Elliptic flow of thermal dileptons in relativistic nuclear collisions

We calculate the transverse momentum and invariant mass dependence of elliptic flow of thermal dileptons for Au+Au collisions at the Relativistic Heavy Ion Collider. The system is described using hydrodynamics, with the assumption of formation of a thermalized quark-gluon plasma at some early time, followed by cooling through expansion, hadronization, and decoupling. Dileptons are emitted throughout the expansion history: by annihilation of quarks and antiquarks in the early quark-gluon plasma stage and through a set of hadronic reactions during the late hadronic stage. The resulting differential elliptic flow exhibits a rich structure, with different dilepton mass windows providing access to different stages of the expansion history. Elliptic flow measurements for dileptons, combined with those of hadrons and direct photons, are a powerful tool for mapping the time evolution of heavy-ion collisions.

Figure 1

The mass spectrum of thermal dileptons from a hydrodynamical simulation of central 200 $A$ GeV Au+Au collisions ($b=0$). The quark and hadronic matter contributions are shown separately. See text for details.

Figure 2

The transverse momentum spectrum (upper panel) and differential elliptic flow $v_2(p_T)$ (lower panel) of thermal dileptons with invariant mass $M=m_{\rho }$. Dashed and dotted lines show quark matter (QGP,QM) and hadron matter (Had,HM) contributions, respectively. In the bottom panel we also show for comparison the elliptic flow of ρ mesons emitted from the hadronic decoupling surface.

Figure 3

Same as Fig. 2, but for dileptons with invariant $M=m_{\varphi }$, and with the elliptic flow of ϕ mesons from the hadronic decoupling surface shown in the bottom panel for comparison.

Figure 4

Transverse momentum spectrum of ϕ mesons, comparing the theoretical prediction from the hydrodynamic model with PHENIX data Ref. [46].

Figure 5

Same as Fig. 2, for $M=2$ GeV.

Figure 6

(Upper panel) $p_T$-integrated elliptic flow parameter for dileptons and various hadrons. (Middle panel) $p_T$ distributions of dileptons with $M=m_{\varphi }$ and $M=m_{\rho }$, and of ϕ and ρ mesons. (Lower panel) Differential elliptic flow for the above.

Figure 7

(Top panel) Dilepton mass dependence of the $p_T$-integrated elliptic flow parameter for thermal dileptons, for a variety of impact parameters ($b=$ 0, 2, 4, 6, 8, 10 fm from bottom to top (solid curves) and $b=$ 1, 3, 5, 7, 9 fm (dashed curves)). Note that $v_2$ for $b=10$ fm is marginally smaller than for $b=$ 9 fm. (Bottom panel) Impact parameter dependence of the $p_T$-integrated elliptic flow parameter scaled by the initial spatial eccentricity $\epsilon$, for a variety of hadrons and dileptons with different masses.