Charm quarks are more hydrodynamic than light quarks in final-state elliptic flow

We study the charm quark elliptic flow $\left(v_2\right)$ in heavy ion as well as small system collisions by tracking the evolution history of quarks of different flavors within a multiphase transport model. The charm quark $v_2$ is studied as a function of the number of collisions the charm quark suffers with other quarks and then compared to the $v_2$ of lighter quarks. We find that the common escape mechanism is at work for both the charm and light quark $v_2$. However, contrary to the naive expectation, the hydrodynamics-type flow is found to contribute more to the final state charm $v_2$ than the light quark $v_2$. This could be explained by the smaller average deflection angle the heavier charm quark undergoes in each collision, so that heavy quarks need more scatterings to accumulate a significant $v_2$, while lighter quarks can more easily change directions with scatterings with their $v_2$ coming more from the escape mechanism. Our finding thus suggests that the charm $v_2$ is a better probe for studying the hydrodynamic properties of the quark-gluon plasma.

Figure 1

AMPT results for Au+Au collisions at $\sqrt{s_{NN}}=200\mathrm{A}$ GeV with impact parameter $b=6.6$–8.1 fm. (a) Normalized $N_{\mathrm{coll}}$ distributions of different quark flavors: light quarks (thin), strange quarks (medium), and charm quarks (thick). (b) Normalized probability distributions of the initial transverse radius $R_{\perp }$ for different quark flavors.

Figure 2

Freezeout partons' $v_2$ within $\left|\eta \right|<1$ as a function of $N_{\mathrm{coll}}$ for light (thin), strange (medium), and charm quarks (thick) in (a) $p$+Pb collisions with $b=0$ fm at $\sqrt{s_{NN}}=5\mathrm{A}$ TeV, (b) Au+Au collisions with $b=6.6$–8.1 fm at $200A$ GeV, and (c) Pb+Pb collisions with $b=8$ fm at $2.76A$ TeV in normal AMPT (solid curves) and $\varphi$-randomized AMPT (dashed curves).

Figure 3

Parton $v_2$ as a function of $p_{\perp }$ at freezeout for different quark flavors: light quarks (thin), strange quarks (medium), and charm quarks (thick) in normal (solid curves) and $\varphi$-randomized (dashed curves) AMPT for three different collision systems.

Figure 4

(a) The rms change of azimuthal angle due to the $N_{\mathrm{coll}}$-th collision for different quark flavors in normal AMPT simulations in Au+Au collisions. The black curves are for light quarks, the blue curves for strange quarks, and red curves for charm quarks. (b) The freezeout partons $\langle v_2\rangle$ as a function of $\langle N_{\mathrm{coll}}\rangle$ for light, strange, and charm quarks from a simple analytical calculation for a transverse geometry of a given ${\epsilon }_2=0.17$, with arbitrary size nucleus-nucleus collision quantified by the variable $\langle N_{\mathrm{coll}}\rangle$.