Probing the in-medium $P_T$-broadening by $\gamma$+HF angular de-correlations

Angular correlations between vector boson and heavy flavors~(HF) are potentially new effective tools to gain insight into the partonic interactions in the quark-gluon plasma (QGP). In this paper, we present the theoretical study of the azimuthal angular de-correlations of $\gamma+$HF in nucleus-nucleus collisions as a new probe of the in-medium $P_T$-broadening effect. The initial production of $\gamma+$HF in p+p is generated by SHERPA which matches the next-to-leading hard processes with parton shower. The in-medium heavy quark evolution is implemented by a Monte Carlo Langevin simulation, which takes into account the collisional and radiative energy loss. We observe considerable suppression at $\Delta\phi_{\gamma D}\sim\pi$ and enhancement at $\Delta\phi_{\gamma D}<2.8$ in $\gamma+$D azimuthal angular distribution in $0-10\%$ Pb+Pb collisions at $\sqrt{s_{NN}}=$5.02 TeV compared to the p+p baseline, which indicates evident in-medium $P_T$-broadening of charm quarks. We also find that the overall modification patterns of $\gamma+$D angular distribution are sensitive to the selection cut of D meson $p_T$. Furthermore, by constructing the 2D ($x_{J}^{\gamma D}, \Delta\phi_{\gamma D}$) correlation diagram, it's possible to display the respective impacts of the two aspects of jet quenching, energy loss and $P_T$-broadening, on the final-state $\gamma+$D observable simultaneously. Additionally, we find weaker angular de-correlations of $\gamma+$B compared to $\gamma+$D which may be helpful to understand the mass hierarchy in heavy-ion collisions. Finally, the nuclear modification of $\Delta \phi_{\gamma D}$ distributions in central $0-10\%$ Au+Au collisions at RHIC energy is provided for completeness.