √ s = 13 TeV. The emission sources of protons and baryons are studied using p-p and p-correlations as a function of the pair m T . After correcting for the effect of strong resonance decays, the overall source size decreases significantly by up to 20% and the values extracted from the different pair combinations are in agreement. The common particle-emitting source described in this work will allow for direct comparisons of the source sizes to the ones resulting from theoretical models and the presence of collective phenomena in small colliding systems to be studied in a complementary way to analyses carried out so far [28-32,38,39].
These analyses concentrated on π-π and K-K correlation studies in pp collisions, probing the k T and m T ranges of up to 1-1.5 GeV/c 2 and observing a decrease of the source radius at higher m T , with the measured radii reaching values even below 1 fm in the case of minimum bias events. The higher m T range is only accessible with baryon femtoscopy. Additionally, recent ALICE studies revealed that small collision systems, such as pp, are a suitable environment to study the interaction potential between more exotic pairs, like p-K − , p-, -, p-0 , and p-− [40 -44]. The data of high-multiplicity triggered pp collisions at √ s = 13 TeV provides a significantly improved precision compared to the previously analyzed minimum bias data. Detailed studies of the interactions will be enabled by a precise knowledge of the size of the common source for particle emission, once corrected for the broadening due to the resonance decays, which depends on the pair type. Moreover, the effective source size is an important input for the modeling of coalescence and has consequences for the prediction of antimatter formation [21-23,45,46].

Data analysis
This paper presents measurements of the p-p, p-p, p-, and p-correlation functions in high-multiplicity pp collisions at √ s = 13 TeV performed with ALICE [47,48]. The high-multiplicity trigger selected events based on the measured amplitude in the V0 detector system [49], comprising two arrays of plastic scintillators at 2.8 < η < 5.1 and −3.7 < η < −1.7. The threshold was adjusted such that the selected events correspond to the highest 0.17% fraction of the multiplicity distribution of all INEL > 0 collisions. In such events, an average of 30 charged-particle tracks are found in the range |η| < 0.5 [50], which constitutes an increase by a factor of about four with respect to the minimum bias data sample [42]. The V0 timing information was evaluated with respect to the LHC clock to distinguish collisions with the beam pipe material or beam-gas interactions. The Inner Tracking System (ITS) [48] and Time Projection Chamber (TPC) [51] are the main tracking devices in ALICE. They cover the full azimuthal angle and the pseudorapidity range of |η| < 0.9.
The solenoid surrounding these detectors creates a homogeneous magnetic field of B = 0.5 T directed along the beam axis which defines the z direction. The spatial coordinates of the primary event vertex (PV) are reconstructed once using global tracks reconstructed with the TPC and ITS and once using ITS tracklets [47]. If both methods yield a vertex, the longitudinal difference between the two, z, is required to be less than 5 mm. The z component of the vertex, preferably determined by global tracks, has to lay within |V z | < 10 cm of the nominal interaction point to ensure a uniform detector coverage. Multiple reactions per bunch crossing are identified by the presence of secondary collision vertices [47]. Approximately 10 9 events fulfill the above requirements and are available for the analysis. The identification of protons and their respective antiparticles follows the complete set of criteria listed in Refs. [41,42]. Primary protons are selected in the transverse-mo-mentum range between 0.5 GeV/c and 4.05 GeV/c within | η |< 0.8. Particle identification (PID) is performed by using the information provided by the TPC and the Time-Of-Flight (TOF) [52] detectors. The energy loss in the TPC gas is measured for each track, while the timing information of TOF is required for tracks with p > 0.75 GeV/c. Particles are identified by a selection on the deviations from the signal hypotheses in units of the respective detector resolution σ TPC and σ TOF , according to n σ = n 2 σ ,TPC + n 2 σ ,TOF < 3.
The distance of closest approach (DCA) to the PV is restricted to a maximum of 0.1 cm in the transverse plane and 0.2 cm in the z direction, in order to suppress weak decay products or particles created in interactions with the detector material. The composition of the sample is obtained following the methods described in [41]. For this purpose, events were generated with Pythia 8.2 [53] (Monash tune [54]), processed by GEANT3 [55], filtered through the ALICE detector response and subsequently handled by the reconstruction algorithm [48]. These simulations were used to estimate that the selected protons and antiprotons have a momentum-averaged purity of 99%. The fraction of primary and secondary contributions was estimated by a fit of templates of their individual DCA distributions from MC to the p T -integrated measured distributions. This way the sample was found to consist of 82% primary particles. The remainder is due to weak decays of ( + ) baryons contributing with 13% (5%). The ( ) candidates are selected following the procedures discussed in [41,42] by reconstructing the weak decay → pπ − ( → pπ + ), which has a branching ratio of 63.9% [56]. The combinatorial background is reduced by requiring the distance of closest approach between the daughter tracks at the secondary vertex to be smaller than 1.5 cm. A straight line connecting the secondary vertex with the PV defines the trajectory of the candidate. Primary baryons are selected by requiring a cosine of the pointing angle (CPA) between the momentum vector of the candidate and its trajectory to be larger than 0.99. The reconstructed daughter particle tracks are required to have an associated hit either in the Silicon Pixel Detector (SPD) or the Silicon Strip Detector (SSD) layers of the ITS or the TOF detector in order to use their timing information to reduce the remaining contributions from out-ofbunch pile-up. The proton-pion invariant mass distribution is fitted using the sum of a double Gaussian to describe the signal and a second order polynomial for the combinatorial background. In the p T range between 0.3 to 4.3 GeV/c, the and candidates are reconstructed with a mass resolution between 1.5 MeV/c 2 and 1.8 MeV/c 2 . Choosing a mass window of 4 MeV/c 2 around the nominal mass [56] results in a p T -averaged purity of 96%. Similarly to the case of protons, CPA templates of the primary and secondary contributions are generated using MC simulations. These and a production ratio between and 0 of 1/3 [57][58][59][60], are used to decompose the sample of selected and candidates. It is found to consist of 59% baryons directly produced in the collision, while 19% originate from electromagnetic decays of a 0 . Additional contributions from weak decays of − and 0 amount to 11% each.

Correlation function
The observable in femtoscopic measurements is the correlation function C (k * ), where k * = 1 2 · |p * 2 − p * 1 | denotes the relative momentum of particle pairs and p * 1 and p * 2 are the particle momenta in the pair rest frame (PRF, p * 1 = −p * 2 ). It is computed as is the relative momentum distribution of correlated particle pairs, obtained from the same event, and B(k * ) the corresponding distribution of uncorrelated pairs. The latter is obtained by pairing identified particles of one event with particles from a different ("mixed") event. In order to avoid Table 1 Weight parameters of the individual components of the p-p and p-correlation function. Misidentifications of particle species X are denoted as X and feed-down contributions have the mother particle listed as a subindex. For the contributions in bold text, the correlation functions are modeled according to the interaction potential, while the others are assumed to be flat.
any bias due to acceptance and reconstruction effects, only those events are mixed, for which the difference between the positions of the vertex in z direction is less than 2 cm and the numbers of global tracks within |η| < 0.8 differ by less than four. The normalization factor N is calculated in the region k * ∈ [240, 340] MeV/c, where no femtoscopic signal is present and C (k * ) theoretically approaches unity. In the laboratory frame, the single-particle trajectories of p-p and p-p pairs at low k * are almost collinear and hence have a η and ϕ * ∼ 0. Here, η refers to the pseudorapidity of the track and ϕ * is the azimuthal track coordinate measured at 9 radii in the TPC, ranging from 85 cm to 245 cm, taking into account track bending because of the magnetic field. Due to detector effects like track splitting and merging [18] the reconstruction efficiency for pairs in same and mixed events differs. In order to avoid a bias in the correlation function, a close-pair-rejection (CPR) criterion is applied by removing p-p and p-p pairs fulfilling η 2 + ϕ * 2 < 0.01. For p-and p-pairs no rejection is considered.
A total number of 1.7 × 10 6 (1.3 × 10 6 ) p-p (p-p) and 0.6 × 10 6 (0.5 × 10 6 ) p-(p-) pairs are found in the region k * < 200 MeV/c. The correlation functions of baryon-baryon pairs agree within statistical uncertainties with their antibaryon-antibaryon pairs [18,61]. Therefore in the following p-p denotes the combination of p-p ⊕ p-p and accordingly for p-. The p-p and pcorrelation functions were obtained separately in 7 and 6 m T intervals, respectively, chosen such that the total amount of particle pairs is evenly distributed.
The theoretical correlation function is related to the twoparticle emitting source S(r * ) and wave function ψ( r * , k * ) [5]. It can be written as where r * is the relative distance between the particle pair defined in the PRF. When fitting this function to the data in this analysis, the free parameters are solely related to S(r * ). The ψ( r * , k * ) and the resulting C (k * ) can be determined with the help of the correlation analysis tool using the Schrödinger equation (CATS) [62]. The framework was developed in order to model the correlation function in small systems, where the strong interaction can give rise to a particularly pronounced correlation signal. Therefore, ψ( r * , k * ) is precisely calculated as the numerical solution of the single-channel Schrödinger equation, such that additionally to quantum statistics and Coulomb interactions the strong interaction can be included via a local potential V (r * ).
Residual correlations from impurities and feed-down of longlived resonances decaying weakly or electromagnetically [34] are taken into account by calculating the model correlation function where the sum runs over all contributions and with the method discussed in Ref. [41]. In particular the weights λ i , which are listed separately for p-p and p-in Table 1, are calculated from purity and feed-down fractions reported in Sec. 2.
To model the p-p (p-) correlation function, residual correlations due to the feed-down from p-(p-0 and p-− ) pairs are explicitly considered, while all other contributions are assumed to be flat. The residual correlations are modeled with CATS assuming the same source radius as the initial particle pair and use theoretical descriptions of their interactions following Ref. [63,64] for p-− and Ref. [65][66][67] for p-0 . The models describing the p-interaction will be discussed later in this section. The contributions of these pairs to the p-p and p-correlation functions have to be scaled by λ i and their signal smeared via a decay matrix [41,68] which is built according to the kinematics of the decay. Therefore, the residual signal of the initial pair is transformed to the momentum basis of the measured pair. Additionally, each contribution C i is smeared to take into account effects of the finite momentum resolution of the ALICE detector. Except for the genuine correlations, these steps result in a C i (k * ) ∼ 1 for all combinations, in particular due to the rather small λ parameters of most residual contributions as shown in Table 1. Either a constant or a linear baseline C non−femto (k * ) is included in the total fit function C fit (k * ) = C non−femto (k * ) · C model (k * ). The constant factor can, if necessary, introduce a slight correction of the normalization N .
The linear baseline function extrapolates any remaining slope of C (k * ) in the normalization region, which may arise due to energy and momentum conservation [41,69], to the femtoscopic region.
The source function S(r * ) is assumed to have a Gaussian profile where r 0 represents the source radius. The best fit to the p-p correlation function with C fit (k * ) is performed in the region k * ∈ [0, 375] MeV/c and determines simultaneously all free parameters, namely r 0 and the ones related to C non−femto (k * ). The genuine p-p correlation function is calculated by using CATS [62] and the strong Argonne v 18 potential [70] in S, P , and D waves. The systematic uncertainties on r 0 associated with the fitting procedure are estimated by i) modifying the upper limit of the fit region to 350 MeV/c and 400 MeV/c, ii) replacing the normalization C non−femto (k * ) = a by a linear function, iii) employing different models describing the residual p-interaction as discussed later in the text, and iv) modifying the λ parameters by varying the composition of secondary contributions by ±20%, while keeping the sum of primary and secondary fractions constant. In comparison to p-p, the theoretical models describing the p-interaction are much less constrained since data from hypernuclei and scattering experiments are scarce [41, [71][72][73][74]. The femtoscopic fit is performed in the range k * ∈ [0, 224] MeV/c. The limited amount of experimental data leaves room for different theoretical descriptions of the p-interaction. In the measurement this is accounted for by performing the fits twice, where the S wave function of the p-pair is obtained once from chiral effective field theory calculations (χ EFT) at leading order (LO) [71] and once from the one at next-to-leading order (NLO) [74]. The systematic uncertainties on r 0 associated with the fit procedure are estimated by i) changing the upper limit of the fit region to 204 MeV/c and 244 MeV/c, ii) replacing the normalization constant C non−femto (k * ) = a by a linear function, and iii) modifying the λ parameters by varying R 0 / by ±20%.
The systematic uncertainties of the experimental p-p and pcorrelation function take into consideration all single-particle selection criteria introduced in the previous section, as well as the CPR criteria on the p-p pairs. All criteria are varied simultaneously up to 20% around the nominal values. To limit the bias of statistical fluctuations, only variations with a maximum change of the pair yield of 20% are considered. To obtain the final systematic uncertainty on the source size, the fit procedure is repeated for all variations of the experimental correlation function, using all possible configurations of the fit function. The standard deviation of the resulting distribution for r 0 is considered as the final systematic uncertainty.
In Fig. 1 the p-p and p-correlation functions of one representative m T interval are shown. The grey boxes represent the systematic uncertainties of the data and correspond to the 1σ interval extracted from the variations of the selection criteria. The resulting relative uncertainty of the p-p (p-) correlation function reaches a maximum of 2.4% (6.3%) in the lowest measured k * interval. Unlike for meson-meson or baryon-antibaryon pairs, the broad background related to mini-jets is absent for baryon-baryon pairs [41,75]. The width of the fit curves corresponds to the 1σ interval extracted from the variations of all the fits. In case of the p-p correlation function, this results in a χ 2 /ndf = 1.9. The fit of the p-correlation function using χ EFT calculations at LO yields a χ 2 /ndf = 0.91 while the fit using χ EFT calculations at NLO yields a χ 2 /ndf = 0.67.
Each correlation function in every m T interval is fitted and the resulting radii are shown in Fig. 2. The central value corresponds to the mean estimated from the distribution of r 0 obtained from the systematic variations. The statistical uncertainties are marked with solid lines, while the boxes correspond to the systematic uncertainties. The relative value of the latter is at most 2.4% for the radii extracted from p-p correlations and 8.3% and 5.7% for those extracted from p-correlations using the NLO and LO calculations, respectively. The decrease of the source size with increasing m T is consistent with a hydrodynamic picture, however, the expected common scaling [16] of the different particle species is not observed for the two considered pair types. The two measurements show a similar trend that is shifted by an offset, indicating that there are differences in the emission of particles.

Modeling the short-lived resonances
The effect of short-lived resonances (cτ 10 fm) feeding into protons and baryons could be a possible explanation for the difference between the source sizes determined from p-p and p-correlations, which was observed in Fig. 2. In the past, Bose-Einstein correlations between identical pions, measured in heavyion collisions, were interpreted in terms of a two-component source. It constitutes a core, which is the origin of primary par- Fig. 3. A sketch representing the modification of r * core into r * (dash-dotted lines), due to the presence of resonances (gray disks), decaying into the particles of interest (blue disks). The coordinate system is determined by the rest frame of the two daughters and consistent with Eq. (1), where k * represents their momenta (solid blue lines). The blue dotted lines represent the remaining decay products, which are assumed to be single pions. In case of a primordial particle in the initial state instead of a resonance, the latter is not considered ( s * res,i = 0). ticles, and a halo, which is the origin of pions produced by the decay of resonances [76]. In a detailed investigation of MC simulations of heavy-ion collisions the source sizes were extracted from π-π pairs for systems both with and without the presence of these contributions, and indeed differences of about 1 fm were found [35,77]. Similar effects are expected to arise for baryons, since short-lived resonances such as and N * decay mainly into a baryon and a pion. The exponential nature of the decay is reflected in the appearance of exponential tails in the source distribution and an effective increase of the source size. Inspired by this picture, a source distribution for baryons is built starting from two components: a Gaussian core and a non-Gaussian halo.
In this work, the resonance yields are taken from the statistical hadronization model (SHM) [78]. Since this study aims at quantifying the effect of strongly decaying resonances on the source distribution, in the following only primordial particles and secondary decay products of short-lived resonances will be considered. According to the SHM, the amount of primordial protons ( baryons) are only P p = 35.8% ( P = 35.6%) [79], implying that the effect of the secondaries is substantial. For protons, 57 different resonances with lifetimes 0.5 fm < cτ < 13 fm are considered. Relative to the total number of protons, 22% originate from the decay of a ++ resonance, 15% from the decay of a + resonance, and 7.2% from a 0 resonance. The remaining secondary protons originate from heavier N * , and resonances, which contribute individually with less than 2%. Similarly, secondary baryons stem from 32 considered resonances with lifetimes 0.5 fm < cτ < 8.5 fm. Most prominently * + , * 0 , and * − are each the origin of 12% of all baryons, while decays of heavier N * , , and resonances individually contribute with less than 1%. The weighted average of the lifetimes (cτ res ) of the resonances feeding into protons ( baryons) is 1.65 fm (4.69 fm), while the weighted average of the masses is 1.36 GeV/c 2 (1.46 GeV/c 2 ). Although the amount of secondaries is similar for protons and baryons, there is a significant difference in the mean lifetime of the corresponding resonances, which is much longer for the . Qualitatively this will imply a larger effective source size for p-, as observed in Fig. 2.
In the following the source function S(r * ) is constructed including the effect of short-lived resonances, assuming that all primordial particles and resonances are emitted from a common Gaussian source of width r core . Consequently, the particles studied in the final state can either be primordials or decay products of short-lived resonances. For a pair of particles there are four different scenarios regarding their origin, the frequency of each given by P 1 P 2 , P 1P 2 , P 1 P 2 and P 1P 2 . Here P 1,2 are the fractions of primordial particles and P 1,2 = 1 − P 1,2 the fractions of particles originating from short-lived resonances. The total source is To evaluate S(r * ), the required ingredients are the fractions of primordial and secondary particles, and the individual source functions corresponding to the possible combinations for the particle emission. Depending on the average mass and lifetime of the resonances feeding to the particle pair of interest, each of these scenarios will result in slightly different source sizes and shapes. These composite source functions are difficult to compute analytically, however, a simple numerical evaluation, outlined in the following, allows to iteratively build the full source distribution S(r * ) for a given r core . The primordial emission of particles with a relative distance r * core is randomly sampled from a Gaussian with width equal to r core . The resulting particles are then, based on the probabilities P 1,2 and P 1,2 , assigned to be either primordial particles or resonances. The resonances are propagated and their decays are simulated. For simplicity it is assumed that each decay produces one proton ( ) and one pion. It was checked that including three-body decays at this stage would have a negligible effect on the extracted radii. Fig. 3 is a schematic representation of the source modification, which in vector form is given as: where s * res,1(2) is the distance traveled by the first (second) resonance. This is linked to the flight time t res , which is sampled from an exponential distribution based on the lifetime of the resonance τ res : where p * res is the momentum and M res the mass of the corresponding resonance. For the one-dimensional source function S(r * ) the absolute value r * = | r * | needs to be evaluated. Given the definitions in Eq. (5) and Eq. (6), the required ingredients are r * core , the momenta, masses and lifetimes of the resonances, as well as the angles formed by the three vectors r * core , s * res,1 and s * res,2 . The masses and lifetimes of the resonances are fixed to the average values reported above. The remaining unknown parameters, the momenta of the resonances and their relative orientation with respect to r * core , are related to the kinematics of the emission. In this work, the EPOS transport model [80] is used to quantify these parameters, by generating high-multiplicity pp events at √ s = 13 TeV and selecting the produced primordial protons, baryons and resonances that feed into these particles. Since the yields of the heavier resonances are over-predicted by EPOS, they are weighted such that their average mass M res reproduces the expectation from the SHM. The source function S(r * ) is built by selecting a random r * core and a random emission scenario based on the weights P 1,2 , which are known from the SHM. A random EPOS event with the same emission scenario is used to determine p * res,1 (2) and their relative direction to r * core . To obtain r * the resonances are propagated, using Eq. (5) and (6), and the k * of their daughters is evaluated. Only events with small k * are relevant for femtoscopy, thus, if the resulting k * > 200 MeV/c, a new EPOS event is picked. The above procedure is repeated until the resulting S(r * ) achieves the desired statistical significance.
With this method, the modification of the source size due to the decay of resonances is fixed based on the SHM and EPOS, while the only free fit parameter is the size r core of the primordial (core) source. This procedure is used to refit the p-p and p-correlation functions. The uncertainties are evaluated in the same way as in the case of the pure Gaussian source. Additional uncertainties due to short-lived resonances decaying into protons ( baryons) are accounted for by repeating the fit and altering the mass by 0.2% (0.6%) and the lifetimes by 2% (13%) [56]. When comparing the individual fits of the correlation functions in one m T interval with the ones assuming a pure Gaussian source the resulting χ 2 is found to be similar. This implies that each system can still be described by an effective Gaussian source, albeit loosing the direct physical interpretation of the source size. This property becomes evident from Fig. 4, in which the different source functions, used to describe the m T bin plotted in Fig. 1, are shown. As expected, after the inclusion of the resonances, the same core function results in different effective sources for p-p and p-. The Gaussian parametrization yields an almost equivalent description of the source function up to about r * ∼ 6 fm, while for larger values the new parametrization with inclusion of the resonances shows an exponential tail. Since most of the particles are emitted at lower r * values, the corresponding correlation functions are similar. However, one major difference with the new approach is the resulting source size, as the Gaussian core is more compact than the effective sources. The resulting m T dependence of r core measured with p-p and p-pairs is shown in Fig. 5. The relative systematic uncertainty is at most 2.6% for the core radii extracted from p-p correlations and 8.4% and 6.2% for those extracted from p-correlations using the NLO and LO calculations, respectively. In contrast to a Gaussian source, the new parametrization of the source function provides a common m T scaling of r core for both p-p and p-. This result is compatible with the picture of a common emission source for all baryons and their parent resonances.

Summary
The results for p-p and p-correlations in high-multiplicity pp collisions at √ s = 13 TeV demonstrate a clear difference in the effective proton and source sizes if a simple Gaussian source is assumed. A new procedure was developed to quantify for the first time the modification of the source function due to the effect of short-lived resonances. The required input is provided by the statistical hadronization model and the EPOS transport model. The ansatz is that the source function is determined by the convolution of a universal Gaussian core source of size r core and a non-Gaussian halo. The former represents a universal emission region for all primordial particles and resonances, while the latter is formed by the decay points of the short-lived resonances. This picture is confirmed by the observation of a common m T scaling of r core for the p-p and p-pairs in high-multiplicity pp collisions, with r core ∈ [0.85, 1.3] fm for m T ∈ [1.1, 2.2] GeV/c 2 . Compared to the values obtained when an effective Gaussian parametrization is used, the overall values are significantly decreased by up to 20%.
The measurement of the core size of a common particleemitting source, corrected for the effect of strong resonances, will allow for direct comparisons with theoretical models. Additionally, detailed studies of the m T dependence of the core radius will enable complementary investigations of collective phenomena in small collision systems.
On the other hand, the assumption of a common core source, modified by the resonances feeding to the particle pair of interest, allows for a quantitative determination of the effective source for any kind of particle pair. First of all, it enables high-precision studies of the interaction potentials of more exotic baryon-baryon pairs [41, 42,44] that rely on two-particle correlation measurements in momentum space and use the p-p correlation as a reference to fix the emission source. It is also relevant for coalescence approaches addressing the production of (anti) (hyper) nuclear clusters. A crucial next step is to investigate the applicability of the new method for meson-meson and baryon-meson correlations. If the same m T scaling is observed as for baryons, this will provide an even more precise quantitative understanding of the common particle-emitting source. In any case, such a study will shed further light on the production mechanism of particles and will be a valuable input for transport models.

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 pro-