In this thesis, analysis of the forward backward asymmetry of high energy electron pairs at the CMS - LHC with a centre of mass energy of 7 TeV is presented and the possibility of search for a new neutral weak boson Z&rsquo / via measuring the forward backward asymmetry AFB of high energy electron pairs is discussed. The forward backward asymmetry is a natural result of the interference between the neutral current mediators: Photon and Z boson. A new neutral gauge boson would also interfere with these mediators and this new interference would either enhance the forward backward asymmetry at high energies or suppress it. In this analysis, 4.67 fb&minus / 1 data collected at the CMS experiment in 2011 is used