Correlations and fluctuations in a magnetized PNJL model with and without inverse magnetic catalysis effect

The correlation $\chi^{BQ}_{11}$ and quadratic fluctuations $\chi^B_2,\ \chi^Q_2,\ \chi^T_2$ of baryon number $B$, electric charge $Q$ and temperature $T$ are investigated in a two-flavor Polyakov loop extended Nambu-Jona-Lasinio (PNJL) model at finite temperature and magnetic field. The inverse magnetic catalysis (IMC) effect is introduced through the magnetic field dependent parameters $G(eB)$ or $T_0(eB)$, and we make comparison of the results in the cases with and without IMC effect. With nonvanishing magnetic field, the correlation $\chi^{BQ}_{11}$ and fluctuations $\chi^B_2,\ \chi^Q_2,\ \chi^T_2$ increase with temperature, and then show the peak around the pseudocritical temperatures of chiral restoration and deconfinement phase transitions in the cases with and without the IMC effect. The correlation and fluctuations along the phase transition line under external magnetic field are characterized by the scaled correlation ${\hat {\chi}}_{11}^{BQ}=\frac{\chi_{11}^{BQ}(eB,T_{pc}^c(eB))}{\chi_{11}^{BQ}(eB=0,T_{pc}^c(eB=0))}$ and scaled fluctuations ${\hat {\chi}}_2^{B(Q,T)}=\frac{\chi_2^{B(Q,T)}(eB,T_{pc}^c(eB))}{\chi_2^{B(Q,T)}(eB=0,T_{pc}^c(eB=0))}$ at the pseudocritical temperature $T_{pc}^c$ of chiral restoration phase transition. ${\hat {\chi}}_{11}^{BQ},\ {\hat {\chi}}_2^{B}$, and ${\hat {\chi}}_2^{Q}$ increase with magnetic fields, and the inclusion of IMC effect leads to some enhancement in their values. However, ${\hat {\chi}}_2^{T}$ is altered by the IMC effect. Without IMC effect, ${\hat \chi}^T_2$ slightly increases and then decreases with magnetic fields. Taking into account of the IMC effect by $G(eB)$, ${\hat \chi}^T_2$ monotonically increases with magnetic fields, and by $T_0(eB)$, it is a nonmonotonic function of magnetic field.