1 Introduction

Low-mass vector meson (LVM) production in high energy p+p and d+Au collisions is a useful tool in understanding the dynamics of the hot matter created in the reaction. In p+p collisions, LVM provides data for tuning the event generator inspired by Quantum Chromodynamics (QCD) and is a good reference for heavy-ion collisions. In heavy-ion collisions, LVM, due to their short lifetime and strong decay in the medium, carry important information on the hot and dense state of matter formed in such collisions [1-6]. Strangeness enhancement [7] is a phenomenon associated with soft particles in bulk matter, which can be studied via ϕ meson production [8-16] and the N(ϕ)/N(ρ+ω) ratio. There are well tuned QCD event generators in p+p collision, such as the PYTHIA [17]. Microscopic transport model calculations including the di-lepton channel, are also available in the literature. For example, the parton-hadron string dynamics (PHSD) covariant transport model [18], which shows a fair agreement with the STAR data [19-21]. We provided another study on LVM production based on a multi-phase transport model (AMPT) and we focused on the forward rapidity region. We found that the N(ϕ)/N(ρ+ω) ratio is sensitive to strange quark dynamics and proposed further experiment measurement on LVM production at froward rapidity in high energy heavy-ion collisions.

The article is organized as follows. Sect. 2 is a brief description of the AMPT model. Section 3 is the results and discussion. A final summary is given in Sect. 4.

2 THE AMPT MODEL

The AMPT model is a hybrid model including the following four main components [22]: the initial condition, the partonic interactions, the conversion from partonic matter into hadronic matter, and the hadronic interactions. The initial condition, which includes the spatial and momentum distributions of minijet partons and soft string excitation, are obtained from the HIJING model [23]. The scatterings among partons are modeled by Zhang’s parton cascade (ZPC) [24], which presently includes only two-body elastic scatterings with cross sections obtained from the pQCD with screening mass. After the freeze-out of partons, two different methods are used in order to describe the conversion from partonic matter into hadronic matter, leading to the two different versions of the AMPT model: 1) the default version and 2) the string-melting version. In the default AMPT model, partons are recombined with their parent strings when they stop the interaction, and the resulting strings are converted to hadrons using a Lund string fragmentation model [25]. In the AMPT model with string melting, a simple quark coalescence model, based on the quark spatial information, is used to combine partons into hadrons. After the hadronization process, in both the default and string-melting versions, the dynamics of the hadronic matter is then described by A Relativistic Transport (ART) model [26]. The details of the AMPT model can be found in Ref. [22]. In the present study, we use the version of AMPT-v1.26-v2.26 with the QCD coupling constant α_s = 0.33, and the screening mass μ = 3.2 fm^-1 to obtain a parton scattering cross section of 1.5 mb in the ZPC stage. These new parameters, i.e. the coupling constant and the screening mass, will help to describe charged particle multiplicity density and the elliptic flow in heavy-ion collisions at the Relativistic Heavy Ion Collider (RHIC) [27]. All the other parameters are from the AMPT manual [22].

3 RESULTS AND DISCUSSION

3.1 Low mass vector meson production in p+p and d+Au collisions

Figure 1 shows the ρ, ω, and ϕ $p_T$ spectra from the AMPT model in comparison to the experimental data. From the figure, one can see that the default AMPT model describes the ρ+ω data better than the string melting version, while for the ϕ meson calculation, which was published elsewhere [29], the AMPT with string melting version describes the data better than the default version. The new findings are consistent with our earlier study on mid-rapidity identified particle production in d+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV [30]: the final state interaction in the default AMPT version is important for proton and π production. However, for the ϕ meson, the strangeness production in the string melting version enhance the rate and describes the data better than the pure hadonic phase version.

Fig. 1.Full-screen View

Invariant yields of ρ, ω, and ϕ as a function of $p_T$ in p+p collisions at $\sqrt{s_{NN}}$ = 200 GeV. Dashed and solid lines represent the results from the AMPT model with string melting scenario and the default version, respectively. Data are results from the PHENIX Collaboration [28].

Figure 2 presents the ρ, ω, and ϕ rapidity in p+p collisions at $\sqrt{s_{NN}}$ = 200 GeV. For the (ρ+ω), the default AMPT describes the data well, while the AMPT with string melting version under predicts the data in the full rapidity range. For the ϕ meson, the AMPT model with string melting version does a better job than the default version. This is consistent with the findings from the $p_T$ spectra [c.f. Fig. 1].

Fig. 2.Full-screen View

Lines represent the rapidity distributions of ρ, ω, and ϕ in the AMPT model, while this data points result from the PHENIX Collaboration [28].

For a heavy system like d+Au collisions, as shown in Fig.3, the default AMPT model predicts a higher yield for (ρ+ω) than the melting version, while for the ϕ meson, the string melting version, has a higher rate than the default version. In comparison to the available ϕ meson data [31], also discussed in the earlier paper [29], the AMPT model with the string melting version predicts the ϕ meson yield in the d-going direction well, while it slightly under-predicted the high $p_T$ yield in the Au-going direction. The reason may be due to the small quark mass used in the model calculation and the particles that are less affected by the radial flow [22]. Future experimental measurement on ρ and ω production will be helpful.

Fig. 3.Full-screen View

Low-mass vector meson $p_T$ spectra in forward rapidity d+Au collisions. Lines represent results from the AMPT model calculation, and data points are experiment result on ϕ meson production from the PHENIX Collaboration [31]. The panel (a) and (b) are the results in the d-going and Au-going direction, respectively.

3.2 N(ϕ)/N(ρ+ω) ratio vs. transverse momentum and impact parameter

Figure 4 shows the N(ϕ)/N(ρ+ω) ratio as a function of $p_T$ in p+p and d+Au collisions. From the figure, one can see that the AMPT model with the sting melting version (the red solid lines) describes the ratio well in p+p collisions (the blue solid circles), while the default version (the dash blue lines) under-predicts the ratio. It may be due to the enhanced strangeness production in the melting version, while the default version is only involved in the pure hadronic transport process. The ratio from the d+Au collisions shows similar behaviour as observed in p+p system. It will be interesting to see how the data will be in future experiment in future.

Fig. 4.Full-screen View

The particle yield ratio vs. $p_T$. The upper panel is the results of p+p collisions, and the bottom panel represents the calculations in d+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV.

Figure 5 predicts the N(ϕ)/N(ρ+ω) in d+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV. Two different types of collisions were selected for systematic study: the nucleon+Au collision type and the d+Au collision type. One can see that the ratios increase as a function of N_part in low N_part and saturate at certain values of N_part: in the n(p)+Au type collisions, the ratio becomes flat after N_part > 3 while for the d+Au type collisions, the ratio becomes flat after N_part > 5. Future experimented measurements on the ratio may help to pin down the possible difference.

Fig. 5.Full-screen View

The ratio of N(ϕ) vs. N(ρ+ω) as a function of the No. of participant nucleons in d+Au collisions from the AMPT model. The upper figure indicates collision type with one nucleon in the d-going direction, and the lower figure indicates collision type with 2 nucleons.

4 Summary

Low-mass vector meson productions in p+p and d+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV are studied within a multiphase transport model. It is found that the pure hadronic scenario of the model describes the ρ+ω data well in p+p collisions, while for the ϕ meson, the string melting version, enhances the strangeness production and shows a fair agreement with the data. Similar behaviours are found in the d+Au collisions. We argued that a measurement of the N(ϕ)/N(ρ+ω) ratio in heavy-ion collisions will bring rich information on the strangeness dynamics. Future experimental effort in this direction is encouraged.