Multiplicity dependence of K*(892)0 and ϕ(1020) production in pp collisions at √s = 13 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/ Multiplicity dependence of K*(892)0 and ϕ(1020) production in pp collisions at √s = 13 TeV © 2020 European Organization for Nuclear Research. Published by Elsevier B.V. Published version ALICE Collaboration ALICE Collaboration. (2020). Multiplicity dependence of K*(892)0 and ϕ(1020) production in pp collisions at √s = 13 TeV. Physics Letters B, 807, Article 135501. https://doi.org/10.1016/j.physletb.2020.135501 2020 Physics Letters B 807 (2020) 135501 Contents lists available at ScienceDirect Physics Letters B www.elsevier.com/locate/physletb Multiplicity dependence of K*(892)0and φ(1020) production in pp collisions at √s=13 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 13 December 2019 Received in revised form 25 March 2020 Accepted 18 May 2020 Available online 28 May 2020 Editor: L. Rolandi The striking similarities that have been observed between high-multiplicity proton-proton (pp) collisions and heavy-ion collisions can be explored through multiplicity-differential measurements of identified hadrons in pp collisions. With these measurements, it is possible to study mechanisms such as collective flow that determine the shapes of hadron transverse momentum (pT) spectra, to search for possible modifications of the yields of short-lived hadronic resonances due to scattering effects in an extended hadron-gas phase, and to investigate different explanations provided by phenomenological models for enhancement of strangeness production with increasing multiplicity. In this paper, these topics are addressed through measurements of the K∗(892)0and φ(1020)mesons at midrapidity in pp collisions at √s=13 TeV as a function of the charged-particle multiplicity. The results include the pTspectra, pT-integrated yields, mean transverse momenta, and the ratios of the yields of these resonances to those of longer-lived hadrons. Comparisons with results from other collision systems and energies, as well as predictions from phenomenological models, are also discussed. ©2020 European Organization for Nuclear Research. 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. 1. Introduction Recent studies of proton-proton (pp) and proton-lead (p–Pb) collisions at the LHC with high charged-particle multiplicities have shown patterns of behavior that are reminiscent of phenomena observed in heavy nucleus-nucleus (A–A) collisions such as Pb–Pb and Xe–Xe. The systems created in these collisions are compared by classifying events according to the final-state charged-particle multiplicity, which is used as a measure of the “activity” of the event. In small collision systems such as pp and p–Pb, multiplicities range from a few to a few tens of charged particles per unit of rapidity, whereas in large systems (A–A collisions), multiplicities of a few thousand charged particles per unit of rapidity can be produced. As discussed below, measurements of azimuthal anisotropies in particle emission [1–7] (quantified using the Fourier coefficients of azimuthal distributions of produced particles), the multiplicity evolution of hadron pTspectra [8–11], and pT-differential baryon-to-meson ratios suggest the possibility of collective flow even in small systems. Furthermore, the observed enhancement of strange hadron production [8,9,12] could indicate the production of a quark–gluon plasma (QGP), while the possible suppression of the yields of short-lived resonances [8,11]may suggest the presence of an extended hadronic phase. However, it remains an open question whether the underlying causes of these behaviors are truly the same in small and large collision systems. E-mail address: alice -publications @cern .ch. In order to investigate this, the ALICE Collaboration has measured the pTspectra and total yields of identified hadrons as a function of the charged-particle multiplicity in p–Pb collisions at √sNN =5.02 TeV [10,11,13–15] and pp collisions at √s=7TeV [8,12,16]for many species, including π±, K±, K0 S, K∗(892)0, p, φ(1020), , −, −, deuterons, and their antiparticles. This paper reports on an extension of these studies: a measurement of the multiplicity evolution of the production of K∗(892)0, K∗(892)0, and φ(1020)mesons in pp collisions at √s=13 TeV, the highest energy reached by the LHC in runs 1 and 2. The present study takes advantage of a pp data set recorded during Run 2 of the LHC in 2015 with an integrated luminosity of 0.88 nb−1and complements other recent ALICE papers on light-flavor hadron production in the same collision system, both in inelastic collisions [17] and as a function of charged-particle multiplicity [9,18,19]. For the remainder of this paper, the average of K∗(892)0and K∗(892)0will be denoted as K∗0, while the φ(1020)will be denoted as φ. The ratios of the yields of strange hadrons to pion yields are observed to be enhanced in A–A collisions relative to minimum bias pp collisions [20–22], with the yields in central A–A collisions being well described by statistical thermal models [23–26]. In central A–A collisions, strangeness is produced from the hadronization of a strangeness-saturated QGP and the relative abundances of hadrons reflect the degree of equilibration of the system. At the LHC, hadron-to-pion yield ratios are observed to increase with the charged-particle multiplicity in pp and p–Pb collisions [8–13]; the magnitude of the change from low to high multiplicity inhttps://doi.org/10.1016/j.physletb.2020.135501 0370-2693/©2020 European Organization for Nuclear Research. 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. 2ALICE Collaboration / Physics Letters B 807 (2020) 135501 creases with the strangeness content of the hadron. The ratios in high-multiplicity pp and p–Pb collisions reach the values observed in peripheral Pb–Pb collisions and generally follow similar trends as the multiplicity increases from pp to p–A to A–A collisions. Furthermore, the yields of strange particles are consistent between √s=7 and 13 TeV for similar charged-particle multiplicities. These results suggest that the yields of these hadrons depend primarily on the charged-particle multiplicity and are independent of the collision system and energy. This is perhaps a surprising result: pp, p–Pb, and A–A collisions involve different physical processes (e.g. different contributions from jets and multiple partonic interactions) and produce pTspectra with different shapes. Nevertheless, the total abundances of hadrons, even rare particles like −and light nuclei, are consistent across the different collision systems for a given charged-particle multiplicity, suggesting that there may be some underlying similarities between the different collision systems. Comparisons of these different collision systems at similar multiplicities may, for example, help to address the question of whether a QGP might be present even in high-multiplicity pp and p–Pb collisions, or alternatively, whether non-QGP effects might explain behavior seen in A–A collisions. Several theoretical explanations of the multiplicity evolution of strange-hadron production have been put forward, including canonical suppression, rope hadronization, and core-corona effects. In statistical thermal models of large collision systems, strangeness production is described through the use of a grand canonical ensemble, where strangeness conservation is realized on average across the volume of the system. In the canonical suppression picture, strangeness production in small systems is instead described using a canonical ensemble, requiring the exact local conservation of strangeness within the small volume [8,27,28]. As the size of the system decreases, it makes a transition from the grandcanonical to the canonical description, leading to a decrease in strange-hadron yields with decreasing multiplicity. In the ropehadronization picture, the larger and denser collision systems form color ropes [29–31], groups of overlapping strings that hadronize with a larger effective string tension. This effect, implemented in models such as DIPSY [32–34], also leads to an increase in the production of strange hadrons with increasing charged-particle multiplicity. Core-corona separation is implemented in a variety of models, including EPOS [35–38] and those described in [39,40]. In these models, the collision is divided into “core” and “corona” regions, with the division determined by the string or parton density. Regions with a density greater than the threshold density become the core, which may evolve as a quark–gluon plasma. This is surrounded by a more dilute corona, for which fragmentation occurs as in the vacuum. Strangeness production is higher in the core region, which makes up a greater fraction of the volume of the larger collision systems. This also results in strangeness enhancement with increasing multiplicity. The φmeson is a useful probe for the study of strangeness enhancement. The φcontains two strange valence (anti)quarks, but has no net strangeness. Its production should therefore not be canonically suppressed, while the production of hadrons with open strangeness (e.g. kaons or ) may be canonically suppressed [8]. It has, in fact, been rather difficult to describe enhancement of φ-meson production in a framework that involves canonical suppression [8]. In contrast, in the rope-hadronization or core-corona interpretations, the yields of φmesons evolve with multiplicity similarly to particles with open strangeness, leading to an expected increase in the pT-integrated φ / πratio with increasing chargedparticle multiplicity. Measurements of φ-meson production as a function of the multiplicity may help to distinguish between the various explanations of strangeness enhancement in small systems. One of the main motivations for studying resonances like K∗0 and φin heavy-ion collisions is to learn more about the properties (temperature and lifetime) of the hadronic phase of the collision. When short-lived resonances (such as ρ(770)0, K∗0, and (1520)) decay, their daughters may re-scatter in the hadronic phase, leading to a reduction in the measurable resonance yields; conversely, resonances may also be regenerated due to quasielastic scattering of hadrons through a resonance state [41–46]. Centrality-dependent suppression of ρ(770)0, K∗0, and (1520) production was observed in Pb–Pb collisions [47–50], and a hint of K∗0suppression was reported for p–Pb collisions [11]. Observations of a similar suppression in high-multiplicity pp collisions (e.g., the K∗0/Kratio in pp collisions at √s=7TeV[8]) might be an indication for a hadronic phase with non-zero lifetime in highmultiplicity pp collisions. Measurements of identified hadrons can also be used to study collective motion in A–A collisions and to search for similar effects in small collision systems. In non-central A–A collisions, the initial spatial anisotropy in the overlap region of the colliding nuclei results in azimuthally anisotropic pressure gradients in the produced medium, leading to azimuthal anisotropies in particle emission. This anisotropic flow is a manifestation of hydrodynamic behavior in the QGP produced in the A–A collision system. Measurements of azimuthal correlations and anisotropies in particle emission [1–7]also suggest the possibility of collective motion in small collision systems. It was observed that the slopes of hadron pTspectra increase with increasing multiplicity in pp and p–Pb collisions [8–11], while an enhancement in pT-differential baryonto-meson ratios (e.g. p/πand /K0 S) is observed at intermediate pT (2 pT7GeV/c). This is at least qualitatively similar to the behavior observed in Pb–Pb collisions [51–54], where the effects can be attributed to a collective expansion of the system. In this interpretation, hadrons receive a momentum boost in the direction transverse to the beam axis, which increases in magnitude with increasing multiplicity and is larger for more massive particles. It should be noted, however, that other effects, including recombination [55–57], may be able to account for the observed behavior. The increase in the slopes of the pTspectra is also mirrored in the trend of the measured mean transverse momenta pT. In contrast to the yields, which evolve along a continuous trend with multiplicity across different collision systems, the pTvalues of lightflavor hadrons follow different trends in pp, p–Pb, and Pb–Pb collisions [10–12,51], with a faster increase for the smaller systems. The pTvalues in the highest multiplicity pp collisions reach, or in some cases exceed, the pTvalues observed in central Pb–Pb collisions. The increase in pTin pp collisions is due to changes in the shapes of the pTspectra at low pT; for pT4GeV/c, the shapes of hadron pTspectra are essentially independent of multiplicity [9,58]. The color reconnection (CR) mechanism [59–63] describes the interconnections and interactions between strings that originate from different multi-parton interactions. It is implemented in various forms, sometimes including the formation of color ropes, in several event generators based on string fragmentation. Color reconnection can also modify the yields of hadron species (e.g. increasing the rate of baryon formation) and can lead to collective flow-like effects, even in small collision systems and in event generators like PYTHIA that do not include QGP formation. The results reported here will allow the study of K∗0and φ production as functions of both energy and multiplicity in pp collisions. The presented results reach higher values of multiplicity than previously measured in pp collisions and therefore provide important additional information on the production of light-flavor hadrons at LHC energies. This paper is organized as follows. The ALICE detector and the criteria adopted for data selection are described in Section 2. A summary of the data analysis procedure is given in Section 3. The results are presented and discussed in Section 4, followed by a summary and conclusions in Section 5. ALICE Collaboration / Physics Letters B 807 (2020) 135501 3 Table 1 Charged-particle multiplicity densities at midrapidity dNch/ dη|η|<0.5for the INEL >0class and the various V0M multiplicity classes [9]. Class dNch/dη|η|<0.5 INEL >06.89±0.11 I 25.75±0.40 II 19.83±0.30 III 16.12±0.24 IV 13.76±0.21 V 12.06±0.18 VI 10.11±0.15 VII 8.07±0.12 VIII 6.48±0.10 IX 4.64±0.07 X2.52 ±0.04 2. Event and track selection The ALICE detector is described in detail in [64,65]. The subdetectors that are relevant to the analysis described in this paper are the Time Projection Chamber (TPC), the Time-of-Flight detector (TOF), the Inner Tracking System (ITS), the V0 detectors, and the T0 detectors. The TPC and ITS are used for tracking and finding the primary vertex, while the TPC and TOF are used for particle identification. The V0 detectors (scintillator arrays) and the T0 detectors (arrays of Cherenkov counters) sit on either side of the nominal center of the detector at small angles with respect to the beamline. The V0 detectors are used for triggering and to define the multiplicity estimator at forward rapidities (pseudorapidity ranges −3.7 <η<−1.7 and 2.8 <η<5.1). The T0 detectors provide timing information, including a start signal for the TOF. The K∗0and φmesons are reconstructed from a sample of 5 ×107pp collisions at √s=13 TeV recorded in 2015. The minimum bias trigger required hits in both V0 detectors in coincidence with proton bunches arriving from both directions. Beam-induced background and pile-up events are removed offline; see [9,65]for details. Selected events must also have a primary collision vertex reconstructed with the two innermost layers of the ITS and located within ±10 cm along the beam axis of the nominal center of the ALICE detector. Results in this paper are presented for different event classes corresponding to subdivisions of the “INEL >0” event class, which is defined as the set of inelastic collisions with at least one charged particle in the range |η| <1[66]. The INEL >0sample is divided into multiplicity classes based on the total charge deposited in both V0 detectors (called the “V0M amplitude”). Thus, the event classes are determined by the number of charged particles at forward rapidities, while the K∗0and φyields are measured at midrapidity (|y| <0.5); this is to avoid correlations between the K∗0and φyields and the multiplicity estimator. Particle yields, yield ratios, and mean transverse momenta are plotted for different multiplicity classes (which correspond to different centralities for A–A collisions) as functions of the corrected mean charged-particle multiplicity density at midrapidity dNch/ dη|η|<0.5, where ηis the pseudorapidity in the lab frame. As in [9], the various multiplicity classes are denoted using Roman numerals, with class I (X) having the highest (lowest) multiplicity. See Table 1for the values of dNch/ dη|η|<0.5measured for each V0M multiplicity class. Since the K∗0and φmesons are short-lived (i.e., their lifetimes are of the order of ∼10−23 s and their decay vertices cannot be distinguished from the primary collision vertex), they cannot be measured directly by the detector. Instead, they are reconstructed via their hadronic decays to charged pions and kaons: K∗0→π±K∓ (branching ratio 66.503 ±0.014%) and φ →K+K−(branching ratio 49.2 ±0.5%) [67]. Charged tracks are selected using a set of standard track-quality criteria, described in detail in [11]. Pions and kaons are identified using the specific ionization energy loss dE/ dxmeasured in the TPC and the flight time measured in the TOF. Where the dE/ dxresolution of the TPC is denoted as σTPC, pions and kaons are required to have dE/ dxvalues within 2σTPC of the expected value for p >0.4GeV/c, within 4σTPC for 0.3 <p < 0.4GeV/c, and within 6σTPC for p <0.3GeV/c(typically, σTPC ∼ 5% of the measured dE/ dxvalue). When a pion or kaon track is matched to a hit in the TOF, the time-of-flight value is required to be within 3σTOF of the expected value (σTOF ∼80 ps) [68]. These eventand track-selection criteria are varied from their default values and the resulting changes in the yields are incorporated into the systematic uncertainties, which are summarized in Table 2. 3. Data analysis The K∗0and φsignals are extracted using the same invariant mass reconstruction method described in [11,17,48]. Invariant mass distributions of unlike-charge πK or KK pairs in the same event are reconstructed after particle identification. The combinatorial background is estimated using multiple methods. In the “like-charge” method, tracks of identical charge from the same event are combined to form pairs. This background is 2√n−−n++, where n−− and n++ are the number of negative-negative and positive-positive pairs in each invariant mass bin, respectively. In the “mixed-event” method, tracks from one event are combined with oppositely charged tracks from up to 5 other events with similar primary vertex positions and multiplicity percentiles. Specifically, it is required that the longitudinal positions of the primary vertices differ by less than 1cm and the multiplicity percentiles computed using the V0M amplitude differ by less than 5%. The mixed-event πK (KK) background is normalized so that it has the same integral as the unlike-charge same-event distribution in the invariant mass range 1.1 <mπK<1.15 GeV/c2 (1.05 <mKK <1.08 GeV/c2). In evaluating the systematic uncertainties, the boundaries of the normalization region for the mixedevent background are varied by ∼100 MeV/c2for the K∗0analysis and ∼10 MeV/c2for φ. After subtraction of the combinatorial background, the invariant mass distribution consists of a resonance peak sitting on top of a residual background of correlated pairs. This correlated background contains contributions from jets, resonance decays in which a daughter is misidentified, and decays with more than two daughters. In the analysis of the φmeson in pp collisions, the signal-to-background ratio is large and the background is observed to vary slowly in the region of the peak. For these reasons, a third approach is also used to describe the background in the φ analysis; the combinatorial background is not subtracted, but is instead parameterized together with the residual background using a function as described below. This has the advantage of providing smaller statistical uncertainties than the other methods. For pT<4GeV/c, all three methods provide good descriptions of the KK background and give φyields within a few percent of each other. The final φyields for pT<4GeV/care the averages of those extracted using the three methods of describing the combinatorial background, while the spread among the results for the different methods is incorporated into the systematic uncertainties. As pTincreases, the yields of hadrons decrease, along with the magnitudes of all of the combinatorial backgrounds studied. The mixed-event background, which lacks any contribution from correlated pairs, is observed to become smaller than the same-event (likeor unlike-charge) combinatorial backgrounds as pTincreases, eventually tending to 0 for pTvalues higher than the ranges considered here. While the mixed-event background could still be used for the φanalysis for 4 ≤pT≤8GeV/c, the two other techniques have smaller statistical fluctuations in this pTrange. Consequently, the mixed-event technique is not used for the analysis 4ALICE Collaboration / Physics Letters B 807 (2020) 135501 Table 2 Sources of systematic uncertainties for the pTspectra of K∗0and φreported for low, intermediate, and high pT. When only one value is given for one particle, the uncertainty does not depend on pT. “Signal extraction” includes variations of the combinatorial background, mixed-event normalization region, fitting region, peak shape, and residual background function. The “signal-loss” uncertainty is multiplicity-dependent, hence values are quoted for the highest and lowest multiplicity classes (I and X, respectively). The text “negl.” indicates a negligible uncertainty and “had. int. cross sec.” is short for “hadronic interaction cross section.” Particle pT(GeV/c) K∗0φ 0.2 2.2 6.5 0.7 2 6 event/track selection 4.3% 1.6% 2.9% 2.7% 2.9% 3.2% signal extraction 10.3% 6.7% 7.7% 2.7% 3.1% 3.1% ITS-TPC matching 2.0% 2.0% branching ratio negl. 1.0% material budget 2.0% 0.5% negl. 5.3% 1.0% negl. had. int. cross sec. 2.6% 1.2% negl. 2.1% 2.6% negl. signal loss, class I negl. negl. signal loss, class X 3.9% 2.4% 0.9% 2.3% 4.8% 2.2% of φfor pT>4GeV/c. The mixed-event technique is the primary method used for the extraction of the K∗0yields; variations of the yield due to the use of a like-charge background are covered by the systematic uncertainties. However, for pT<0.8GeV/cin multiplicity class I, the like-charge method is preferred, since it provides a better description of the background. At high pT, the mixed-event background for the K∗0analysis exhibits the same behavior as for the φ, but the problems appear at higher pTvalues than for φ. The mixed-event technique therefore remains the best available option for this K∗0analysis, even at the high end of the pTrange that was studied. The invariant mass distributions are fitted with a peak function added to a smooth residual background function. For K∗0, the peak is described using a Breit-Wigner function. The mass resolution of the detector for the φ →K−K+channel is of the same order of magnitude as the φwidth. Therefore, the φpeak is described using a Voigt function: a convolution of a Breit-Wigner function and a Gaussian which accounts for the mass resolution of the detector. The K∗0and φwidth parameters are by default fixed to their vacuum values; to calculate the systematic uncertainties, these parameters are allowed to vary freely and the φresolution parameter is fixed to the values (approximately 1–2 MeV/c2) extracted from the Monte Carlo simulations described below. The residual background is parameterized using a second-order polynomial. To evaluate the systematic uncertainties in the K∗0yields, a third-order polynomial is used instead. For the φsystematic uncertainties, a first-order polynomial and a function of the form A+BmKK +CmKK −2M(K±)are used. Here, A, B, and Care free parameters, mKK is the kaon-kaon pair invariant mass, and M(K±)is the mass of the K±. The fits are performed in the invariant mass intervals 0.75 <mπK<1.07 GeV/c2for the K∗0analysis and 0.995 <mKK <1.09 GeV/c2for the φ. The ranges of the fits are varied by ∼20 MeV/c2for K∗0and ∼10 MeV/c2for φ; the resulting changes in the yields are included in the systematic uncertainties. Finally, particle yields are extracted by integrating the invariant mass distribution in the peak region (0.798 ≤mπK≤ 0.994 GeV/c2for K∗0and 1.01 ≤mKK ≤1.03 GeV/c2for φ), subtracting the integral of the residual background function under the peak, and adding the yields in the tails of the peak fit function outside the integration region. The systematic uncertainty arising from “signal-extraction”, as quoted in Table 2, covers the aforementioned variations in the combinatorial background, mixed-event normalization region, residual background function, peak function, and fit range. An additional uncertainty originates from the procedure used to match track segments in the ITS with tracks in the TPC. The branching ratio correction for the φyield introduces a 1% uncertainty, while the corresponding uncertainty for K∗0is negligible. Uncertainties in the yields due to uncertainties in the material budget of the detector and the cross sections for hadronic interactions in that material are taken from a previous study [11]. The raw particle yields are corrected for the branching ratios, as well as the acceptance and efficiency of the reconstruction procedure. The correction for acceptance and efficiency (denoted as A ×ε) is calculated using several different event generators (PYTHIA6 Perugia 2011 tune [69], PYTHIA8 Monash 2013 tune [70], and EPOS-LHC [38]), with particles propagated through a simulation of the detector using GEANT3 [71]. No dependence on the generator is observed and the average A ×εfor the three generators is used in order to reduce statistical fluctuations. This correction is of the same order as reported in [11]. A dependence on multiplicity is observed; for pT<3GeV/c, A ×εincreases by ∼10% from multiplicity class I to class X. In the calculation of A ×ε, a weighting procedure is used to account for the fact that (1) A ×εmay vary significantly over the width of a pTbin in the measured spectrum and (2) the simulated pTdistributions used in the calculation do not necessarily have the same shapes as the measured pTdistributions. In the Monte Carlo simulations, the generated and reconstructed pTspectra (the denominator and numerator in the A ×εcalculation, respectively) are constructed in narrow pTbins and then weighted using a fit of the measured pT spectra. The simulated pTspectra after this weighting are used to recalculate A ×εin the wider pTbins used for the measured pT spectra. This procedure (also used in [8,9,47,48,50] and others) is repeated until the changes in the correction factor become negligible between iterations; no more than three iterations are needed for the process to converge. A “signal-loss” correction is also applied, which accounts for K∗0and φmesons in non-triggered events. This is evaluated using the same simulations as the acceptance and efficiency. To calculate this correction factor, the simulated resonance pTspectrum before triggering and event selection is divided by the corresponding pTspectrum after those selections for each multiplicity class. The signal-loss correction typically deviates from unity by <1%, but can deviate by ∼10% at low pTfor the lowest multiplicity class. Different event generators provide different descriptions of the non-triggered component of the various multiplicity classes. Following [9], the PYTHIA6 simulation is used to obtain the central values for this correction, while an uncertainty is evaluated by comparing the central values to those given by PYTHIA8 and EPOS-LHC. Finally, the pTspectra are normalized by the number of accepted events and corrected as in [9]to account for INEL >0 events that do not pass the event-selection criteria. This correction, which is calculated using the PYTHIA6 simulation, is most important (24%) for the lowest multiplicity class and is <1% for high-multiplicity collisions (classes I-VIII). 4. Results The pTspectra for K∗0and φin the various multiplicity classes, as well as the ratios of these spectra to the inclusive INEL >0spectrum, are shown in Fig. 1. For pT4GeV/cthe increase in the slopes of the pTspectra from low to high multiplicity is clearly visible. For higher pT, the spectra in different multiplicity classes all have the same shape, indicating that the processes that change the shape of the pTspectra in different multiplicity classes are dominant primarily at low pT. A similar behavior was reported for unidentified charged hadrons, K0 S, , , and for the same collision system [9,58]. The pT-integrated yields dN/ dyand mean transverse momenta pTare extracted from the pTspectra in the different multiplicity classes. For each multiplicity class, the φyield is extrapolated to the unmeasured region (pT<0.5GeV/c) by fitting a Lévy-Tsallis function [72–74]to the measured pTspectra. For multiplicity class ALICE Collaboration / Physics Letters B 807 (2020) 135501 5 Fig. 1. pTspectra of K∗0and φin pp collisions at √s=13 TeV for different multiplicity classes, scaled by factors as indicated. The lower panels show the ratios of the multiplicity-dependent pTspectra to the multiplicity-integrated INEL >0spectra (with both linear and logarithmic vertical scales). Fig. 2. Mean transverse momenta pTof K∗0and φas functions of dNch/ dη|η|<0.5. Results are shown for pp collisions at √s=13 and 7TeV[8], as well as for p–Pb collisions at √sNN =5.02 TeV [11]. The measurements in pp collisions at √s=13 TeV are also compared to values from common event generators [33,38,69,70]. Bars represent statistical uncertainties, open boxes represent total systematic uncertainties, and shaded boxes show the systematic uncertainties that are uncorrelated between multiplicity classes (negligible for p–Pb). I (X) the extrapolated φyield is 12% (34%) of the total yield. The K∗0is measured down to pT=0 and no low-pTextrapolation is needed to calculate dN/ dyfor that particle. The extrapolated yield at high pTis negligible for both particles. The pTis evaluated using the mean value of the fit function within each pTbin, weighted by the measured yield in each bin. For φ, the fit function is used to calculate the yield and mean pTin the low-pTextrapolation region, but this is not needed for K∗0. The sources of systematic uncertainty for the pTspectra also contribute to the systematic uncertainties of dN/ dyand pT, except for the ITS-TPC matching and branching ratio uncertainties, which are pT-independent and do not contribute to the uncertainties of the pTvalues. Additional uncertainties in dN/ dyand pTof φare evaluated by varying the fit range and the form of the extrapolation function: Bose-Einstein, Boltzmann, and Boltzmann-Gibbs blast-wave [75] distributions, as well as an exponential in mT(where mT≡M2+p2 T/c2and Mis the mass of the particle). The uncertainty in the total φyield due to the extrapolation in class I (X) is 1% (4.4%). There is no extrapolation uncertainty for the dN/ dyof K∗0. Varying the fit function produces a negligible change in pTfor K∗0and such variations are not included in the systematic uncertainties. The systematic uncertainties on the yield and pTare obtained by varying the parameters used in the default analysis. To investigate whether the changes in the yield dN/ dyand pTare correlated between different multiplicity bins, the effect of changing each parameter is simultaneously evaluated for both the minimum bias event class and each individual multiplicity class. The multiplicity-correlated and uncorrelated components of the systematic uncertainties are separated, with the latter being plotted as shaded boxes in Figs. 2-5. The mean transverse momenta pTfor K∗0and φare shown in Fig. 2as functions of dNch/ dη|η|<0.5and compared with other ALICE measurements and results from model calculations. The pT values in pp collisions at √s=7TeV[8] and 13 TeV follow approximately the same trend. The pTvalues of K∗0and φrise slightly faster as a function of dNch/ dη|η|<0.5in pp collisions than in p–Pb collisions for dNch/ dη|η|<0.55; the pTvalues in pp and p–Pb collisions both rise faster than those in Pb–Pb 6ALICE Collaboration / Physics Letters B 807 (2020) 135501 Fig. 3. Mean transverse momenta for K∗0and φare compared with those for K0 S, (anti)protons,  +, −++, and −++in pp collisions at √s=13 TeV as a function of dNch/ dη|η|<0.5[9,18]. The values for  +in the lowest multiplicity class and for −++are shifted horizontally for visibility. Bars represent statistical uncertainties, open boxes represent total systematic uncertainties, and shaded boxes show the systematic uncertainties that are uncorrelated between multiplicity classes. collisions as discussed in [8,11]. The measured pTvalues are compared with five different model calculations: PYTHIA6 (Perugia 2011 tune) [69], PYTHIA8 (Monash 2013 tune, both with and without color reconnection) [70], EPOS-LHC [38], and DIPSY [33]. PYTHIA8 without color reconnection provides an almost constant pTas dNch/ dη|η|<0.5increases; this is a very different behavior with respect to the trends measured by ALICE and given by the other model calculations. Turning color reconnection on in PYTHIA8 gives better qualitative agreement with the measurements, although the calculation still somewhat underestimates the pTvalues for hadrons containing strange quarks (K0 S, K∗0, φ, , , and )[9]. Color reconnection in PYTHIA8 introduces a flowlike effect, resulting in an increase in pTvalues with increasing multiplicity without assuming the formation of a medium that could flow [62]. PYTHIA 6 provides a good description of the pT values for φ, but underestimates pTfor K∗0. The pTvalues predicted by EPOS-LHC are consistent with the measured values for φ, but slightly below the values for K∗0. Among the model results obtained for the present work, EPOS-LHC gives the best agreement with the measured data. DIPSY gives a larger increase in pTfrom low to high dNch/ dη|η|<0.5than is actually observed; this discrepancy is greater for the φand is also observed for other strange hadrons [9]. The values of pTfor K∗0and φare compared with those for K0 S, (anti)protons, and strange baryons in the same collision system in Fig. 3. In central A–A collisions, a mass ordering of the pTvalues is observed; particles with similar masses (e.g., K∗0, p, and φ) have similar pT[11,51]. This behavior has been interpreted as evidence that radial flow could be a dominant factor in determining the shapes of hadron pTspectra in central A–A collisions. However, this mass ordering breaks down for peripheral Pb–Pb collisions, as well as p–Pb and pp collisions (see Fig. 7 in [14] and measurements reported in [8,9,18]). In pp collisions at √s=13 TeV, the pTvalues for K∗0are greater than those for the more massive proton and for the same multiplicity classes. The pTvalues for φexceed those for and even approach those for , despite the approximately 30% larger mass of the . This could be a manifestation of differences between the pTspectra of mesons and baryons or different behavior for resonances in comparison to the longer lived particles. In [8], the Boltzmann-Gibbs blast-wave model was used to predict the pTspectra of lightflavor hadrons based on a combined fit of π±, K±, and (anti)proton pTspectra. This study suggested that strange hadrons (K0 S, , , and ) and other light-flavor hadrons might participate in a common radial flow, even in pp collisions, but that K∗0and φdo not follow this common radial expansion (for details of this study, see [8]). The same behavior could result in the violation of mass ordering for pTseen at √s=13 TeV. Adeviation of the pTvalues of short-lived resonances above the trend for other hadrons could in principle be explained by re-scattering of the resonancedecay daughters during the hadronic phase of the collision, which is expected to be most important at low pT[41]. However, the strongest re-scattering phenomena occur in central A–A collisions, where no deviation from mass ordering is observed. In addition, such effects would be stronger for the shorter lived K∗0than for the φ, which decays predominantly outside the hadronic phase (even in central A–A collisions) and should be minimally affected by re-scattering. On the other hand, the observed violation of mass ordering could be due to differences between baryon and meson pTspectra. Baryon-to-meson ratios such as p/πand /K0 Sare observed [8,10]to be enhanced at intermediate pT(∼3GeV/c), even in pp and p–Pb collisions, while similar enhancement is not observed in meson-to-meson ratios like K/π. Differences between baryons and mesons have also been observed in the mTspectra of hadrons measured at RHIC energies [76,77]. For mT1GeV/c, meson mTspectra follow one common trend, while baryons follow a different, more steeply falling trend as a function of mT. Such differences between the shapes of baryon and meson spectra may result in mesons having larger pTvalues than baryons with comparable masses. The breakdown of mass ordering, with pT(p) < pT(K∗0) ≈pT() <pT(φ) ≈pT(), is a common feature of the models shown in Fig. 2. This behavior may be a consequence of hadron production via fragmentation at high pTor mT; meson formation requires only the production of a quark-antiquark pair, while baryon formation requires a diquark-antidiquark pair [76]. The pT-integrated yields of K∗0and φare shown in Fig. 4as functions of dNch/ dη|η|<0.5. For both particles, dN/ dyexhibits an approximately linear increase with increasing dNch/ dη|η|<0.5. Results for pp collisions at √s=7 and 13 TeV and for p–Pb collisions at √sNN =5.02 TeV follow approximately the same trends. This indicates that, for a given multiplicity, K∗0and φproduction rates do not depend on the collision system or energy. Similar results are seen for strange hadrons [9]. The dN/ dyvalues are also compared with those obtained from the same models studied for the discussion of pT. For the K∗0, EPOS-LHC and PYTHIA8 without color reconnection give the best descriptions, the other PYTHIA calculations exhibit fair agreement with the measured data, and DIPSY tends to overestimate the K∗0yields. The φyields tend to be slightly overestimated by EPOS-LHC and slightly underestimated by DIPSY, while the PYTHIA calculations underestimate the φyields by about 40%. The selected PYTHIA tunes also underestimate the yields of , , and by similar factors [9]. For these baryons, the EPOS-LHC description becomes less accurate with increasing strangeness content; DIPSY describes the and yields well, but underestimates the yields of [9]. The ratios of the pT-integrated particle yields K∗0/K, φ / π, φ /K, and  / φare shown in Fig. 5as functions of dNch/ dη|η|<0.5[9,18]. Within their uncertainties the ratios in pp collisions at √s=7 and 13 TeV and in p–Pb collisions at √sNN =5.02 TeV are consistent for similar values of dNch/ dη|η|<0.5. There is a hint of a decrease in K∗0/Kwith increasing dNch/ dη|η|<0.5in all three collision systems; for pp collisions at √s=13 TeV the K∗0/Kratio in the highest multiplicity class is below the low-multiplicity value at the 2.3σlevel (considering only the multiplicity-uncorrelated uncertainties). The decrease in K∗0/Kin central Pb–Pb collisions [11, 48,49] has been attributed to re-scattering of the K∗0decay products in the hadronic phase of the collision [46]. It remains an open question whether a decrease in pp collisions could be caused by the same mechanism. EPOS-LHC provides the best description of the K∗0/Kratio in pp collisions at √s=13 TeV. PYTHIA and DIPSY ALICE Collaboration / Physics Letters B 807 (2020) 135501 7 Fig. 4. pT-integrated yields dN/ dyof K∗0(average of the particle and antiparticle) and φas functions of dNch/ dη|η|<0.5. Results are shown for pp collisions at √s=13 and 7TeV[8], as well as for p–Pb collisions at √sNN =5.02 TeV [11]. The measurements in pp collisions at √s=13 TeV are also compared with values from common event generators [33,38,69,70]. Bars represent statistical uncertainties, open boxes represent total systematic uncertainties, and shaded boxes show the systematic uncertainties that are uncorrelated between multiplicity classes. Fig. 5. Ratios of pT-integrated particle yields K∗0/K, φ / π, φ /K, and  / φin pp collisions at √s=13 TeV as functions of dNch/ dη|η|<0.5[9,18]. These measurements are compared with data from pp collisions at √s=7TeV[8], p–Pb collisions at √sNN =5.02 TeV [11,13], and Pb–Pb collisions at √sNN =2.76 TeV [48,49]. The widths of the boxes for pp collisions at √s=13 TeV and p–Pb collisions do not represent the uncertainties of dNch/ dη|η|<0.5. The measurements for pp collisions at √s=13 TeV are also compared to results from common event generators [33,38,69,70]and a Canonical Statistical Model calculation [8]. tend to overestimate the ratio for large multiplicities and do not reproduce the apparent decrease with increasing dNch/ dη|η|<0.5. The φ / πratio gradually increases from the lowest-multiplicity pp collisions to mid-central Pb–Pb collisions. This ratio compares the yields of two mesons with zero net strangeness, one of which has hidden strangeness. The canonical statistical model (CSM) [8] with a chemical freeze-out temperature of 156 MeV predicts that this ratio should have little dependence on the multiplicity, since the φwould not be subject to canonical suppression. The results of the CSM calculation are inconsistent with the observed trend of the φ / πratio. For pp collisions at √s=13 TeV, the increasing trend of the φ / πratio is reproduced fairly well by the EPOS-LHC and DIPSY models, while the PYTHIA calculations underestimate the magnitude of the ratio. The φ /Kratio also follows a similar trend in the three collision systems. It is fairly constant as a function of dNch/ dη|η|<0.5, although there is an apparent small increase with dNch/ dη|η|<0.5from the lowest multiplicities up to dNch/ dη|η|<0.5≈400. EPOS-LHC somewhat overestimates the φ /Kratio, but is closer to the measured values than PYTHIA, which significantly underestimates φ /K. While PYTHIA6 and DIPSY underestimate the φ /Kratio, both results exhibit small increases with increasing multiplicity, which is qualitatively similar to the measured trend. The CSM calculation does not describe the behavior of the measured φ /Kratio for the dNch/ dη|η|<0.5range spanned by the ALICE pp measurements. In addition to comparing the yields of φto pions and kaons, it may be instructive to compare and φ. These two particles contain the same number of strange valence (anti)quarks: φis a s¯ sbound state and contains two strange valence quarks. However, would be subject to canonical suppression, unlike the strangeness-neutral φ. Fig. 5also shows the  / φratio in pp, p–Pb, and Pb–Pb collisions. The ratio increases with increasing dNch/ dη|η|<0.5for low-multiplicity collisions and is then fairly constant for a wide range of multiplicities: from pp and p–Pb collisions at dNch/ dη|η|<0.5≈7to central Pb–Pb collisions. There is a possible small increase in the  / φratio from dNch/ dη|η|<0.5≈7 to the highest-multiplicity p–Pb collisions, as well as a difference on the 1.5σlevel between the p–Pb and Pb–Pb measurements at dNch/ dη|η|<0.5≈50. Nevertheless, there is no clear increase in the ratio for dNch/ dη|η|<0.5≥7. The decrease in  / φwith decreasing dNch/ dη|η|<0.5for low multiplicities could be interpreted as evidence of canonical suppression in small systems; the canonical statistical model predicts a decrease in the  / φratio with decreasing dNch/ dη|η|<0.5that is qualitatively similar to the measured data. However, canonical suppression would also result in an increase in the φ /Kratio with decreasing dNch/ dη|η|<0.5, which is not observed. Given that and K have different numbers of strange valence (anti)quarks, it is expected that would be more affected by canonical suppression [8]. It will be interesting to extend the study of the φ /Kratio to lower multiplicities to test if there is any increase in this ratio due to canonical suppression of kaon yields. The measured multiplicity evolution of the  / φand φ /Kratios suggests that the φmeson behaves as if it had between 1 and 2 units of strangeness: i.e., is enhanced more than φ, which is (possibly) enhanced more than K. In addition, there are indications of increases in the p/πand /K0 Sratios with increasing dNch/ dη|η|<0.5[8,9] which are qualitatively similar to the increase in  / φ, but smaller in magnitude. This suggests that baryon-meson differences (e.g., baryon suppression or meson enhancement) might be a contributing factor, but not the only reason, for the low-multiplicity behavior of the  / φratio. EPOS-LHC, which includes core-corona effects, gives an increasing trend in 8ALICE Collaboration / Physics Letters B 807 (2020) 135501 Fig. 6. Ratios of particle yields K∗0/K0 Sand φ /K0 Sas functions of pT[9]for low (X) and high (II) multiplicity classes. The middle panels show the double ratios: the measurements in class II divided by those in class X. The significance of the deviations of the double ratios from unity is plotted in the lower panels, with dashed lines indicating a deviation at the 3σlevel. Bars represent the statistical uncertainties, while boxes represent the part of the systematic uncertainty that is uncorrelated between multiplicity classes II and X.  / φwith increasing dNch/ dη|η|<0.5, although the values of the ratio and its flattening at high multiplicity are not particularly well described. In contrast, PYTHIA gives a constant or decreasing value of  / φwith increasing dNch/ dη|η|<0.5, which is inconsistent with the observed trend. DIPSY, which includes rope hadronization, describes the  / φratio over a wide dNch/ dη|η|<0.5range, only failing to describe the decrease in the ratio with decreasing multiplicity for the lowest dNch/ dη|η|<0.5values. The pTdependence of the particle ratios K∗0/K0 Sand φ /K0 S is shown in Fig. 6for low and high multiplicity classes (X and II, respectively). Both ratios increase at low pTand saturate for pT2.5GeV/c; however, for pT2.5GeV/cthe K∗0/K0 Sand φ /K0 S ratios in the high multiplicity class (II) are less than in the lowest multiplicity class (X). This behavior is qualitatively consistent with observations in Pb–Pb collisions at √sNN =2.76 TeV [49], where the K∗0/K and φ /Kratios at low pTin central collisions are lower compared to pp collisions. The decrease in the low-pTK∗0/Kratio in central Pb–Pb collisions with respect to pp collisions is larger than the decrease in the φ /Kratio, which could be expected due to the presence of re-scattering effects. To quantify the decrease in these particle ratios in pp collisions at √s=13 TeV, the middle panels of Fig. 6show the double ratios: the high-multiplicity values divided by the low multiplicity values. The double ratios are consistent with unity for pT2.5GeV/c, which suggests a common evolution of the pTspectra for these three mesons. However for pT2.5GeV/c, the suppression of the K∗0/K0 Sratio from low to high-multiplicity collisions is greater than the suppression of the φ /K0 Sratio. This is quantified in the lower panels of Fig. 6, where the significance of the deviations of the double ratios from unity is shown. For pT<1.2GeV/c, the K∗0/K0 Sdouble ratio deviates from unity by 4–6.6 times its standard deviation, while the φ /K0 Sdouble ratio deviates from unity at about the 3σlevel for 0.6 <pT<1.4GeV/c. This difference may be a hint of rescattering in small collision systems. 5. Conclusions The ALICE Collaboration has reported measurements of the K∗0 and φmesons at midrapidity in pp collisions at √s=13 TeV in multiplicity classes. The results have many qualitative similarities to those reported for longer lived hadrons in the same collision system [9,18,19] and are consistent with previous measurements [8]of K∗0and φin pp collisions at √s=7TeV. The slopes of the pTspectra of K∗0and φare observed to increase with increasing multiplicity for pT4GeV/c, which is qualitatively similar to the collective radial expansion observed in Pb–Pb collisions, but can also be explained through color reconnection. In contrast, the shapes of the pTspectra are the same for all multiplicity classes at high pT. Both the pT-integrated yields and the mean transverse momenta increase with increasing chargedparticle multiplicity at midrapidity, with approximately linear increases for the yields. It appears that, for a given multiplicity value, the yields of these particles are independent of collision system and energy, while the pTvalues follow different trends for different collision systems. The mass ordering of the pTvalues observed in central Pb–Pb collisions is violated in pp collisions, with the K∗0and φmesons having greater pTthan baryons with similar masses. The EPOS-LHC model describes the multiplicity dependence of the yields and pTfairly well for pp collisions at √s=13 TeV. There are hints that the yields of K∗0may be reduced, particularly at low pTand high multiplicity, by rescattering of its decay daughters in a short-lived hadron-gas phase in pp collisions; similar behavior is observed in Pb–Pb collisions. The φ / πratio increases with increasing dNch/ dη|η|<0.5and the yields of the φmeson evolve similarly to particles with 1 and 2 units of open strangeness. The φ /K and  / φratios are both fairly constant, exhibiting only slow increases over wide multiplicity ranges, although the  / φratio decreases with decreasing dNch/ dη|η|<0.5for the lowest multiplicity pp and p–Pb collisions. In high-multiplicity pp and p–Pb collisions, these ratios reach values observed in central Pb–Pb collisions. This multiplicity evolution is not consistent with simple descriptions of canonical suppression, but is qualitatively described by the DIPSY model, which includes rope hadronization effects. These new measurements of the φprovide further constraints for theoretical models of strangeness production in small collision systems. 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 ALICE Collaboration / Physics Letters B 807 (2020) 135501 15 94 Nuclear Physics Institute of the Czech Academy of Sciences, ˇ Rež u Prahy, Czech Republic 95 Oak Ridge National Laboratory, Oak Ridge, TN, United States 96 Ohio State University, Columbus, OH, United States 97 Petersburg Nuclear Physics Institute, Gatchina, Russia 98 Physics department, Faculty of science, University of Zagreb, Zagreb, Croatia 99 Physics Department, Panjab University, Chandigarh, India 100 Physics Department, University of Jammu, Jammu, India 101 Physics Department, University of Rajasthan, Jaipur, India 102 Physikalisches Institut, Eberhard-Karls-Universität Tübingen, Tübingen, Germany 103 Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany 104 Physik Department, Technische Universität München, Munich, Germany 105 Politecnico di Bari, Bari, Italy 106 Research Division and ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum für Schwerionenforschung GmbH, Darmstadt, Germany 107 Rudjer Boškovi´c Institute, Zagreb, Croatia 108 Russian Federal Nuclear Center (VNIIEF), Sarov, Russia 109 Saha Institute of Nuclear Physics, Homi Bhabha National Institute, Kolkata, India 110 School of Physics and Astronomy, University of Birmingham, Birmingham, United Kingdom 111 Sección Física, Departamento de Ciencias, Pontificia Universidad Católica del Perú, Lima, Peru 112 St. Petersburg State University, St. Petersburg, Russia 113 Stefan Meyer Institut für Subatomare Physik (SMI), Vienna, Austria 114 SUBATECH, IMT Atlantique, Université de Nantes, CNRS-IN2P3, Nantes, France 115 Suranaree University of Technology, Nakhon Ratchasima, Thailand 116 Technical University of Košice, Košice, Slovakia 117 Technische Universität München, Excellence Cluster ‘Universe’, Munich, Germany 118 The Henryk Niewodniczanski Institute of Nuclear Physics, Polish Academy of Sciences, Cracow, Poland 119 The University of Texas at Austin, Austin, TX, United States 120 Universidad Autónoma de Sinaloa, Culiacán, Mexico 121 Universidade de São Paulo (USP), São Paulo, Brazil 122 Universidade Estadual de Campinas (UNICAMP), Campinas, Brazil 123 Universidade Federal do ABC, Santo Andre, Brazil 124 University of Cape Town, Cape Town, South Africa 125 University of Houston, Houston, TX, United States 126 University of Jyväskylä, Jyväskylä, Finland 127 University of Liverpool, Liverpool, United Kingdom 128 University of Science and Technology of China, Hefei, China 129 University of South-Eastern Norway, Tonsberg, Norway 130 University of Tennessee, Knoxville, TN, United States 131 University of the Witwatersrand, Johannesburg, South Africa 132 University of Tokyo, Tokyo, Japan 133 University of Tsukuba, Tsukuba, Japan 134 Université Clermont Auvergne, CNRS/IN2P3, LPC, Clermont-Ferrand, France 135 Université de Lyon, Université Lyon 1, CNRS/IN2P3, IPN-Lyon, Villeurbanne, Lyon, France 136 Université de Strasbourg, CNRS, IPHC UMR 7178, F-67000 Strasbourg, France, Strasbourg, France 137 Université Paris-Saclay Centre d’Etudes de Saclay (CEA), IRFU, Départment de Physique Nucléaire (DPhN), Saclay, France 138 Università degli Studi di Foggia, Foggia, Italy 139 Università degli Studi di Pavia, Pavia, Italy 140 Università di Brescia, Brescia, Italy 141 Variable Energy Cyclotron Centre, Homi Bhabha National Institute, Kolkata, India 142 Warsaw University of Technology, Warsaw, Poland 143 Wayne State University, Detroit, MI, United States 144 Westfälische Wilhelms-Universität Münster, Institut für Kernphysik, Münster, Germany 145 Wigner Research Centre for Physics, Budapest, Hungary 146 Yale University, New Haven, CT, United States 147 Yonsei University, Seoul, Republic of Korea iDeceased. ii Dipartimento DET del Politecnico di Torino, Turin, Italy. iii M.V. Lomonosov Moscow State University, D.V. Skobeltsyn Institute of Nuclear, Physics, Moscow, Russia. iv Department of Applied Physics, Aligarh Muslim University, Aligarh, India. vInstitute of Theoretical Physics, University of Wroclaw, Poland.