Magnetic field influence on the early-time dynamics of heavy-ion collisions

In high-energy heavy-ion collisions, the magnetic field is very strong right after the nuclei penetrate each other and a nonequilibrium system of quarks and gluons builds up. Even though quarks might not be very abundant initially, their dynamics must necessarily be influenced by the Lorentz force. Employing the (3+1)-d partonic cascade Boltzmann approach to multiparton scatterings (BAMPS), we show that the circular Larmor movement of the quarks leads to a strong positive anisotropic flow of quarks at very soft transverse momenta. We explore the regions where the effect is visible and explicitly show how collisions damp the effect. As a possible application, we look at photon production from the flowing nonequilibrium medium.

Figure 1

Geometry of our model. The magnetic field is constant and homogeneous.

Figure 2

The two simple parametrizations of the homogeneous magnetic field. Param 2 follows Ref. [24].

Figure 3

After the increase of $p_x$, the momentum asymmetry $v_2$ is in all cases positive for $\mathrm{\Delta }{p}_x>p_T$. The result is symmetric in $\mathrm{\Delta }{p}_x$.

Figure 4

For three different initial $p_T$ distributions (power-law exponent $n)$, we show how the spectra change after $0.3\mathrm{fm}/\mathrm{c}$ under the influence of a magnetic field. Here we use an arbitrary number of particles and magnetic field parametrization 1.

Figure 5

Final average $v_2$ per particle for three different $p_T$ ranges as function of initial rapidity $y_{\text{initial}}$ of the particle. Here we use an initial state with power law exponent $n=2$ and magnetic field parametrization 1. The result for $n=3,4$ looks very similar, only the maximal value of the final $v_2$ increases by up to $25\%$.

Figure 6

The $p_T$-differential $v_2$ in a collisionless toy model for initial power law spectra with exponent $n=2,3,4$. Here we do not assign formation times. We show results for forward- and midrapidity with magnetic field parametrization 1.

Figure 7

Same as Fig. 6, but here formation times had been assigned. For the shown snapshot at $t=0.3\mathrm{fm}/\mathrm{c}$, the minimum occurring momentum at midrapidity is $p_T\approx 0.66\mathrm{GeV}$.

Figure 8

Transverse momentum spectra of quarks under the influence of a magnetic field in a free streaming and a collisional medium. We use an arbitrary number of particles and magnetic field parametrization 1. Particles collide with constant isotropic cross sections, ${\sigma }_{\text{tot}}=10\mathrm{mb}$.

Figure 9

The $p_T$-differential $v_2$ from BAMPS for the ultrasoft $p_T$ range with and without magnetic field. The initial state is equivalent to Sec. 2a, with exponent $n=2$. The initial geometry is equivalent to an impact parameter of $b=8.5\text{fm}$. We ignore formation times here. For a rough comparison, we show data from PHENIX [38] (unidentified charged hadrons, $\sqrt{s_{NN}}=200\mathrm{GeV},20–60\%$ centrality, $\left|\eta \right|<0.35)$.

Figure 10

Same as Fig. 9, but here we compare the magnetic field parametrizations 1 and 2.

Figure 11

Photon $v_2$ as function of $p_T$ compared to quark $v_2$ for magnetic field parametrization 1. Here we use an initial state with power law exponent $n=3$. Photons and quarks are evaluated at midrapidity at $t=2\mathrm{fm}/\mathrm{c}$.