1. Vorlesung im Rahmen der Erwin-Schrödinger-Gastprofessur 2024
We present a systematic formalism based on a factorization theorem in Soft-Collinear Effective Theory (SCET) to describe non-global observables at hadron colliders, such as gap-between-jets cross sections. The cross sections are factorized into convolutions of hard functions, capturing the dependence on the partonic center-of-mass energy √s, and low-energy matrix elements, which are sensitive to the low scale Q0≪√s characteristic of the veto imposed on energetic emissions into the gap region between the jets. The scale evolution of both objects is governed by a renormalization-group equation, whose form we derive. With the help of this equation, we develop an EFT-based approach to the resummation of so-called “non-global logarithms'', including the “super-leading logarithms” discovered by Forshaw et al. in 2006, which only appear in hadron-collider processes.
Part 1:
By solving the evolution equation for the hard functions for arbitrary 2-to-M jet processes in the leading logarithmic approximation, we accomplish for the first time the all-order resummation of super-leading logarithms, thereby solving an old problem of quantum field theory. We study the numerical size of the corresponding effects for different partonic scattering processes and explain why they are sizable for pp-to-2 jets processes, but suppressed in H/Z and H/Z+ jet production. The super-leading logarithms are given by an alternating series, whose individual terms can be much larger than the resummed result, even in very high orders of the loop expansion. Resummation is therefore essential to control these effects. We find that the asymptotic fall-off of the resummed series is much weaker than for standard Sudakov form factors.
