Production of charm quarks in a parton cascade model for relativistic heavy ion collisions at $\sqrt{s_{\mathit{NN}}}=200$ GeV

We study the production and dynamics of heavy quarks in the parton cascade model for relativistic heavy ion collisions. The model is motivated by the QCD parton picture and describes the dynamics of an ultrarelativistic heavy ion collision in terms of cascading partons which undergo scattering and multiplication while propagating. We focus on the dynamics of charm quark production and evolution in $p+p$ and Au + Au collisions for several different interaction scenarios, viz., collisions only between primary partons without radiation of gluons, multiple collisions without radiation of gluons, and multiple collisions with radiation of gluons, allowing us to isolate the contributions of parton rescattering and radiation to charm production. We also discuss results of an eikonal approximation of the collision which provides a valuable comparison with minijet calculations and clearly brings out the importance of multiple collisions.

Figure 1

(a) The rapidity ($y$) integrated $p_T$ spectra of charm quarks using minijet calculations (solid curves) and eikonal approximation. The lower panel (b) gives the $p_T$ integrated rapidity spectra.

Figure 2

The $p_T$ spectra for charm quarks using minijet calculations (solid curves) and eikonal approximation at $y=0$ (a), $y=2$ (b), and $y=3$ (c).

Figure 3

(a) The rapidity integrated $p_T$ spectra and (b) $p_T$ integrated rapidity spectra for charm quarks using eikonal approximation and primary-primary collisions for $pp$ system at $\sqrt{s_{NN}}$ = 200 GeV.

Figure 4

(a) The rapidity integrated $p_T$ spectra and (b) $p_T$ integrated rapidity spectra for charm quarks using eikonal approximation and multiple collisions for $pp$ system at $\sqrt{s_{NN}}=200$ GeV.

Figure 5

(a) The rapidity integrated $p_T$ spectra and (b) $p_T$ integrated rapidity spectra for charm quarks using multiple collisions only and multiple collisions as well as fragmentation of partons scattered off the final-state partons, following a semihard scattering in evolution of the cascade for $pp$ system at $\sqrt{s_{NN}}$ = 200 GeV.

Figure 6

The $p_T$ spectra for charm quarks using multiple collisions as well as fragmentation of partons scattered off the final-state partons, following a semihard scattering in evolution of the cascade for $pp$ system at $\sqrt{s_{NN}}$ = 200 GeV. The data are from the STAR experiment [63].

Figure 7

The distribution of $z$ coordinates of production vertices of charm (or anticharm) quarks for the cases involving only primary-primary collisions (a), only multiple collisions (b), and multiple collisions and radiations of gluons (c).

Figure 8

The distribution of production times of charm (or anticharm) quarks for the cases involving only primary-primary collisions (a), only multiple collisions (b), and multiple collisions and radiations of gluons (c). Note that $t=0$ is defined to occur when the two nuclei are in full overlap.

Figure 9

The $z$ and $t$ coordinates of production vertices of charm (or anticharm) quarks for the cases involving only primary-primary collisions (a), only multiple collisions (b), and multiple collisions and radiations of gluons (c). Note the change of scale along the $z$ axis for the primary-primary case.

Figure 10

The $x$ and $y$ coordinates of production vertices of charm (or anticharm) quarks for the cases involving only primary-primary collisions (a), only multiple collisions (b), and multiple collisions and radiations of gluons (c).

Figure 11

(a) The distribution of number of collisions encountered by charm quarks when only multiple scattering among partons is permitted and (b) when both multiple scattering and radiations are permitted.

Figure 12

The distribution of number of gluons radiated off charm quarks following a semihard scattering.

Figure 13

(a) The $y$-integrated $p_T$ spectra of charm quarks using eikonal approximation and only primary-primary collisions for the $\text{Au}+\text{Au}$ system at $\sqrt{s_{NN}}$ = 200 GeV. The lower panel (b) gives the $p_T$ integrated rapidity spectra for the same cases.

Figure 14

(a) The $y$-integrated $p_T$ spectra of charm quarks using eikonal approximation and multiple collisions for the $\text{Au}+\text{Au}$ system at $\sqrt{s_{NN}}$ = 200 GeV in parton cascade model. The lower panel (b) gives the $p_T$-integrated rapidity spectra for the same cases.

Figure 15

(a) The $y$-integrated $p_T$ spectra of charm quarks using multiple collisions and multiple collisions and fragmentations for $\text{Au}+\text{Au}$ system at $\sqrt{s_{NN}}$ = 200 GeV in parton cascade model. The lower panel (b) gives the $p_T$-integrated rapidity spectra for the same cases.

Figure 16

The $p_T$ spectrum of charm quarks at central rapidity along with the spectrum of $D$ mesons obtained with STAR Collaboration [64] for the most central collisions for $\text{Au}+\text{Au}$ system at $\sqrt{s_{NN}}$ = 200 GeV. The parton cascade calculation includes multiple scatterings as well as radiations of gluons off final-state partons in semihard scatterings.

Figure 17

Rapidity-integrated nuclear modification factor for eikonal approximation (a), multiple collisions (b), and multiple collisions along with the parton multiplications (c) for central collisions for $\text{Au}+\text{Au}$ system at $\sqrt{s_{NN}}$ = 200 GeV.

Figure 18

Nuclear modification factor for central rapidity in the parton cascade model using multiple collisions along with the parton multiplications for central collisions for the $\text{Au}+\text{Au}$ system at $\sqrt{s_{\mathit{NN}}}=200$ GeV. The experimental data (with only statistical errors) are from the STAR Collaboration [64, 65].