Towards stability of NLO corrections in high-energy factorization via modified multi-Regge kinematics approximation

Maxim Nefedov

doi:10.1007/jhep08(2020)055

Abstract

The perturbatively-stable scheme of Next-to-Leading order (NLO) calculations of cross-sections for multi-scale hard-processes in DIS-like kinematics is developed in the framework of High-Energy Factorization. The evolution equation for unintegrated PDF, which resums log 1/z-corrections to the coefficient function in the Leading Logarithmic approximation together with a certain subset of Next-to-Leading Logarithmic and Next- to-Leading Power corrections, necessary for the perturbative stability of the formalism, is formulated and solved in the Doubly-Logarithmic approximation. An example of DIS-like process, induced by the operator tr [GμνGμν ], which is sensitive to gluon PDF already in the LO, is studied. Moderate (O(20%)) NLO corrections to the inclusive structure function are found at small xB< 10−4, while for the pT -spectrum of a leading jet in the considered process, NLO corrections are small (< O(20%)) and LO of kT -factorization is a good approximation. The approach can be straightforwardly extended to the case of multi-scale hard processes in pp-collisions at high energies.

Highlights

Results of pioneering papers [12, 13], always where major drawbacks of High-Energy factorization program
The perturbative instability of Balitsky-Fadin-Kuraev-Lipatov(BFKL)formalism [14,15,16], first observed in a celebrated calculation of Next-to-Leading order (NLO) BFKL kernel [17,18,19] is a main reason of a slow development of kT -factorization beyond LO
The main source of large NLO corrections to the BFKL kernel was immediately identified in the ref. [20], these are large logarithms of transverse momentum, coming from the collinear region of the NLO correction, which are not reproduced by the iteration of LO kernel

Summary

Basic formalism and UPDF evolution in MRK approximation

We will always refer to a particular example of hard process — the DIS-like process (momenta of particles are given in parentheses): O(q) + p(P ) → X,. Below we will derive the real-emission term of evolution equation for C in the standard MRK approximation, which eventually will coincide with the LO BFKL equation with real emissions ordered in physical rapidity, but rewritten in terms of light-cone momentum fractions z and transverse momenta. To this end let’s consider the kT -factorized expression for the contribution to the coefficient function of CPM (2.7) with n − 1 real emissions already factorized into evolution factor Cn−1 and emission of one additional gluon with four-momentum kn in the PRA matrix element (see the figure 1): dCn(z) dΠ(MLO). The UPDF obtained from doubly-logarithmic solution of this simplified equation is used for illustrative numerical calculations throughout this paper

Modified MRK approximation: subtraction terms and UPDF evolution

Virtual correction and subtractions

Numerical results

A UPDF in doubly-logarithmic approximation

Findings

B Taking iterations of MRK-evolution kernel