One-loop electroweak Sudakov logarithms: a revisitation and automation

Abstract

In this work we revisit the algorithm of Denner and Pozzorini for the calculation of one-loop electroweak Sudakov logarithms and we automate it in the MadGraph5_aMC-@NLO framework. We adapt the formulas for modern calculations, keeping light-quarks and photons strictly massless and dealing with infrared divergences via dimensional regularisation. We improve the approximation by taking into account additional logarithms that are angular dependent. We prove that an imaginary term has been previously omitted and we show that it cannot be in general neglected for 2 → n processes with n > 2. We extend the algorithm to NLO EW corrections to squared matrix-elements that involve also QCD corrections on top of subleading LO terms. Furthermore, we discuss the usage of this algorithm for approximating physical observables and cross sections. We propose a new approach in which the QED component is consistently removed and we show how it can be superior to the commonly used approaches. The relevance of all the novelties introduced in this work is corroborated by numerical results obtained for several processes in a completely automated way. We thoroughly compare exact NLO EW corrections and their Sudakov approximations both at the amplitude level and for physical observables in high-energy hadronic collisions.

Muon Collider Physics Summary

“…More recent progress includes resummation at the next to leading logarithm in the Soft-Collinear Effective Theory framework [55][56][57][58][59], the operatorial definition of the distribution functions for EW partons [48,60,61] and the calculation of the corresponding evolution, as well as the calculation of the EW splitting functions [62] for EW showering and the proof of collinear EW emission factorization [63][64][65]. Additionally, fixed-order virtual EW logarithms are known for generic process at the 1-loop order [66,67] and are implemented in Sherpa [68] and MadGraph5_aMC@NLO [69]. Exact EW corrections at NLO are available in an automatic form for arbitrary processes in the SM, for example in MadGraph5_aMC@NLO [70] and in Sherpa+Recola [71].…”

Event Generators for High-Energy Physics Experiments

“…However, in the mixed case, loop matrix element evaluation time can be more of a limiting factor than for pure QCD corrections. Depending on the kinematic regime being probed, it is possible to build efficient and fast approximants leveraging the dominance of so-called Sudakov EW logarithms [502]. One challenge in computing one-loop EW matrix elements is the support for the complex-mass scheme that was completed in [503] together with the generalization in MADGRAPH5 aMC@NLO of FKS subtraction [504] for infrared singularities in mixed QCD and EW perturbative computations.…”

The Effective Vector Boson Approximation in high-energy muon collisions

“…[69] or modern treatments like ref. [89]. However, investigating and quantifying the impact of these improvements as well as those related to γ T /Z T mixing [4,26,56,[90][91][92][93], which we also neglect, is left to future work.…”

“…(2.2) by an EW Sudakov form factor and/or RG evolution for weak boson PDFs, as studied in refs. [4,26,56,89,90,93,[116][117][118].…”