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Constituent Quark Number Scaling from Strange Hadron Spectra in Pp Chinese Physics C Vol. 44, No. 1 (2020) 014101 Constituent quark number scalingp from strange hadron spectra in pp collisions at s = 13 TeV* 1 2 1;1) 2;2) Jian-Wei Zhang(张建伟) Hai-Hong Li(李海宏) Feng-Lan Shao(邵凤兰) Jun Song(宋军) 1School of Physics and Engineering, Qufu Normal University, Shandong 273165, China 2Department of Physics, Jining University, Shandong 273155, China p − Abstract: We show that the pT spectra of Ω and ϕ at midrapidity in the inelastic events in pp collisions at s = 13 TeV exhibit a constituent quark number scaling property, which is a clear signal of quark combination mechanism at hadronization. We use a quark combination model with equal velocity combination approximation to systematically p study the production of identified hadrons in pp collisions at s= 13 TeV. The midrapidity pT spectra for protons, Λ, Ξ−, Ω−, ϕ and K∗ in the inelastic events are simultaneously fitted by the model. The multiplicity dependence of the yields of these hadrons are also well understood. The strong pT dependence of the p/ϕ ratio is well explained by the model, which further suggests that the production of two hadrons with similar masses is determined by their quark content at hadronization. The p spectra of strange hadrons at midrapidity in different multiplicity classes in pp colli- p T sions at s = 13 TeV are predicted for further tests of the model. The midrapidity p spectra of soft (p < 2 GeV/c) p T T strange quarks and up/down quarks at hadronization in pp collisions at s = 13 TeV are extracted. Keywords: strange hadron production, quark combination, hadronization, quark-gluon plasma DOI: 10.1088/1674-1137/44/1/014101 1 Introduction ness [4-6]. Theoretical studies of these new phenomena mainly focus on how the features of a small partonic sys- tem are related to these observations by considering dif- Most hadrons produced in high energy collisions have ferent mechanisms, such as the color re-connection, string a relatively low (transverse) momentum perpendicular to the beam axis. The production of soft hadrons is mainly overlap and/or color rope [7-10], or by considering the driven by the soft QCD processes, and in particular the creation of mini-QGP or the phase transition [11-16]. non-perturbative hadronization. Experimental and theor- In our latest works [17-21], by studying the available etical studies of soft hadron production are important for data for the hadronic pT spectra and yields, we proposed understanding the properties of the soft parton system a new understanding of the novel features of hadron pro- created in collisions, and for testing and/or developing duction in small quark/parton systems created in pp phenomenological models. Heavy-ion physics at the SPS, and/or p-Pb collisions at the LHC energies, i.e. a change RHIC and LHC energies shows that quark-gluon plasma of the hadronization mechanism from the traditional frag- (QGP) is created in the early stage of collisions. In pp mentation to quark (re-)combination. In the quark (re-) and/or pp¯ collisions, it is usually assumed that QGP is combination mechanism (QCM), some typical features of not created, at least not up to the RHIC energies. the identified hadron production appear, such as the en- However, recent measurements at the LHC energies show hanced baryon-to-meson ratio and quark number scaling a series of new hadron production phenomena in pp colli- of hadron elliptical flow at intermediate pT . These fea- sions, such as the ridge and collectivity behavior [1-3], tures were observed in the relativistic heavy-ion colli- increased baryon-to-meson ratio, and increased strange- sions [22-24], and recently also in pp and p-Pb collisions Received 3 June 2019, Revised 1 October 2019, Published online 19 November 2019 * Supported by National Natural Science Foundation of China (11575100), and by Shandong Province Natural Science Foundation(ZR2019YQ06, ZR2019MA053), and by A Project of Shandong Province Higher Educational Science and Technology Program (J18KA228) 1) E-mail: [email protected], Corresponding author 2) E-mail: [email protected], Corresponding author Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must main- tain attribution to the author(s) and the title of the work, journal citation and DOI. Article funded by SCOAP3 and published under licence by Chinese Physical Society and the Institute of High Energy Physics of the Chinese Academy of Sciences and the Institute of Modern Physics of the Chinese Academy of Sciences and IOP Pub- lishing Ltd 014101-1 Chinese Physics C Vol. 44, No. 1 (2020) 014101 at the LHC energies in the high multiplicity classes [3, 4, Ω− and ϕ in QCM 6, 25]. In particular, a quark number scaling property of 1=2 = κ 1=3 = κ1=2 ; fϕ (2pT ) ϕ,Ω fΩ (3pT ) ϕ fs (pT ) (3) the hadron transverse momentum spectra was observed inp = : κ = κ1=2/κ1=3 p-Pb collisions at sNN 5 02 TeV [17]. where ϕ,Ω ϕ Ω is independent of momentum. In or- Recently, the ALICE collaboration reported pT spec- der to check this scaling property, we apply the follow- − tra of the identified hadronsp in different multiplicity ing operation on the dN=(dpT dy) data for Ω and ϕ at = − classes in pp collisions at s 7 TeV [26], and prelimin-p midrapidity [26]: (i) we divide the pT bin for Ω (ϕ) by 3 ary data for the inelastic events in pp collisions at s = 13 (2), (ii) take the 1=3 (1=2) power of the measured − 1=3 TeV [27]. For the first time, a clear signal of the quark dN=(dpT dy) for Ω (ϕ), and (iii) multiply (dNΩ=(dpT dy)) number scaling property in the hadronic pT spectra in pp by a constant factor κϕ,Ω , so that the data points for small collisions is seen. Considering the production of baryons pT (pT . 0.5 GeV/c) are in coincidence with the scaled Ω− (sss) and mesons ϕ(ss¯), the momentum distribution data for ϕ as much as possible. We show in Fig. 1 the ≡ = − ϕ functions f (pT ) dN dpT in QCM with the equal velo- scaled data for Ω pand in different multiplicity classes city combination approximation read as in pp collisions at s = 7 TeV. The relative statistical un- [ ( )] 3 pT certainties of the scaled data are only a few percent, and fΩ (p ) = κΩ f ; (1) T s 3 are shown as rectangles with filled colors in the figure. ( ) ( ) [ ( )] We see that in the high multiplicity classes, e.g. Fig.1(a) 2 pT pT pT and (b), the scaled data for Ω− are consistent with those fϕ (pT ) = κϕ fs fs¯ = κϕ fs : (2) 2 2 2 for ϕ, and therefore the quark number scaling property Here, κϕ and κΩ are coefficients independent of mo- holds. This verifies our argument in the recent work [21], mentum. fs;s¯ (pT ) is the s (s¯) quark distribution at hadron- and is a clear signal of quark combination hadronization ization, and we assume fs (pT ) = fs¯ (pT ) in the center in pp collisions at the LHC energies. In the low multipli- rapidity region at the LHC energies. With the above two city classes, Fig. 1(c) and (d), the scaled data for Ω− are formulas, we get a correlation between the production of somewhat flatter than for ϕ at pT & 1 GeV/c, and the Fig. 1. (color online) The scaling property in the dN=dp dy data for Ω− and ϕ at midrapidity in different multiplicity classes in pp col- p T − lisions at s = 7 TeV. The coefficient κϕ,Ω in the four multiplicity classes is taken as (1.76, 1.82, 1.83, 1.93). The data for Ω and ϕ are taken from Ref. [26]. 014101-2 Chinese Physics C Vol. 44, No. 1 (2020) 014101 quark number scaling property seems to be broken to a tios or correlations of the hadronic yields and pT spectra. certain extent. We note that this is probably due to the We compare our results with the available experimental threshold effects of strange quark production [21]. data to test the quark combination hadronization in pp − In Fig. 2, we show the scaled data forp Ω and ϕ in pp collisions at the LHC energies. Predictions are made for collisions at s = 7 and 13 TeV [26-29] as a guide for en- future tests. ergy dependence. We see that the quark number scalingp The paper is organized as follows: Sec. 2 briefly in- property in the inelastic events in pp collisions at s = 7 troduces the model of quark (re)combination mechanism TeV is broken to a certain extent, but it holds well in thep with the equal velocity combination approximation. Sec. inelastic events in pp collisions at s = 13 TeV. This is 3 and Sec. 4 present our results and relevant discussions an indication of the quark combination hadronization at for the inelastic events and different multiplicity classes. higher collision energies. A summary and discussion is given in Sec. 5. On the other hand, we performed a run of event gen- erators Pythia8 [30, 31] and Herwig6.5 as a naive test of 2 Quark combination model with the equal the string andp cluster fragmentation mechanisms in pp velocity combination approximation collisions at s = 13 TeV. Fig. 3 shows the results for the scaled pT spectra of Ω and ϕ at mid-rapidity given by the two event generators. Here, we adopted the Pythia ver- Quark (re-)combination/coalescence mechanism was proposed in the 1970s [32] and has many applications in sion 8240 and Herwig version 6521.
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