Electromagnetic fields in small systems from a multiphase transport model

We calculate the electromagnetic fields generated in small systems by using a multiphase transport (AMPT) model. Compared to $A+A$ collisions, we find that the absolute electric and magnetic fields are not small in $p+\mathrm{Au}$ and $d+\mathrm{Au}$ collisions at energies available at the BNL Relativistic Heavy Ion Collider and in $p+\mathrm{Pb}$ collisions at energies available at the CERN Large Hadron Collider. We study the centrality dependencies and the spatial distributions of electromagnetic fields. We further investigate the azimuthal fluctuations of the magnetic field and its correlation with the fluctuating geometry using event-by-event simulations. We find that the azimuthal correlation $〈cos2({\mathrm{\Psi }}_{\mathrm{B}}-{\mathrm{\Psi }}_2)〉$ between the magnetic field direction and the second-harmonic participant plane is almost zero in small systems with high multiplicities, but not in those with low multiplicities. This indicates that the charge azimuthal correlation $〈cos({\varphi }_{\alpha }+{\varphi }_{\beta }-2{\mathrm{\Psi }}_{\mathrm{RP}})〉$ is not a valid probe to study the chiral magnetic effect (CME) in small systems with high multiplicities. However, we suggest searching for possible CME effects in small systems with low multiplicities.

Figure 1

The electromagnetic fields at $t=0$ and $\mathbf{r}=\mathbf{0}$ for $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s}=200$ GeV.

Figure 2

The electromagnetic fields at $t=0$ and $\mathbf{r}=\mathbf{0}$ for $\mathrm{Pb}+\mathrm{Pb}$ collisions at $\sqrt{s}=2.76$ TeV.

Figure 3

The special geometrical illustration for $p+\mathrm{Pb}$ collisions with an impact parameter of $b$.

Figure 4

The electromagnetic fields at $t=0$ and $\mathbf{r}={\mathbf{r}}_c$ as functions of the impact parameter $b$ in $p+\mathrm{Au}$ collisions (a) and $d+\mathrm{Au}$ collisions (b) at $\sqrt{s}=200$ GeV and in $p+\mathrm{Pb}$ collisions at $\sqrt{s}=5.02$ TeV (c).

Figure 5

The electromagnetic fields at $t=0$ and $\mathbf{r}={\mathbf{r}}_c$ as functions of $N_{\mathrm{part}}$ in $p+\mathrm{Au}$ collisions (a) and $d+\mathrm{Au}$ collisions (b) at $\sqrt{s}=200$ GeV and in $p+\mathrm{Pb}$ collisions at $\sqrt{s}=5.02$ TeV (c).

Figure 6

The electromagnetic fields at $t=0$ and $\mathbf{r}={\mathbf{r}}_c$ as functions of $N_{\mathrm{track}}$ in $p+\mathrm{Au}$ collisions (a) and $d+\mathrm{Au}$ collisions (b) at $\sqrt{s}=200$ GeV and in $p+\mathrm{Pb}$ collisions at $\sqrt{s}=5.02$ TeV (c).

Figure 7

The spatial distributions of the electromagnetic fields in the transverse plane at $t=0$ for $b=0$ (upper panels) and $b=6$ fm (lower panels) for $p+\mathrm{Pb}$ collisions at $\sqrt{s}=5.02$ TeV, where the unit is $m_{\pi }^2$.

Figure 8

The event-by-event histograms of ${\mathrm{\Psi }}_B-{\mathrm{\Psi }}_2$ at impact parameters $b=0$, 3, 6, and 9 fm [(a)–(d)] for $p+\mathrm{Pb}$ collisions at $\sqrt{s}=5.02$ TeV. Here ${\mathrm{\Psi }}_{\mathrm{B}}$ is the azimuthal direction of the B field (at $t=0$ and $\mathbf{r}={\mathbf{r}}_c$) and ${\mathrm{\Psi }}_2$ is the second-harmonic participant plane.

Figure 9

The scatter plots on the ${\mathrm{\Psi }}_B-{\mathrm{\Psi }}_2$ plane at impact parameters $b=0$, 3, 6, and 9 fm [(a)–(d)] for $p+\mathrm{Pb}$ collisions at $\sqrt{s}=5.02$ TeV, where ${\mathrm{\Psi }}_{\mathrm{B}}$ is the azimuthal direction of the B field (at $t=0$ and $\mathbf{r}={\mathbf{r}}_c$) and ${\mathrm{\Psi }}_2$ is the second-harmonic participant plane.

Figure 10

The correlation $〈cos2({\mathrm{\Psi }}_{\mathrm{B}}-{\mathrm{\Psi }}_2)〉$ as a function of the impact parameter $b$ (a) and as a function of $N_{\mathrm{track}}$ (b) in $p+\mathrm{Au}$ and $d+\mathrm{Au}$ collisions at $\sqrt{s}=200$ GeV and in $p+\mathrm{Pb}$ collisions at $\sqrt{s}=5.02$ TeV.