Studies on gluon evolution and geometrical scaling in kinematic constrained unitarized BFKL equation: application to high-precision HERA DIS data.

We suggest a modified form of a unitarized BFKL equation imposing the so-called kinematic constraint on the gluon evolution in multi-Regge kinematics. The underlying nonlinear effects on the gluon evolution are investigated by solving the unitarized BFKL equation analytically. We obtain an equation of the critical boundary between dilute and dense partonic system, following a new differential geometric approach and sketch a phenomenological insight on geometrical scaling. Later we illustrate the phenomenological implication of our solution for unintegrated gluon distribution $f(x,k_T^2)$ towards exploring high precision HERA DIS data by theoretical prediction of proton structure functions ($F_2$ and $F_L$) as well as double differential reduced cross-section $(\sigma_r)$. The validity of our theory in the low $Q^2$ transition region is established by studying virtual photon-proton cross-section in light of HERA data. We also investigate the claim that the longitudinal structure function $F_L$ is a sensitive probe of the gluon distribution and extract colinear gluon density $xg(x, Q^2)$ from $F_L$. Finally, we portray a dipole picture of kinematic constraint improved unitarized BFKL equation and examined $r$ (transverse size of the dipole) dependence of dipole cross-section.