Incomplete electromagnetic response of hot QCD matter

The electromagnetic response of hot QCD matter to decaying external magnetic fields is investigated. We examine the validity of Ohm's law and find that the induced electric current increases from zero and relaxes towards the value from Ohm's law. The relaxation time is larger than the lifetime of the external magnetic field for the QCD matter in relativistic heavy-ion collisions. The lower-than-expected electric current significantly suppresses the induced magnetic field and makes the electromagnetic response incomplete. We demonstrate the incomplete electromagnetic response of hot QCD matter by calculations employing the parton transport model combined with the solution of Maxwell's equations. Our results show a strong suppression by two orders of magnitude in the magnetic field relative to calculations assuming the validity of Ohm's law. This may undermine experimental efforts to measure magnetic-field-related effects in heavy-ion collisions.

Figure 1

The electric current density along the $\varphi$ direction at $r=2.5\text{fm}$. Solid curves are the results from BAMPS calculations, while the dashed lines are the results from Ohm's law $j_{\varphi }^{\mathrm{Ohm}}={\sigma }_{el}{E}_{\varphi }$. The total cross section is set to be 1 or $2\text{mb}$.

Figure 2

The induced magnetic field at $\mathbf{r}=0$. The solid curves are the results from BAMPS calculations, while the dashed lines are the results with Ohm's law.

Figure 3

The electric current density at $(x=2\text{fm}$, $y=0$, $z=0.2\text{fm})$. The solid curves are the results from BAMPS, while the dashed curves are the results by solving Eqs. (10) and (11) and using Ohm's law.

Figure 4

The magnetic field at $\mathbf{r}=0\text{fm}$. The dotted curve depicts the external field, the solid curves are the total magnetic field (induced plus external field) from BAMPS calculation, and the dashed curves are the total magnetic field by solving Eqs. (10) and (11).