Estimation of Stopped Protons at Energies Relevant for a Beam Energy Scan at the BNL Relativistic Heavy-Ion Collider

The recent net-proton fluctuation results of the STAR (Solenoidal Tracker At RHIC) experiment from beam energy scan (BES) program at the BNL Relativistic Heavy Ion Collider (RHIC) have drawn much attention to exploring the QCD critical point and the nature of deconfinement phase transition. There has been much speculation that the non-monotonic behavior of $kappasigma^{2}$ of the produced protons around $sqrt{s_{rm NN}}$ = 19.6 GeV in the STAR results may be due to the existence of QCD critical point. However, the experimentally measured proton distributions contain protons from heavy resonance decays, from baryon stopping and from direct production processes. These proton distributions are used to estimate the net-proton number fluctuation. Because it is difficult to disentangle the protons from the above-mentioned sources, it is better to devise a method which will account for the directly produced baryons (protons) to study the dynamical fluctuation at different center-of-mass energies. This is because, it is assumed that any associated criticality in the system could affect the particle production mechanism and hence the dynamical fluctuation in various conserved numbers. In the present work, we demonstrate a method to estimate the number of stopped protons at RHIC BES energies for central $0-5%$ auau collisions within STAR acceptance and discuss its implications on the net-proton fluctuation results.