Constraining neutron-proton effective mass splitting from nuclear giant dipole resonance data within a 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 ${\ensuremath{\sigma}}^{*}$ on the isovector giant dipole resonance (IVGDR) in $^{208}\mathrm{Pb}$, 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 ${\ensuremath{\sigma}}^{*}$, while the width $\mathrm{\ensuremath{\Gamma}}$ of the IVGDR is primarily governed by ${\ensuremath{\sigma}}^{*}$ with a moderate sensitivity to ${m}_{v,0}^{*}$. From a Bayesian analysis of both ${m}_{1}$ and $\mathrm{\ensuremath{\Gamma}}$, we infer that the ${m}_{v,0}^{*}/m$ = $0.{730}_{\ensuremath{-}0.034}^{+0.036}$, where $m$ is the bare nucleon mass. Furthermore, by incorporating the isoscalar nucleon effective mass ${m}_{s,0}^{*}/m=0.820\ifmmode\pm\else\textpm\fi{}0.030$, extracted from the isoscalar giant quadrupole resonance in $^{208}\mathrm{Pb}$, the linear neutron-proton effective mass splitting coefficient at saturation density ${\ensuremath{\rho}}_{0}$ is determined to be $\mathrm{\ensuremath{\Delta}}{m}_{1}^{*}({\ensuremath{\rho}}_{0})/m=0.{202}_{\ensuremath{-}0.114}^{+0.118}$.