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 $m^*_{v,0}$ and the in-medium nucleon-nucleon cross section $\sigma^*$ on the isovector giant dipole resonance~(IVGDR) in $^{208}{\rm Pb}$, 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 $m^{*}_{v,0}$ and only mildly dependent on $\sigma^*$, while the width $\Gamma$ of the IVGDR is primarily governed by $\sigma^*$ with a moderate sensitivity to $m^*_{v,0}$. From a Bayesian analysis of both $m_1$ and $\Gamma$, we infer the isovector effective mass $m^{*}_{v,0}/m$ = $0.731^{+0.027}_{-0.023}$, where $m$ is the bare nucleon mass. Furthermore, by incorporating the isoscalar effective mass $m^*_{s,0}/m = 0.820 \pm 0.030$, extracted from the isoscalar giant quadrupole resonance in $^{208}{\rm Pb}$, the linear neutron-proton effective mass splitting coefficient at saturation density $\rho_0$ is determined to be $\Delta m^*_1 (\rho_0)/m = 0.200 ^{+0.101}_{-0.094}$.