Transverse momentum dependent gluon density in a proton at low x in the Laplace transform method

We investigate the gluon distribution in a proton at very low x , both integrated and transverse momentum dependent, using the Laplace transform technique. By accounting for leading and main next-to-leading contributions, we derive compact analytical expressions for the gluon densities under rather arbitrary initial conditions valid in the asymptotic limit x → 0. Our results closely match those from other analytical and numerical approaches, with the main advantage being the simplicity of the expressions, which capture the essential features of more complex calculations. Moreover, for the first time we present analytic expressions for the Sudakov form factor with angular and strict ordering conditions.