Sheng-Hui Zhang? Rong-Rong Ma? Yi-Fei Zhang? Xiao-Long Chen ?Xiu-Jun Li? Fan Si? Cheng Li ? Ming Shao? Yong-Jie Sun ?Ze-Bo Tang? Wang-Mei Zha

Abstract We present a comprehensive study on the individual sources of an inclusive photon production during high-energy hadronic collisions. The cross section and invariant yields of inclusive photons are obtained as a function of pT at mid-rapidity(|y|＜0.5)in p+p and Au+Au collisions at= 200 GeV, respectively. These results provide crucial inputs to separate measurements of open bottom and charm hadron yield suppression in heavyion collisions,which are used to test the mass hierarchy of the parton energy loss in the quark gluon plasma created during these collisions. The procedure developed in this study can also be applied to other measurements of electrons from an open heavy-flavor hadron decay,such as the collective flow in the RHIC beam energy scan program.

Keywords Inclusive photon · Cross section · Invariant yields · Mass hierarchy · Technical reference

1 Introduction

Searching for a novel form of nuclear matter with deconfined quarks and gluons, created during ultra-relativistic heavy-ion collisions, is one of the main goals of high-energy nuclear physics.Many measurements from the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider(LHC)experiments show that this strongly coupled matter, usually referred to as quark-gluon plasma(QGP),have indeed been formed[1–4].The next step is to study its properties in detail.

Heavy quarks (c and b) are predominantly produced during the early stages of heavy-ion collisions before the creation of the QGP [5,6].They subsequently traverse the QGP throughout its evolution and thus can serve as an excellent probe for studying the properties of the QGP.Heavy flavor quarks are expected to suffer from collisional and radiative energy losses through interactions with the QGP. The nuclear modification factor (RAA) is utilized to quantify such energy loss by comparing the yields of open heavy flavor production in heavy-ion collisions with those during p + p collisions. Significant suppression of the charm meson yielded at large transverse momenta (pT),resulting from the substantial energy loss of heavy quarks in the QGP,has been observed at both the RHIC and LHC[7–12], indicating strong interactions between heavy quarks and the medium.This energy loss is expected to be different for bottom and charm quarks owing to their different masses[13].Separate measurements of open bottom and open charm hadron production during heavy-ion collisions are crucial to testing the mass hierarchy of the parton energy loss in the QGP.

In the measurements of HFE spectra in p+p and Au+Au collisions, the HFE sample can be obtained by statistically subtracting the background photonic electrons from the inclusive electron sample.Photonic electrons arise from Dalitz decay of light-neutral mesons and photon conversions in the detector material. Owing to the extremely low signal-to-background ratio, it is crucial to extract the background electron yields and kinematic distributions accurately for precise measurements of HFE spectra. Furthermore, the contribution of the open bottom hadron decays to the HFE sample in Au + Au collisions is obtained through a template fitting to the distribution of the distance of the closest approach (DCA) to the collision vertex for inclusive electrons [14]. Contributions from photonic electrons are included in the templates. Another important observation is the charm angular correlation,which is believed to be a sensitive probe of the medium dynamics during the early stage of the collisions [18].Measurements of the charm angular correlation when reconstructing the open charm mesons are extremely challenging,and an indirect measurement of the correlation between their decay electrons requires inclusive photon yields as well. However, it is difficult to directly measure the inclusive photon spectrum experimentally, and a cocktail-like method is usually applied.

The paper is organized as follows: PYTHIA settings,cross section, and invariant yields as a function of pTfor inclusive photons in p + p and Au + Au collisions are presented in Sect. 2. A summary is given in Sect. 3.

2 Results

2.1 PYTHIA decay process

PYTHIA is an event generator widely used in high-energy particle and nuclear physics communities[20].In this study, PYTHIA6.319 was used to decay π0and η mesons into photons through both two-photon and Dalitz decay channels for both p+p and Au+Au collisions. The pTand rapidity distributions of π0and η mesons are obtained from experimental measurements. Information on daughter particles was stored for further analysis.

2.2 p+p Collisions at s = 200 GeV

Fig.3 a Invariant yields of direct photons as a function of pT at midrapidity(|y|＜1)for different centrality classes in Au+Au collisions at =200 GeV as measured using STAR[42].Error bars indicate point-to-point uncertainties.Solid lines represent fits to the data points with an exponential function plus the fit to the corresponding distribution measured during p + p collisions scaled by Ncoll. Error bands depict uncertainties in the parameterization and Ncoll. b Direct photon dN/dy/〈0.5Npart〉 as a function of Npart along with a fit utilizing the second-order polynomial function. Error bars denote point-to-point uncertainties, and the error band shows the parameterization uncertainty. c Direct photon invariant yields as a function of pT from measurements and extrapolation for different centrality classes of Au+Au collisions. For the 0–10% and 10–20% centrality classes, the error bands show uncertainties from extrapolated inclusive direct photon yields, Npart values, and parameterization of the direct photon pT spectrum in the 0–20% centrality bin

? Fit dN/dy/〈0.5Npart〉 versus Npartwith a second-order polynomial function, and extrapolate the inclusive direct photon yields in desired centrality bins. Such a distribution and the fit are shown in Fig.3b.

? The shapes of the invariant yields for direct photons in 0–10% and 10–20% centrality bins are taken to be the same as that of the 0–20%centrality class,as shown in Fig.3a. Normalization is based on the extrapolated inclusive direct photon yields.

The resulting invariant yields of direct photons in 0–10%and 10–20% centrality bins are shown in Fig.3c as dashdotted curves.

With all ingredients in hand, invariant yields of inclusive photons are obtained with contributions from π0and η two-body and Dalitz decays,and direct photon production.These are shown as solid curves in Fig.4 with different panels corresponding to different centrality classes. The dashed and dotted lines represent individual sources. The integrated IPT yields per unit rapidity at mid-rapidity for different centrality classes are summarized in Table 1,along with those from each component. The contribution from π0two-body decay is the dominant source of photon production at low pT, whereas the contribution from direct photon production increases with increasing pTand overtakes that from π0two-body decay at high pT.In all cases,the neutral meson Dalitz decays constitute less than 1% of inclusive photons within the entire kinematic range.

3 Summary

Table 1 dN/dy at mid-rapidity for inclusive photon production and individual sources in different centrality classes

Author contributionsAll authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by Sheng-Hui Zhang. The first draft of the manuscript was written by Sheng-Hui Zhang and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.