The longitudinal asymmetry arises in relativistic heavy ion collisions due to fluctuation in the number of participating nucleons. This asymmetry causes a shift in the center of mass rapidity of the participant zone. The rapidity shift as well as the
longitudinal asymmetry have been found to be significant at the top LHC energy for collisions of identical nuclei. We study the longitudinal asymmetry and its effect on charged particle rapidity distribution and anisotropic flow parameters at relatively lower RHIC energies using a model calculation. The rapidity shift is found to be more pronounced for peripheral collisions, smaller systems and also for lower beam energies due to longitudinal asymmetry. A detailed study has been done by associating the average rapidity shift to a polynomial relation where the coefficients of this polynomial characterize the effect of the asymmetry. We show that the rapidity shift may affect observables significantly at RHIC energies.
The particle momentum anisotropy ($v_n$) produced in relativistic nuclear collisions is considered to be a response of the initial geometry or the spatial anisotropy $epsilon_n$ of the system formed in these collisions. The linear correlation between
$epsilon_n$ and $v_n$ quantifies the efficiency at which the initial spatial eccentricity is converted to final momentum anisotropy in heavy ion collisions. We study the transverse momentum, collision centrality, and beam energy dependence of this correlation for different charged particles using a hydrodynamical model framework. The ($epsilon_n -v_n$) correlation is found to be stronger for central collisions and also for n=2 compared to that for n=3 as expected. However, the transverse momentum ($p_T$) dependent correlation coefficient shows interesting features which strongly depends on the mass as well as $p_T$ of the emitted particle. The correlation strength is found to be larger for lighter particles in the lower $p_T$ region. We see that the relative fluctuation in anisotropic flow depends strongly in the value of $eta/s$ specially in the region $p_T <1$ GeV unlike the correlation coefficient which does not show significant dependence on $eta/s$.
