Abstract
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.
Highlights
This constraint arises as a consequence of BFKL multi-Regge kinematics which suggests the exchanged gluon virtuality is dominated by transverse components while the longitudinal components of the gluon momentum are required to be small i.e. k 2 ≈ kT2
Page 3 of 25 507 (c) c, d Two simple examples of the inhomogeneous driving term of (10) which correspond to the shaded region of gluon-virtual photon coupling in b In Sect. 4 we explore the phenomenological implication of our solution for unintegrated gluon distribution towards prediction of DIS structure function F2 and longitudinal structure function FL at HERA
We have presented a phenomenological study on the behavior of unintegrated gluon distribution at smallx and moderate kT2 region 10−6 ≤ x ≤ 10−2 and 2 GeV2 ≤ kT2 ≤ 1000 GeV2 which is the accessible kinematic range to experiments performed at HERA ep collider
Summary
Where f (x, kT2 ) denotes the gluon distribution unintegrated over the transverse momentum of gluon kT and k. To simplify the distribution function f kT2 corresponding to real emission term in (12) we have incorporated Regge like behavior of gluon distribution. The leading order calculations in ln(1/x) with fixed αs predicts a steep power law behavior of f(x, k2) ∼ x−λBFKL [22,29] This motivates us to consider a simple form of Regge factorization as follows, f kT2 x −λBFKL kT2 kT2. In the vicinity of saturation limit, our interpretation of gluon distribution for the nonlinear term has to be reviewed In this region, the gluon distribution becomes flat which makes our Regge factorization for the nonlinear term in (14) invalid. The shadowing contribution becomes twice as that of antishadowing effect forecasting a net shadowing effect in the evolution
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