# Small $x$ phenomenology on gluon evolution through BFKL equation in light of a constraint in multi-Regge kinematics

## TL;DR

This paper explores how implementing a kinematic constraint affects small-x gluon evolution via the BFKL equation, providing analytical solutions and comparing predictions with global data fits.

## Contribution

It introduces a modified BFKL equation with a kinematic constraint, solves it analytically, and analyzes its impact on gluon distributions compared to the original BFKL approach.

## Key findings

- Kinematic constraint significantly alters gluon evolution predictions.
- Analytical solutions show different x and $k_t^2$ dependencies.
- Predictions are consistent with global data fits for certain parameters.

## Abstract

We investigate the impact of so called kinematic constraint on gluon evolution at small $x$. Implanting the constraint on the real emission term of gluon ladder diagram, we obtain an integro-differential form of BFKL equation. Later we solve the equation analytically using the method of characteristics. We sketch the Bjorken x and transverse momentum $k_t^2$ dependence of our solution of unintegrated gluon distributions $f(x,k_t^2)$ in kinematic constraint supplemented BFKL equation and contrasted the same with original BFKL equation. Then we extract the collinear gluon density $xg(x,Q^2)$ from unintegrated gluon distributions $f(x,k_t^2)$ and compared our theoretical prediction with that of global data fits viz. NNPDF3.1sx and CT14. Finally we assess the sensitivity of $f(x,k_t^2)$ towards BFKL intercept $\lambda$ for three canonical choices of $\lambda$ viz. o.4, 0.5 and 0.6.