Charm and beauty isolation from heavy flavor decay electrons in Au+Au collisions at $\sqrt{s_{\rm NN}}$ = 200 GeV at RHIC

We present a study of charm and beauty isolation based on a data-driven method with recent measurements on heavy flavor hadrons and their decay electrons in Au+Au collisions at $\sqrt{s_{\rm NN}}$ = 200 GeV at RHIC. The individual electron $p_{\rm T}$ spectra, $R_{\rm AA}$ and $v_2$ distributions from charmed and beauty hadron decays are obtained. We find that the electron $R_{\rm AA}$ from beauty hadron decays ($R_{\rm AA}^{\rm b\rightarrow e}$) is suppressed in minimum bias Au+Au collisions but less suppressed compared with that from charmed hadron decays at $p_{\rm T}$ $>$ 3.5 GeV/$c$, which indicates that beauty quark interacts with the hot-dense medium with depositing its energy and is consistent with the mass-dependent energy loss scenario. For the first time, the non-zero electron $v_2$ from beauty hadron decays ($v_2^{\rm b\rightarrow e}$) at $p_{\rm T}$ $>$ 3.0 GeV/$c$ is observed and shows smaller elliptic flow compared with that from charmed hadron decays at $p_{\rm T}$ $<$ 4.0 GeV/$c$. At 2.5 GeV/$c$ $<$ $p_{\rm T}$ $<$ 4.5 GeV/$c$, $v_2^{\rm b\rightarrow e}$ is smaller than a number-of-constituent-quark (NCQ) scaling hypothesis. This suggests that beauty quark is unlikely thermalized and too heavy to be moved in a partonic collectivity in heavy-ion collisions at the RHIC energy.

The pursuit of Quark-Gluon Plasma (QGP) is one of the most interesting topics in strong interaction physics [1][2][3][4]. Recent experimental results from Relativistic Heavy-Ion Collider (RHIC) and Large Hadron Collider (LHC) support that a strongly coupled QGP matter (sQGP) has been created in ultra-relativistic heavy-ion collisions [5,6]. Studying the properties of the QGP matter and understanding its evolution in the early stage of the collisions are particularly helpful for broadening our knowledge of the early born of the universe.
Heavy quark (charm and beauty) masses, different from that of light quarks, are mostly coming from initial Higgs field coupling, which is hardly affected by the strong interactions [7]. Thus heavy quarks are believed to be produced predominately via hard scatterings in the early stage of the collisions and sensitive to the initial gluon density. And their total production yields can be calculated by perturbative-QCD (pQCD) and are number of binary collision (N coll ) scaled [8]. Theoretical calculations predict that the heavy quark energy loss is less than light quarks due to suppression of the gluon radiation angle by the quark mass. Beauty quark mass is a factor of three larger than charm quark mass, thus one would expect less beauty quark energy loss than charm quark when they traverse the hot-dense medium created in the heavy-ion collisions [9][10][11]. Experimentally, the nuclear modification factor (R AA ), which is defined as the ratio of the production yield in A+A collisions divided by the yield in p+p collisions scaled by the number of binary collisions, is used to extract the information of the medium effect, such as the parton energy loss [12]. Recent measurements on the R AA of open charm hadrons and leptons from heavy flavor (HF) decays show strong suppression at high transverse momentum (p T ), and with a similar magnitude as light flavor hadrons, which indicates strong interactions between charm quark and the medium [13][14][15][16][17]. However, due to technique challenges, most of the electron measurements are the sum of the products from HF decays without charm and beauty contributions isolated. Recently, with the help of vertex detectors, some of the experiments extracted the charm and beauty contributions from the heavy flavor electron (HFE) measurements but with large uncertainties [18,19].
Naively, heavy quarks are too heavy to be pushed moving together with the collective flow during the expansion of the partonic matter unless the interactions between heavy quarks and surrounding dense light quarks are strong and frequent enough. After sufficient energy exchange, the system could reach thermal equilibrium. Therefore, heavy quark collectivity could be an evidence of light quark thermalization. And its elliptic flow, defined as a second harmonic Fourier coefficient (v 2 ) for momentum space anisotropy [20], is proposed to be an ideal probe to the properties of the partonic matter, such as the thermalization, intrinsic transport parameters, drag constant and entropy [8,[21][22][23][24][25][26]. Apparently, measuring charm and beauty v 2 separately is crucial to constrain the diffusion parameters extracted from quenched lattice QCD [27,28]. In particular, beauty mass is about three times larger than charm mass, its final state behavior could be different from that of charm. Unfortunately we are very ignorant of that. Up to date, there are many measurements of heavy flavor hadron spectra and v 2 , but most of them are for charmed hadrons or electrons from heavy quark decays. Some attempts for arXiv:1906.08974v1 [nucl-ex] 21 Jun 2019 separation of charm and beauty contributions in heavy flavor decay electrons are only for their momentum distributions. There is no measurement for beauty v 2 either in hadronic decays or indirect electron channels at RHIC.
We developed a data-driven method to isolate charm and beauty contributions from the inclusive HFE measurements based on most recent open charm hadron measurements in minimum bias (Min Bias) Au+Au collisions at √ s NN = 200 GeV at RHIC. Taking the advantage of the Heavy Flavor Tracker (HFT), the STAR experiment has achieved precision measurements on p T spectra of D 0 -mesons at 0 < p T < 10 GeV/c [13][14][15], as well as other charmed hadrons (D ± , D s and Λ c ) at 2 GeV/c p T < 8 GeV/c [29,30] and J/ψ at 0 < p T < 10 GeV/c [31,32]. The parameterized uncertainties of D 0 spectrum and the extrapolation to unmeasured region include three parts: a) 1-σ band of the D 0 spectrum by fitting with a Levy [33] function with uncorrelated uncertainties; b) Half of the difference between Levy and power-law [34] fits; c) For correlated systematic uncertainties the spectrum is scaled to upper and lower limits. The total uncertainty is then quadratically summed from above three components. The D s and J/ψ uncertainties are obtained in the same way. The uncertainties of D 0 (D s and J/ψ) p T spectrum are 10.7% (19.2% and 8.4%) at low p T up to 88.7% (95.9% and 96.5%) at high p T where functional extrapolation uncertainty dominates. The D ± spectrum is obtained by scaling the D 0 spectra with a constant fitted from the measured D ± /D 0 ratio (0.429 ± 0.038), since there is no clear p T dependence observed. The Λ c spectrum is fitted and extrapolated down to zero p T with the measured D 0 spectrum multiplying different model calculations on Λ c /D 0 [35][36][37]. The uncertainty of Λ c is mainly from the average of the three models and contributes to the total electron spectrum from charm decays less than 15.2%. The above spectra of charmed hadrons, with parameterized p T spectra are used as inputs and forced to decay to electrons via semileptonic decay channels, of which the J/ψ spectrum is input in a Pythia decayer [38] and decay to e + e − . Figure 1 shows the electron spectra from D 0 (blue dashed curve), D ± (brown dot-dot-dashed curve, scaled by 1/10), D s (green dot-dashed curve), Λ c (cyan longdot-dashed curve) and J/ψ (magenta long-dashed curve) decays and the sum of all charm contributions (c → e, black solid curve) in Au+Au collisions at √ s NN = 200 GeV. The electron spectra from charmed hadron decays are normalized by measured parent particle cross sections and decay branching ratios. The uncertainties of the charmed hadron p T inputs analyzed from above process are propagated into the decay electron spectra. The uncertainties of branching ratios are also taken into account. In particular, the uncertainty of D ± /D 0 ratio is propagated into the spectrum of D ± → e. Electron spectra from D s , Λ c and J/ψ are scaled by N coll to 0-80% centrality from 10-40%, 10-80% and 0-60%, respectively,  [29,30,[35][36][37], J/ψ [31,32] and the sum of them (c → e)) and the spectrum of inclusive HFE [39] in minimum bias Au+Au collisions at √ sNN = 200 GeV. The spectrum of beauty decay electrons (b → e) is obtained by subtracting the c → e contributions from the HFE data. Uncertainties are shown as shaded bands.
since there is no clear centrality dependence observed from current precision and the normalization uncertainties are taken into account. The total uncertainties of the electrons from individual charmed hadron decays are shown as shaded bands in Fig. 1. Components of relative uncertainties of the total c → e spectrum are shown in Table I. The black solid squares denote the inclusive HFE spectrum measured by STAR [39]. The electron spectrum from beauty decays (b → e), shown as the solid circles, is then calculated by subtracting c → e contribution from the inclusive HFE spectrum from p T = 1.5 GeV/c to 10 GeV/c. The uncertainties of the last two points at p T > 7 GeV/c are quoted safely with 2-σ uncertainties from c → e due to higher p T extrapolation. TABLE I. Uncertainty components of the total c → e spectrum (0 -10 GeV/c) from electron spectra of charmed hadron decays.
The beauty contribution fraction in total inclusive HFE in Au+Au collisions (f b→e AA ) can be obtained by taking the ratio of b → e and the inclusive HFE, shown as solid circles in Fig. 2. Here we compare the results with previous measurements in p+p collisions by STAR via an electron-hadron correlation approach (red open squares) [39] and by PHENIX with recent built-in vertex detector (green crosses) [40]. The fixed-order nextto-leading log (FONLL) calculation [8] is presented as gray dashed curves. The STAR p+p data are parameterized with the FONLL function (cyan dashed curve with band). The averaged f b→e pp (blue solid squares) are the average of the STAR p+p data and the PHENIX p+p data with half of their differences taken into account in the uncertainty bars. The beauty contributions in the inclusive HFE in Au+Au collisions are clearly modified compared with those in p+p collisions. At p T ∼ 4 GeV/c, beauty and charm contributions are comparable and at p T > 7 GeV/c beauty contribution is up to 90%, which is significantly higher than those in p+p collisions. Since charm is strongly suppressed, the enhanced beauty fraction is consistent with less beauty suppression compared to charm in Au+Au collisions at √ s NN = 200 GeV.
The R AA of individual charm and beauty contributions (R c→e AA and R b→e AA ) can be extracted by where f b→e AA is the beauty fraction in Au+Au collisions and f b→e pp is the averaged beauty fraction of the STAR and PHENIX data in p+p collisions from Fig. 2. The R ince AA is the nuclear modification factor of inclusive electrons from heavy flavor decays measured by STAR [39]. Figure 3 shows the R c→e AA and R b→e AA as a function of p T extracted from Eq. (1) and (2) as blue solid squares and red solid circles, respectively. The results are consistent with an impact parameter template analysis with STAR HFT (open green symbols) [19] and show an improved precision. The DUKE model predictions [41] are consistent with R b→e AA result, but overestimate the R c→e AA data at p T > 4 GeV/c. Two dashed curves of b(c) → e/FONLL are obtained directly by the definition of R AA with the parameterized b(c) → e spectra from Fig. 1 divided by the FONLL calculations as a cross-check, which shows in a good agreement with data. Clear suppression at p T >∼ 3.5 GeV/c is observed for both R c→e AA and R b→e AA , which indicates charm/beauty quarks strongly interact with the hot-dense medium and lose energy. However, R b→e AA shows less suppression compared with R c→e AA at p T > 3.5 GeV/c, which is consistent with mass-dependent energy loss that beauty loses less energy due to suppressed gluon radiation and smaller collisional energy exchange with the medium by its three-times larger mass compared to charm [9][10][11]. From the Eq. (2), the uncertainty of R b→e AA can be calculated by where δ devotes the relative uncertainty and f cb = f c→e AA f b→e AA = 1 − f b→e AA f b→e AA , and the uncertainty of R c→e AA is obtained in a similar way. Table II shows the components of relative uncertainties of R c→e AA and R b→e AA . The v 2 of D 0 (0-80%) measured from STAR [42] is parameterized with the function below, which is modified from [43] with adding a linear term forced to pass through the origin according to the natural properties of v 2 , where n is the number of constituent quarks, p i (i = 0, 1, 2, 3) are free parameters. Assuming Λ c (n quarks = 3) also follows NCQ scaling as D-mesons (n quarks = 2), the v 2 of charmed hadrons in each p T bin can be sampled from Eq. (4). The azimuthal angle (φ) distributions of charmed hadrons can be obtained following the function [43] dN dφ = 1 + 2v 2 cos(2φ).
where v ince 2 denotes the v 2 of inclusive HFE from the parameterized average of the measurements of STAR [39] and PHENIX [44] by Eq. (4).
The uncertainties from the parameterization of the D 0 v 2 with the quadratic sum of statistical and systematic uncertainties, including the high p T extrapolation, are propagated into the uncertainties of v D→e with the φ-meson spectrum [45] and v 2 (0-80%) [46] as the inputs in a Pythia decayer. The non-zero electron v 2 from beauty decays at p T > 3.0 GeV/c is observed and is consistent with electrons from decays of hadrons containing charm or strangeness within uncertainties at p T > 4.5 GeV/c. This flavor independent v 2 at high p T could be due to the initial geometry anisotropy. A smaller v b→e 2 compared with v c→e 2 is observed at p T < 4.0 GeV/c, which may be driven by the larger mass of beauty than that of charm. The black dashed curve represents the v b→e 2 assuming that B-meson v 2 follows the NCQ scaling. The v b→e 2 deviates the curve at 2.5 < p T < 4.5 GeV/c with a confidence level of 98.2% (χ 2 /ndf = 11.92/4), which indicates that beauty is unlikely thermalized and too heavy to be moved following the collective flow of lighter partons. In summary, this paper reports the individual electron transverse momentum spectra, R AA and v 2 distributions from charm and beauty decays in minimum bias Au+Au collisions at √ s NN = 200 GeV at RHIC. We found that the electron R AA from beauty decays are suppressed at high p T > 3.5 GeV/c but less suppressed compared with that from charm decays, which indicates that beauty interacts with the hot-dense medium and loses energy and is consistent with the mass-dependent energy loss scenario. At the first time, the non-zero electron v 2 from beauty decays at p T > 3.0 GeV/c is observed and consistent with hadrons containing charm or strangeness at p T > 4.5 GeV/c, which could be mainly due to initial geometry anisotropy. And its smaller flow compared with that from charm decays at p T < 4.0 GeV/c is observed. At 2.5 < p T < 4.5 GeV/c, v b→e 2 is smaller than a numberof-constituent-quark (NCQ) scaling hypothesis, which indicates that the extremely heavy mass of beauty quark prevents itself participating in the partonic collectivity and the first non-thermalized particle (beauty quark) is observed in heavy-ion collisions at RHIC energy.