Neutral pion masses within a hot and magnetized medium in a lattice-improved soft-wall AdS/QCD model

We investigate chiral phase transitions and the screening masses, pole masses, and thermal widths of neutral pion meson with finite temperature $T$ and magnetic field $B$ in a lattice-improved AdS/QCD model, which is constructed by fitting the lattice results of the pseudo-critical temperatures ( T_{\text{pc}}(B) ). Specifically, we have that the chiral condensate (\sigma) undergoes a crossover phase transition demonstrating distinct magnetic catalysis and inverse magnetic catalysis effects in very low and high-temperature regions with fixed finite $B$, respectively. For the screening masses, we find that the longitudinal component decreases with $B$ at very low and high temperatures and increases with $B$ near $T_{\text{pc}}$. The transverse component always increases with $B$ at fixed $T$. However, both the longitudinal and transverse screening masses increase with $T$ at fixed $B$. Furthermore, we find that the pole mass decreases with the increasing of $B$ or $T$. Besides, it is interesting to note that the thermal width shows similar behavior to the longitudinal screening masses in the very high temperature region.