Orateur
Description
We assume a relatively weak magnetic field at $0.01-0.1 m_{\pi}^{2}$ level in the QGP. In approximate equilibrium, the quark distribution function is modified by the electromagnetic field. The quark and anti-quark tend to move back to back in the plane. As a consequence, the virtual photons are produced in the polarized states. Virtual photon polarization is characterized by coefficients $\lambda_{\theta}$ and $\lambda_{\phi}$, which are sensitive to the magnetic field and hydrodynamic behaviors.
In a static QGP, a magnetic field with an intensity of $0.05m_\pi^2$ enhances the observable quantity $\lambda_\theta$ by 0.07. This implies that within the precision range of heavy-ion collision experiments, the residual magnetic field in the late-stage evolution of the quark-gluon plasma can be probed. Thermal dileptons emitted by the QGP contribute significantly in the intermediate invariant mass region. Our research indicates that $\lambda_{\theta}$ exhibits good sensitivity to the magnetic field throughout the entire intermediate invariant mass region. In the range of M=0.6-3 GeV, the deviation caused by a nonzero weak magnetic field is $\lambda_\theta\left(M,eB=0\right)-\lambda_\theta\left(M,eB=0.075m_\pi^2\right)\sim0.06-0.07$, and its sensitivity remains stable. Furthermore, we investigated the effects of transverse momentum, rapidity, azimuthal angle, QGP temperature, and electric conductivity on the coefficient $\lambda_\theta$ and $\lambda_{\phi}$.
Finally, we considered the longitudinal expansion effect of the QGP. In addition to the previous factors, the polarization effect becomes more pronounced. Overall, the current research confirms the sensitivity of virtual photon polarization and dilepton anisotropy to the late-stage magnetic field evolution.
