Constraining neutron-proton effective mass splitting through nuclear giant dipole resonance within transport approach

Based on the Boltzmann-Uehling-Uhlenbeck equation, we investigate the effects of the isovector nucleon effective mass $m_{v,0}^{\ast }$ and the in-medium nucleon-nucleon cross section ${\sigma }^{\ast }$ on the isovector giant dipole resonance~(IVGDR) in ${}^{208}\mathrm{P}\mathrm{b}$, employing a set of representative Skyrme energy density functionals. We find that the energy-weighted sum rule $m_1$ of the IVGDR is highly sensitive to $m_{v,0}^{\ast }$ and only mildly dependent on ${\sigma }^{\ast }$, while the width $\mathrm{\Gamma }$ of the IVGDR is primarily governed by ${\sigma }^{\ast }$ with a moderate sensitivity to $m_{v,0}^{\ast }$. From a Bayesian analysis of both $m_1$ and $\mathrm{\Gamma }$, we infer the isovector effective mass $m_{v,0}^{\ast }\mathrm{/}m$ = $0.731_{-0.023}^{+0.027}$, where $m$ is the bare nucleon mass. Furthermore, by incorporating the isoscalar effective mass $m_{s,0}^{\ast }\mathrm{/}m=0.820\pm 0.030$, extracted from the isoscalar giant quadrupole resonance in ${}^{208}\mathrm{P}\mathrm{b}$, the linear neutron-proton effective mass splitting coefficient at saturation density ${\rho }_0$ is determined to be $\mathrm{\Delta }{m}_1^{\ast }({\rho }_0)\mathrm{/}m=0.200_{-0.094}^{+0.101}$.