Rapidity-even directed flow splitting of protons and antiprotons as a probe of baryon stopping in relativistic heavy-ion collisions

We compare the rapidity-even directed flow $v_1^{\rm even}$ in Au+Au collisions at Beam Energy Scan (BES) energies for baryons and anti-baryons within a (3+1)-dimensional viscous relativistic hydrodynamics coupled to hadronic transport framework. The double-junction baryon stopping picture motivates a rapidity-even component in the baryon deposition in the initial state. We demonstrate that the split in the $v_1^{\rm even}$ of protons and anti-protons is sensitive to the rapidity extension of the baryon deposition that we associate with the double junction baryon stopping. Particularly, we find that the mid-rapidity curvature $\frac{d^2 \Delta v_1^{\rm even} (p-\bar{p})}{dy^2}\vert_{y=0}$ is a robust discriminator of the initial state baryon rapidity profiles. A simultaneous measurement of $\Delta v_1^{\rm even}$ and its curvature at mid-rapidity could constrain both the baryon diffusion strength and the baryon stopping profile, providing access to the physics of baryon stopping in relativistic heavy ion collisions.