Speaker
Description
The high energy limit of QCD is a storehouse of rich phenomenology. In this limit, perturbative series receive logarithmic (small-$x$) enhancements associated with wide-rapidity separations necessitating their all-order resummation. However, reliably and comprehensively incorporating the NLL corrections associated with this limit consistent with collinear resummation and PDF factorization has been a longstanding challenge. Existing approaches rely somewhat heavily on the simplifications that break down beyond leading logarithmic accuracy, making their higher-order extension challenging.
In this talk, I will describe recent progress in tackling this problem using the Glauber extension of SCET. In previous work [JHEP 09 (2023) 089], a factorization theorem for small-$x$ resummation in DIS was derived, that involved a universal process-independent collinear function and a process-dependent soft function. This work constitutes the first resummation in the high energy limit and has provided a promising approach for higher-order extension. In this talk, I will focus on the two-loop computation of the collinear function whose rapidity evolution is governed by the BFKL equation. The two-loop result thus gives direct access to the NLO BFKL kernel and provides a strong cross-check of the calculation by Fadin and Lipatov in 1998. Given the importance of keeping track of rapidity divergences, this result cannot be extracted reliably from a QCD process and necessitates automation of (Glauber) SCET Feynman rules and diagrams. I will further show how exploiting the Glauber Collapse Rule enables us to efficiently filter out a small subset of diagrams and master integrals, making an otherwise daunting calculation tractable.