Two-Loop Infrared Renormalization with On-shell Methods

Abstract

Within the framework proposed by Caron-Huot and Wilhelm, we give a recipe for computing infrared anomalous dimensions purely on-shell, efficiently up to two loops in any massless theory. After introducing the general formalism and reviewing the one-loop recipe, we extract a practical formula that relates two-loop infrared anomalous dimensions to certain two-and three-particle phase space integrals with tree-level form factors of conserved operators. We finally provide several examples of the use of the two-loop formula and comment on some of its formal aspects, especially the cancellation of 'one-loop squared' spurious terms.

Building blocks of the flavourful SMEFT RG

“…Some substructure within the matrix has been found [18]; in particular many zeroes in the matrix can be understood based on helicity arguments [19]. More recently, on-shell methods have been found to be powerful in calculating also its non-zero entries [20][21][22][23][24][25][26][27][28][29]. In this paper, we explore the additional substructure that can be uncovered once gauge and flavour information is included.…”

“…If we do not neglect y b (and/or y τ ), things become more complicated, and a fuller flavour decomposition analysis encompassing also the ψψXH, ( LR)( LR) and ( LR)( RL) operators must be performed, as well as the O Hud and O LedQ operators that we excluded from the analysis. 23 We leave this for future work.…”

“…[13] + c [23] [23] , c8,6 = 2 3 −2c [12] [12] + c [13] [13] + c [12] + c [13] [13] + c Open Access. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.…”