Baryon diffusion coefficient of the strongly interacting medium

We propose that the transverse momentum ($p_T$) differential splitting of directed flow ($\mathrm{\Delta }{v}_1$) between proton and anti-proton can serve as a sensitive observable to extract the baryon diffusion coefficient (${\kappa }_B$) of the hot and dense strongly interacting matter produced in relativistic heavy ion collisions. We use relativistic dissipative hydrodynamics framework with Glauber model based initial condition for the energy as well as baryon deposition that is calibrated to capture the rapidity dependence of charged particle multiplicity, net proton yield as well as the elusive $v_1$ splitting between proton and anti-proton. We employ the commonly used kinetic theory motivated ansatz: ${\kappa }_B=C_B\frac{n_B}{T}(\frac{1}{3}\text{coth}\left(\frac{{\mu }_B}{T}\right)-\frac{n_{B}T}{\epsilon +P})$ where $n_B$, $\epsilon$, $P$, $T$ and ${\mu }_B$ are baryon number density, energy density, pressure, temperature and baryon chemical potential respectively while $C_B$ is an arbitrary constant which is largely unknown for the Quantum Chromodynamics (QCD) medium. We find that the variation of $\mathrm{\Delta }{v}_1$ with $p_T$ is strongly influenced by the choice of $C_B$. Further, we find that the recent STAR measurement of the centrality dependence of the rapidity slope of $\mathrm{\Delta }{v}_1$ prefers $0.5<C_B<1.5$.