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

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 [G _μνG ^μν], 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 x _B< 10 ⁻⁴, while for the p _T -spectrum of a leading jet in the considered process, NLO corrections are small (< O(20%)) and LO of k _T -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.