Effect of magnetic fields on pairs of oppositely charged particles in ultrarelativistic heavy-ion collisions

The initial strong magnetic field produced in high-energy nuclear collisions will distort the distribution of the relative angle between oppositely charged particles within a pair. In this paper, two experimental observables are examined to quantify such effects: one based on the framework for detecting the hyperon global polarization, and the other based on the balance function. We also discuss the optimization of the signal, as well as the expected magnitude ranges for the two observables.

Figure 1

The setup of the coordinate system. See text for details.

Figure 2

Simulated $\mathrm{\Delta }\alpha$ distributions for $e^{+}{e}^{-}$ pairs from decays of virtual particles with mass of 0.5 GeV/$c^2$, and momentum of 0.5 GeV/$c$ (solid line) or 0.2 GeV/$c$ (dotted line). The momentum directions of the virtual particles have been randomized.

Figure 3

The upper panel shows the $\mathrm{\Delta }\alpha$ distribution for random electrons and positrons, before (solid line) and after (dashed line) the turning on of the magnetic field. The lower panel shows the same distribution for $e^{+}{e}^{-}$ pairs originating from decays of virtual particles with a mass of 0.5 GeV/$c^2$ and momentum of 0.5 GeV/$c$, before (solid line) and after (dashed line) the turning on of the magnetic field.

Figure 4

The simulated $\mathrm{\Delta }\alpha$ distribution using the $e^{+}{e}^{-}$ continuum taken from the STAR publication [23], in which the $e^{+}{e}^{-}$ continuum is for $p_T<1.5\mathrm{GeV}/c,\left|\eta \right|<1$ and invariant mass from $0.4\mathrm{GeV}/c^2$ to $0.76\mathrm{GeV}/c^2$. The blue solid line represents the distribution without the magnetic field, and the red dashed line denotes the case with the magnetic field.

Figure 5

$\langle sin\mathrm{\Delta }\alpha \rangle$ for $e^{+}{e}^{-}$ pairs from free-decay parents, as a function of the parents' mass and momentum. The applied magnetic field is $eB=5\times {10}^{-3}{\mathrm{GeV}}^2$ for a period of 1 fm/$c$.

Figure 6

($-P_s$) versus relative production time (${\tau }_r$) of $e^{+}{e}^{-}$ pairs, for two cases of the initial magnetic fields. Solid lines (KMW) are based on Fig.A.2 in Ref. [1], for $b=8$ fm. Dashed lines (HSD) are based on Fig. 4 in Ref. [28], for $b=10$ fm. For both cases, the $P_s$ calculation is done for three divisions of $e^{+}{e}^{-}$ invariant mass ($M_{ee}$) according to Ref. [23].

Figure 7

${\mathcal{B}}_P$ and ${\mathcal{B}}_N$ calculated for $e^{+}{e}^{-}$ pairs from virtual-particle decays, with and without the magnetic field. The magnetic field and its acting time, mass, and momentum of the virtual particle are the same as those in Fig. 3.

Figure 8

Upper panel: skewness of ${\mathcal{B}}_P$ and ${\mathcal{B}}_N$ versus relative production time (${\tau }_r$) of $e^{+}{e}^{-}$ pairs, for two cases of the initial magnetic field. Solid lines (KMW) are based on Fig.A.2 in Ref. [1], for $b=8$ fm. Dashed lines (HSD) are based on Fig. 4 in Ref. [28], for $b=10$ fm. For both cases, the calculation is done for three divisions of $e^{+}{e}^{-}$ invariant mass ($M_{ee}$) according to Ref. [23]. Lower panel: the same calculation, but presented with normalized skewness difference, $\frac{S_{{\mathcal{B}}_N}-S_{{\mathcal{B}}_P}}{2}$, in log scale for clear view of small values.

Figure 9

The sensitivity for $e^{+}{e}^{-}$ (top panel) and ${\pi }^{+}{\pi }^{-}$ (bottom panel) pairs, based on studies with simulated pairs. See text for details. The invariant mass spectrum for signal pair of ${\pi }^{+}{\pi }^{-}$ is taken from [36].