Open-Charm Hadron Measurements in Au+Au Collisions at √^sNN = 200 GeV by the STAR Experiment ^†

Abstract

Study of the open-charm hadron production in heavy-ion collisions is crucial for understanding the properties of the Quark-Gluon Plasma. In these papers, we report on a selection of recent STAR measurements of open-charm hadrons in Au+Au collisions at $\sqrt{s_{\mathrm{NN}}}=200\mathrm{GeV}$, using the Heavy-Flavor Tracker. In particular, the nuclear modification factors of D${}^0$ and D${}^{\pm }$ mesons, elliptic and directed flow of D${}^0$ mesons, D${}_{\mathrm{s}}$/D${}^0$ and ${\mathsf{\Lambda }}_{\mathrm{c}}/{\mathrm{D}}^0$ yield ratios are discussed. The observed suppression of D${}^0$ and D${}^{\pm }$ mesons suggests strong interactions of the charm quarks with the QGP. The measured elliptic flow of D${}^0$ mesons is large and follows the NCQ scaling, suggesting that charm quarks may be close to thermal equilibrium with the QGP medium. Both D${}_{\mathrm{s}}$/D${}^0$ and ${\mathsf{\Lambda }}_{\mathrm{c}}/{\mathrm{D}}^0$ yield ratios are found to be enhanced in Au+Au collisions. The enhancement can be explained by models incorporating coalescence hadronization of charm quarks. In addition, the directed flow of the D${}^0$ mesons is measured to be negative and larger than that of light-flavor mesons which is in a qualitative agreement with hydrodynamic model predictions with a tilted QGP bulk.

1. Introduction

One of the main goals of the STAR experiment is to study the properties of the Quark-Gluon Plasma (QGP), which can be produced in ultra-relativistic heavy-ion collisions. Charm quarks are an excellent probe of the medium created in these collisions since they are produced predominantly in initial hard partonic scatterings and therefore experience the whole evolution of the medium.

As the charm quark propagates through the QGP, it interacts with the QGP and loses energy. The most common way to access the energy loss is by studying the modification of open-charm hadron yields in heavy-ion collisions with respect to those in p+p collisions using the nuclear modification factor:

$$R_{\mathrm{AA}}(p_{\mathrm{T}})=\frac{\mathrm{d}{N}^{\mathrm{AA}}/\mathrm{d}{p}_{\mathrm{T}}}{\langle N_{\mathrm{coll}}\rangle \mathrm{d}{N}^{\mathrm{pp}}/\mathrm{d}{p}_{\mathrm{T}}},$$

(1)

where $\langle N_{\mathrm{coll}}\rangle$ is the mean number of binary collisions, calculated using the Glauber model [1]. $R_{\mathrm{AA}}<1$ for high-$p_{\mathrm{T}}$ open-charm hadrons is considered a signature connected with the presence of the QGP and the level of the suppression gives access to the strength of the interaction between the charm quark and the medium [2,3].

Another way to obtain information about the charm quark interaction with the QGP is to measure the azimuthal anisotropy of the produced charm hadrons ($v_2$). The magnitude of the $v_2$ that the charm quarks develop through the interaction with the surrounding medium carries important information about the transport properties of the medium [2,3].

To have a more complete picture of the open-charm hadron production in heavy-ion collisions, it is also important to understand the charm quark hadronization process. The charm quark hadronization mechanism can be studied through the measurements of the ${\mathsf{\Lambda }}_{\mathrm{c}}/{\mathrm{D}}^0$ and D${}_{\mathrm{s}}$/D${}^0$ yield ratios [4,5].

Since the charm quarks are created very early in the heavy-ion collisions, they can be used to probe initial conditions in such collisions. Recent theoretical calculations suggest that measurement of the directed flow $v_1$ of open-charm mesons can be sensitive to the initial tilt of the QGP bulk and also to the initial electro-magnetic field induced by the passing spectators [6,7].

The following section summarizes recent STAR measurements of open-charm hadrons in the context of the observables and phenomena described above.

2. Open-Charm Measurements with the HFT

All results presented in this summary are from Au+Au collisions at $\sqrt{s_{\mathrm{NN}}}=200\mathrm{GeV}$ which were collected by the STAR experiment in years 2014 and 2016. Topological reconstruction of the decays, using an excellent vertex position resolution from the Heavy-Flavor Tracker (HFT) [8], was used to extract the signals of the open-charm hadrons listed in

Table 1. List of open-charm hadrons measured using the HFT. The left column contains decay channels used for the reconstruction, $c\tau$ is the proper decay length of a given hadron, and $BR$ is the branching ratio. Charge conjugate particles are measured as well. Values are taken from Ref. [9].

Decay Channel	$\mathit{c}\mathit{\tau }[\mathsf{\mu }\mathbf{m}]$	$\mathit{BR}$ [%]
D${}^{+}\to$ K${}^{-}{\mathsf{\pi }}^{+}{\mathsf{\pi }}^{+}$	$311.8\pm 2.1$	$9.46\pm 0.24$
D${}^0\to$ K${}^{-}{\mathsf{\pi }}^{+}$	$122.9\pm 0.4$	$3.93\pm 0.04$
D${}_{\mathrm{s}}^{+}\to \mathsf{\varphi }{\mathsf{\pi }}^{+}\to$ K${}^{-}$ K${}^{+}{\mathsf{\pi }}^{+}$	$149.9\pm 2.1$	$2.27\pm 0.08$
${\mathsf{\Lambda }}_c^{+}\to$ K${}^{-}{\mathsf{\pi }}^{+}$p	$59.9\pm 1.8$	$6.35\pm 0.33$

.

The reconstruction of D${}^{\pm }$ mesons in data from 2016 will be used as an example as the steps of reconstruction of all the aforementioned particles are similar. First, a series of selection criteria is applied to the events and tracks. Specific values of the criteria, used in the analysis of D${}^{\pm }$ mesons, are listed in

Table 2. Summary of selection criteria used for extraction of D${}^{\pm }$ candidates from the data. For more details, see the text.

Event selection	$|V_{\mathrm{z}}|$		$<6\mathrm{cm}$
	$|V_{\mathrm{z}}-V_{\mathrm{z}(\mathrm{VPD})}|$		$<3\mathrm{cm}$
Track selection	$p_{\mathrm{T}}$		$>500\mathrm{MeV}$
	$|\eta |$		$<1$
	$\mathrm{nHitsFit}$		$>20$
	$\mathrm{nHitsFit}/\mathrm{nHitsMax}$		$>0.52$
	HFT tracks = PXL1 + PXL2 + (IST or SSD)
Particle identification	TPC	$|\mathrm{n}{\sigma }_{\mathsf{\pi }}|$	$<3$
		$|\mathrm{n}{\sigma }_{\mathrm{K}}|$	$<2$
	TOF	$|1/\beta -1/{\beta }_{\mathsf{\pi }}|$	$<0.03$
		$|1/\beta -1/{\beta }_{\mathrm{K}}|$	$<0.03$
Decay topology	$DC{A}_{\mathrm{pair}}$		$<80\mathsf{\mu }\mathrm{m}$
	$30\mathsf{\mu }\mathrm{m}<L_{{\mathrm{D}}^{\pm }}$		$<2000\mathsf{\mu }\mathrm{m}$
	$cos(\theta )$		$>0.998$
	${\mathsf{\Delta }}_{\max }$		$<200\mathsf{\mu }\mathrm{m}$
	$DC{A}_{\mathsf{\pi }-\mathrm{PV}}$		$>100\mathsf{\mu }\mathrm{m}$
	$DC{A}_{\mathrm{K}-\mathrm{PV}}$		$>80\mathsf{\mu }\mathrm{m}$

.

The events are selected so that the position of the primary vertex (PV) along the beam axis ($V_{\mathrm{z}}$), which is determined using the HFT and Time Projection Chamber (TPC) [10], is no further than 6 cm from the center of the STAR detector. This is necessary due to physical dimensions and acceptance of the HFT. The value of $V_{\mathrm{z}}$ is also compared to that measured by the Vertex Position Detector [11] ($V_{\mathrm{z}(\mathrm{VPD})}$) which helps with rejection of pile-up events as the VPD is a fast detector.

From these events, only tracks with sufficiently large transverse momentum ($p_{\mathrm{T}}>300\mathrm{MeV}/c$) are selected to reduce the combinatorial background. The pseudorapidity criterion $|\eta |<1$ is given by the STAR detector acceptance. All tracks are also required to have sufficient number of hits used for track reconstruction inside the TPC (nHitsFit) and to be properly matched to the HFT to ensure their good quality. In this case, a good HFT track is required to have one hit in each of the inner layers (PXL1 and PXL2) and at least one hit in one of the two outer layers (IST or SSD) 1.

Next, all the selected tracks are identified using the TPC and the Time Of Flight (TOF) [12] detectors. The particle identification (PID) with the TPC is done based on energy loss of charged particles in the TPC gas. The measured energy loss is compared to the expected one, which is calculated with Bichsel formula, using n$\sigma$ variable [13]. The PID using TOF is done by comparing velocity of given particle measured by TOF ($\beta$) and that calculated from its momentum and rest mass (${\beta }_{\mathsf{\pi }}$ or ${\beta }_{\mathrm{K}}$).

When charged pions and kaons are identified they are combined into K$\mathsf{\pi }\mathsf{\pi }$ triplets within each event. The topology of the triplet is then constrained using variables shown in Figure 1. More specifically they are: the maximum distance of closest approach of track pairs ($DC{A}_{\mathrm{pair}}$), D${}^{\pm }$ meson decay length $L_{{\mathrm{D}}^{\pm }}$, cosine of the pointing angle $cos(\theta )$, maximum distance between reconstructed secondary vertices of track pairs (${\mathsf{\Delta }}_{\max }$), and the distance of closest approach to the primary vertex of the kaon ($DC{A}_{\mathrm{K}-\mathrm{PV}}$) and each of the pions ($DC{A}_{\mathsf{\pi }-\mathrm{PV}}$). Specific values used for D${}^{\pm }$ signal extraction are listed in Table 2. The topological selection criteria used for D${}^{\pm }$ mesons will be optimized using the TMVA [14] in near future, as was done for other open-charm hadron results presented in the following section, in order to improve statistical significance and also to extend the $p_{\mathrm{T}}$ range.

The D${}^{\pm }$ signal is subsequently extracted from the invariant mass spectrum of the K$\mathsf{\pi }\mathsf{\pi }$ triplets which are divided into two sets. The first consists of only correct-sign charge combinations, which may come from decay of D${}^{\pm }$ mesons (see Table 1) and contains the signal together with a combinatorial and a correlated background. The combinatorial background shape can be determined using the second set which contains only wrong-sign charge combinations which cannot originate from decay of D${}^{\pm }$ mesons 2. The correct-sign and the scaled 3 wrong-sign invariant mass spectrum of the K$\mathsf{\pi }\mathsf{\pi }$ triplets near invariant mass of the D${}^{\pm }$ mesons is shown in top panel of Figure 2. The scaled wrong-sign spectrum can be then subtracted from the correct-sign one which leads to the spectrum shown in the bottom panel of Figure 2. The invariant mass peak is fitted with Gaussian function in order to determine its width $\sigma$ and mean. The raw yield $Y_{\mathrm{raw}}$ is calculated using bin counting method in $\pm 3\sigma$ region around the peak mean.

The invariant spectrum of the D${}^{\pm }$ mesons is then calculated from the raw yield $Y_{\mathrm{raw}}$ as:

$$\frac{{\mathrm{d}}^{2}N}{2\pi p_{\mathrm{T}}\mathrm{d}{p}_{\mathrm{T}}\mathrm{d}y}=\frac{1}{2\pi p_{\mathrm{T}}}\frac{Y_{\mathrm{raw}}}{N_{\mathrm{evt}}BR\mathsf{\Delta }{p}_{\mathrm{T}}\mathsf{\Delta }y\epsilon (p_{\mathrm{T}})},$$

(2)

where $N_{\mathrm{evt}}$ is number of recorded MB events, $BR$ is the branching ratio (see Table 1) and $\epsilon (p_{\mathrm{T}})$ is the total reconstruction efficiency calculated using the data-driven fast-simulator. More details about the efficiency calculation can be found in article [15]. An example of reconstruction efficiency of D${}^{\pm }$ mesons in 0%–10% central Au+Au collisions extracted with selection criteria from Table 2 is shown in Figure 3.

3. Results

Figure 4 shows the nuclear modification factor $R_{\mathrm{AA}}$ of D${}^0$ [15] and D${}^{\pm }$ mesons as a function of $p_{\mathrm{T}}$ in 0%–10% central Au+Au collisions. Both D${}^0$ and D${}^{\pm }$ are significantly suppressed in high-$p_{\mathrm{T}}$ region which suggests a significant energy loss of charm quarks in the QGP. The low to intermediate $p_{\mathrm{T}}$ bump structure is consistent with predictions of models incorporating large collective flow of charm quarks [15].

STAR has also measured and published the elliptic flow ($v_2$) of D${}^0$ mesons using 2014 data [17]. Results with improved precision from the combined 2014+2016 data are shown in Figure 5a. The results clearly shows that charm quarks gain significant elliptic flow as they transverse through the medium. It is also of importance to test the Number of Constituent Quarks (NCQ) scaling. In Figure 5b is shown the $v_2/n_{\mathrm{q}}$ as a function of $(m_{\mathrm{T}}-m_0)/n_{\mathrm{q}}$, where $n_{\mathrm{q}}$ is the number of constituent quarks, $m_{\mathrm{T}}$ is the transverse mass and $m_0$ is the rest mass. In both panels, the D${}^0$ results are compared to similar measurements for light-flavor hadrons [18]. As can be seen in Figure 5b, a similar scaling is observed for all particle species within the uncertainties. The observation of sizable D${}^0$ mesons flow which follows the NCQ scaling, similarly as light-flavor hadrons, suggests that the charm quarks may be in thermal equilibrium with the QGP at RHIC.

To study the charm hadronization and its possible modification in the presence of the QGP, STAR has measured the ${\mathsf{\Lambda }}_{\mathrm{c}}/{\mathrm{D}}^0$ yield ratio as a function of $p_{\mathrm{T}}$ and collision centrality, results of which are shown in Figure 6. As can be seen in panel (a), the ratio is significantly enhanced compared to PYTHIA model predictions. The data are also compared to models that include coalesence hadronization of charm quarks [4,5] which predict an enhancement of the ratio with a qualitatively similar $p_{\mathrm{T}}$ dependence. The ${\mathsf{\Lambda }}_{\mathrm{c}}/{\mathrm{D}}^0$ yield ratio increases from peripheral to central Au+Au collisions, as shown in Figure 6b. This and the qualitative agreement with the coalescence models indicates that the ${\mathsf{\Lambda }}_{\mathrm{c}}$ enhancement could be a consequence of coalescence hadronization of charm quarks in the medium.

A complementary measurement to the one discussed above is the measurement of the D${}_{\mathrm{s}}$/D${}^0$ ratio. As shown in Figure 7, the D${}_{\mathrm{s}}$ is enhanced with respect to the averaged result from elementary collisions [21] as well as PYTHIA model calculations. The TAMU model [22], which includes coalescence hadronization of charm quarks, also shows an enhancement of the ratio, but underpredicts the data. This result also suggests that charm quarks hadronize via coalescence in heavy-ion collisions.

The last result presented in this overview is from the measurement of (rapidity odd) directed flow ($v_1$) of D${}^0$ mesons. There are two main models predicting the origin and magnitude of the $v_1$ of D${}^0$ mesons. The first one is a hydrodynamical model which predicts larger $v_1$ slope ($\mathrm{d}{v}_1/\mathrm{d}y$) for heavy-flavor hadrons than for light-flavor hadrons, arising from a difference in the charm quark production profile and the tilted QGP bulk [6]. The second one calculates the $v_1$ from EM field induced by the passing spectators and predicts opposite $v_1$ slope for D${}^0$ and $\overline{{\mathrm{D}}^0}$ [7]. When combined, the prediction is that the $v_1$ slope for both D${}^0$ and $\overline{{\mathrm{D}}^0}$ mesons is negative, larger for D${}^0$ than for $\overline{{\mathrm{D}}^0}$, and much larger than for kaons [23]. As can be seen in Figure 8, the measured slope of $v_1$ is indeed negative and larger in magnitude for both charmed mesons than for the light-flavor hadrons. On the other hand, the available statistics does not allow firmly concluding on the D${}^0$–$\overline{{\mathrm{D}}^0}$ splitting.

4. Summary

STAR experiment has extensively studied the open-charm hadron production using the excellent vertex position resolution provided by the HFT. In this summary it is shown that D${}^0$ and D${}^{\pm }$ mesons are significantly suppressed in high $p_{\mathrm{T}}$ region which suggests strong interactions of the charm quarks with the QGP. The D${}^0$ mesons also show large elliptic flow $v_2$ which follows the NCQ scaling, similarly as the light-flavor hadrons, suggesting that the charm quarks may be close to a local thermal equilibrium with the QGP medium at RHIC. Moreover, the ${\mathsf{\Lambda }}_{\mathrm{c}}/{\mathrm{D}}^0$ and D${}_{\mathrm{s}}$/D${}^0$ yield ratios are found to be enhanced in Au+Au collisions. Comparison to model predictions suggests that the coalescence plays an important role in charm quark hadronization in heavy-ion collisions at RHIC. The measurement of the D${}^0$ directed flow $v_1$ shows significantly larger values compared to those from light-flavor hadrons and is in qualitative agreement with hydrodynamic model predictions with a tilted QGP bulk [6]. The $v_1$ values for D${}^0$ and $\overline{{\mathrm{D}}^0}$ are consistent with each other within the current measurement precision.