Next-to-leading power endpoint factorization and resummation for off-diagonal "gluon" thrust

Abstract

The lack of convergence of the convolution integrals appearing in next-to-leadingpower (NLP) factorization theorems prevents the applications of existing methods to resum power-suppressed large logarithmic corrections in collider physics. We consider thrust distribution in the two-jet region for the flavour-nonsinglet offdiagonal contribution, where a gluon-initiated jet recoils against a quark-antiquark pair, which is power-suppressed. With the help of operatorial endpoint factorization conditions, we obtain a factorization formula, where the individual terms are free from endpoint divergences in convolutions and can be expressed in terms of renormalized hard, soft and collinear functions in four dimensions. This allows us to perform the first resummation of the endpoint-divergent SCET I observables at the leading logarithmic accuracy using exclusively renormalization-group methods. The presented approach relies on universal properties of the soft and collinear limits and may serve as a paradigm for the systematic NLP resummation for other 1 → 2 and 2 → 1 collider physics processes.

Endpoint divergences in inclusive $\bar B \to X_s \gamma$

“…Recently new techniques [18][19][20][21] were presented in specific collider applications, which allow for an operator-level reshuffling of terms within the factorisation formula so that all endpoint divergences cancel out. This idea of refactorisation was now implemented in this flavour example of the resolved contributions, which includes nonperturbative soft functions, and the subleading shape functions, not present in collider applications [17].…”