Abstract
We present detailed numerical analysis of the unintegrated double gluon distribution which includes the dependence on the transverse momenta of partons. The unintegrated double gluon distribution was obtained following the Kimber-Martin-Ryskin method as a convolution of the perturbative gluon splitting function with the collinear integrated double gluon distribution and the Sudakov form factors. We analyze the dependence on the transverse momenta, longitudinal momentum fractions and hard scales. We find that the unintegrated gluon distribution factorizes into a product of two single unintegrated gluon distributions in the region of small values of x, provided the splitting contribution is included and the momentum sum rule is satisfied.
Highlights
JHEP01(2018)141 a non-homogeneous term which originates from the perturbative splitting of two partons
As a general conclusion from the presented analysis, the transverse momentum dependent double gluon distribution is shifted towards larger values of transverse momenta with increasing values of the hard scales Q1,2 and decreasing values of the longitudinal momentum fractions x1,2
The model with angular ordering in the last step of the evolution leads to a distribution which extends further in transverse momenta than in the strong ordering scenario in which the transverse momenta are cut off by the hard scales
Summary
We shall start by recalling the evolution equations for the collinear double parton distribution functions. We shall review first the evolution equations for the integrated double parton distribution functions, following results of ref. We note that the DPDFs depend on the transverse momentum vector, q⊥, which we set to zero This means that in the Fourier space one integrates over the relative position of the two partons b, see [25, 53]. The functions Eab are parton-to-parton evolution distributions which obey the DGLAP evolution equation,. The first, homogenous term, Da(h1)a2, is proportional to the double parton distribution and corresponds to the independent evolution of two partons from the initial scale Q0 to Q1 and from Q0 to Q2. The single distributions Da are evaluated at (x1 + x2) due to conservation of the parton longitudinal momentum in the evolution
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