Abstract
We perform a detailed analysis of the different forms of the kinematical constraint imposed on the low x evolution that appear in the literature. We find that all of them generate the same leading anti-collinear poles in Mellin space which agree with BFKL up to NLL order and up to NNLL in N=4 sYM. The coefficients of subleading poles vanish up to NNLL order for all constraints and we prove that this property should be satisfied to all orders. We then demonstrate that the kinematical constraints differ at further subleading orders of poles. We quantify the differences between the different forms of the constraints by performing numerical analysis both in Mellin space and in momentum space. It can be shown that in all three cases BFKL equation can be recast into the differential form, with the argument of the longitudinal variable shifted by the combination of the transverse coordinates.
Highlights
Given the increased precision of the experimental data and progress in theoretical computations, especially the informa- 647 Page 2 of 14Eur
In the paper we have performed a detailed analysis of the three versions of kinematical constraints imposed onto the momentum space BFKL equation
We observed that the leading poles in Mellin space generated by the kinematical constraint obey maximal transcendentality principle
Summary
Given the increased precision of the experimental data and progress in theoretical computations, especially the informa-. In the analysis performed in this work we found that the constrains all generate the same structure in the Mellin space for the leading and first subleading anti-collinear poles up to NLL order in ln 1/x in QCD and in N = 4 sYM and up to NNLL in N = 4 sYM. As such they are all consistent up to the highest known order of perturbation theory.
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