  In collisions of identical nuclei at a given impact parameter, the number of
nucleons participating in the overlap region of each nucleus can be unequal due
to nuclear density fluctuations. The asymmetry due to the unequal number of
participating nucleons, referred to as longitudinal asymmetry, causes a shift
in the center of mass rapidity of the participant zone. The information of the
event asymmetry allows us to isolate and study the effect of longitudinal
asymmetry on rapidity distribution of final state particles. In a Monte Carlo
Glauber model the average rapidity-shift is found to be almost linearly related
to the asymmetry. Using toy models, as well as Monte Carlo data for Pb-Pb
collisions at 2.76 TeV generated with HIJING, two different versions of AMPT
and DPMJET models, we demonstrate that the effect of asymmetry on final state
rapidity distribution can be quantitatively related to the average rapidity
shift via a third-order polynomial with a dominantly linear term. The
coefficients of the polynomial are proportional to the rapidity shift with the
dependence being sensitive to the details of the rapidity
distribution.Experimental estimates of the spectator asymmetry through the
measurement of spectator nucleons in a Zero Degree Calorimeter may hence be
used to further constrain the initial conditions in ultra-relativistic
heavy-ion collisions.
