Model calculations of φ-meson production in small collision systems

Ultrarelativistic ion collisions provide the unique possibility to study the quark-gluon plasma, a state of matter formed in the universe at the very first moments after the Big Bang. The minimal temperature and baryon density for the quark-gluon plasma formation requires scrutiny, since the signatures of the quark-gluon plasma formation are observed in large systems (such as Au+Au) at sNN=200GeV , whereas collective effects in p+p collisions are not revealed. The φ-meson production measurements are considered to be a convenient tool to investigate the collision dynamics, as it is sensitive to the quark-gluon plasma effects. To interpret the nuclear modification effects and to study the process of the possible QGP formation the comparison with different theoretical models predictions is needed. This paper presents the comparison of the obtained experimental results on φ-meson production in small collision systems (p+Al, p+Au) at sNN=200GeV to default and string melting versions of the AMPT model and PYTHIA model predictions. The results indicate that the minimal conditions (temperature and baryon density) for a QGP formation may lie in between in p+Al and p+Au collisions.


Introduction
It is generally accepted that in the first moments after the Big Bang, a first order/cross-over phase transition from nuclear matter consisting of hadrons to an unbound state of quarks and gluons, also known as Quark Gluon Plasma (QGP) [1], occured in the universe.
The detailed study of heavy-ion collisions at RHIC and LHC suggested, that the colliding system evolution is the same as the one of the early Universe [2]. Therefore, investigation of medium with partonic degrees of freedom (i.e. QGP) is one of the most significant directions of research in relativistic ion collision physics.
It was established that QGP is formed in large collision systems such as Au+Au [3], Cu + Au at √ s N N = 200 GeV and U+U at √ s N N = 192 GeV [4] whereas p+p collisions dynamics is well described with pQCD calculations [5]. The recent observation of the collective behavior in small collision systems such as p+Au, d+Au, 3 He+Au provides the possibility to assume that QGP could be formed in these collisions [6]. To reveal the minimal conditions for the QGP formation in small collision systems further study is required.
One of the ways to study QGP widely used in relativistic ion collisions is measurements of light hadron production [3]. The study of nuclear modification in the collision allows observation of various hot (suggesting that QGP is formed) [7,8] and cold (reflecting the initial state of the collision) [9,10]  Among the large variety of light hadrons, ϕ-meson is of particular interest since it contains strange quarks (ss), has relatively small hadronic interaction cross-section, and longer than QGP lifetime (42 fm/c vs. 5 fm/c [2]) [11].
This paper presents the experimental results on ϕ-meson production in small collision systems (p+Al, p+Au) at √ s N N = 200 GeV and its comparison to default and string melting versions of the AMPT model [12] and PYTHIA model [13,14] predictions.

Data analysis
Experimental data sets used in the analysis were collected by PHENIX experiment at RHIC [15] at the energy of √ s N N = 200 GeV for p+Al and p+Au collisions at midrapidity (η < 0.35). The ϕ-meson production was measured using the kaon decay channel. The values of the ϕ-meson mass, mean lifetime and probability of decay via the kaon channel (Br) are presented in Table 1 [11].
Nuclear modification factors R AB [16] of nuclei collisions are used to study collective effects, affecting the spectra and are calculated as where d 2 N AB /dydp T is the ϕ-meson invariant yield for a certain centrality bin of A+B collision, d 2 N pp /dydp T -is the corresponding ϕ-meson invariant yield for p+p collisions, N coll -the number of nucleon-nucleon collisions in the A + B system for selected centrality intervals, estimated with the Glauber Monte-Carlo simulation, and f bias -Bias factor [17]. The p+p reference data used in the analysis is taken from [18]. In case R AB = 1, it is likely that there are no nuclear matter effects in the nucleus collision, and the interaction can be represented as a superposition of the elementary nucleon-nucleon collisions. Otherwise, if R AB > 1(< 1), then the particle yields are enhanced (suppressed), which might indicate the presence of various hot and cold nuclear matter effects in the A+B collision. Experimental values of ϕ-meson nuclear modification factors in p+Al and p+Au collisions at √ s N N = 200 GeV are compared with theoretical predictions obtained using the PYTHA and AMPT software packages.
The Lund string fragmentation model is widely used to describe p+p collisions and for QCD calculations [19]. It implies that the strong interaction, that is the gluon exchange between quarks, is represented in the form of a string, endings with quarks.
In 1997, on its basis, the PYTHIA software package was created, which aims to simulate the hadronization process, soft and hard QCD processes. The modern implemented version of the model is PYTHIA 8.303 [13], that was used in the current study for calculation of ϕ-meson invariant spectra in p+p collisions.
To generate the collisions with heavy ions (heavier than p), a new PYTHIA/Angantyr hybrid model [14] was developed. In this model the A + B collision is described as combination of the binary nucluon-nucleon collisions, considering a distinction between its different types. The ϕmeson R AB were estimated following the procedure used for experimental data as a ratio of the ϕ-meson production spectrum in p+Al, p+Au, d+Au or 3 He+Au collision to the same hadron production spectrum in p+p collision at the same energy √ s N N = 200 GeV, normalized by the same as in experiment N coll values. Thereby the inaccuracy of the ϕ-meson spectra description in p+p collisions cancels. Another theoretical model widely used for describing the relativistic ions collision evolution is AMPT model [12], which provides a possibility to study the process of the possible QGP formation. The AMPT default model consists of the following components: the initial conditions; partonic cascade, considering confined state of quarks and gluons; the conversion from the partonic to the hadronic matter based on Lund string fragmentation model; and hadronic interactions. In the extended string melting version of the AMPT model, the strings melt into partonic degrees of freedom (QGP phase is being formed) and a quark coalescence model [20] is used to combine partons into hadrons. The baseline for the AMPT calculations of R AB is ϕ-meson invariant p T spectra from experimental p+p collisions [18].   The ϕ-meson R AB in p+Al collisions are well described with PYTHIA model and default version of AMPT model predictions, which might indicate the absence of collective effects in the interaction.

Results
Contrary to this, ϕ-meson R AB in p+Au collisions are in agreement with string melting version of AMPT model predictions within uncertainties, whereas PYTHIA model and default version of AMPT model predictions underestimates the experimental data. This might indicate that QGP is beeing formed in p+Au collisions at √ s N N = 200 GeV.
In conclusion, the minimal conditions (temperature and baryon density) for a QGP formation may lie in between the conditions of p+Al and p+Au collisions.
The further study of QGP effects in small system collisions, such as 3 He+Au, and comparison of all available experimental results to theoretical predictions considering hot and cold nuclear matter effects is necessary to reveal possible QGP formation.