Charge-dependent directed flow in asymmetric nuclear collisions

The directed flow of identified hadrons is studied within the parton-hadron-string-dynamics (PHSD) approach for the asymmetric system Cu + Au in noncentral collisions at $\sqrt{s_{\mathit{NN}}}=200$ GeV. It is emphasized that due to the difference in the number of protons of the colliding nuclei an electric field emerges, which is directed from the heavy to the light nucleus. This strong electric field is only present for about 0.25 fm/c at $\sqrt{s_{\mathit{NN}}}=200$ GeV and leads to a splitting of the directed flow $v_1$ for particles with the same mass but opposite electric charges in case of an early presence of charged quarks and antiquarks. The microscopic calculations of the directed flow for ${\pi }^{\pm },K^{\pm },p$, and $\overline{p}$ are carried out in the PHSD by taking into account the electromagnetic field induced by the spectators as well as its influence on the hadronic and partonic quasiparticle trajectories. It is shown that the splitting of the directed flow as a function of pseudorapidity $\eta$ and in particular as a function of the transverse momentum $p_t$ provides a direct access to the electromagnetic response of the very early (nonequilibrium) phase of relativistic heavy-ion collisions and allows us to shed light on the presence (and number) of electric charges in this phase.

Figure 1

Time evolution of event-averaged components of the magnetic (left-hand side) and electric (right-hand side) fields in the center of the overlap region of colliding Cu + Au (solid lines) and Au + Au (dotted lines) systems at $\sqrt{s_{\mathit{NN}}}=200$ GeV and $b=7$ fm. The distributions are averaged over 70 events.

Figure 2

Event-averaged electric field in the transverse plane for a Cu + Au (left) and Au + Au (right) collision at 200 GeV at time $t=0.05$ fm/c for the impact parameter $b=7$ fm. Each vector represents the direction and magnitude of the electric field at that point.

Figure 3

Rapidity dependence of the directed flow of pions and kaons created in off-central Cu + Au collisions at $\sqrt{s_{\mathit{NN}}}=200$ GeV. The PHSD results for positive pions and kaons $v_1^{+}$ and for negative ones $v_1^{-}$ are plotted by the solid and dashed histograms, respectively. Results by including the effect of the electromagnetic field on early charges are marked by filled and empty circles for $v_1^{+}$ and $v_1^{-}$, respectively.

Figure 4

Rapidity dependence of the pion directed flow in Au + Au collisions at $\sqrt{s_{\mathit{NN}}}=200$ GeV. The solid histogram is calculated in PHSD for ${\pi }^{+}$ and the dashed one for ${\pi }^{-}$ mesons. Results from PHSD by including the effect of the electromagnetic field on early charges are marked by filled and empty circles for $v_1^{+}$ and $v_1^{-}$, respectively. Experimental data points (stars) are from Ref. [6].

Figure 5

Rapidity dependence of the directed flow of protons and antiprotons in Cu + Au collisions at $\sqrt{s_{\mathit{NN}}}=200$ GeV. The notation is the same as in Fig. 3.

Figure 6

Transverse momentum dependence of the directed flow for ${\pi }^{\pm }$ (top) and protons and antiprotons (bottom) produced in peripheral Cu + Au collisions for forward (right) and backward (left) emitted hadrons at $\sqrt{s_{\mathit{NN}}}=200$ GeV. The notation is the same as in Fig. 3.