APPROXIMATE ANALYTICAL LOWER BOUNDS ON DOUBLE ASYMPTOTIC SCALING VARIABLES AND PHYSICS AT HERA

We analytically examine the asymptotic solution of gluon evolution equ ation in terms of the 'double scaling variables' rho and sigma of pert urbative QCD and find the approximate lower bounds on these, above whi ch the solution is considered to be valid. Comparison of this asymptot ic solution is made with the fit obtained from data and the estimated lower bound on rho is nearly equal to our analytical finding. To analy ze the data below the lower bound on rho, other analytical solutions o f gluon evolution equation are to be used which depend highly on the i nput x-distributions of gluon to study the physics at low-x of HERA ra nge.