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.
Highlights
After more than ten years of operation of the Large Hadron Collider (LHC), we have tremendously improved our knowledge of the fundamental interactions of elementary particles
Being aware of all the possible limitations given by the conditions (2.2) and (2.4), we describe the DP algorithm and some modifications we have introduced in order to achieve the formal leading and subleading logarithmic accuracy (LA), i.e., taking into account only enhanced DL and SL terms of the form (2.1), for one-loop EW virtual corrections to any Standard Model (SM) amplitudes, in Dimensional Regularisation (DR) and with possibly massless particles
The most important point, in order to understand the novelties introduced is that the DP algorithm splits twice the logarithms of the form in (2.5); both splittings are connected to the modifications of the DP algorithm that we present in this work
Summary
After more than ten years of operation of the Large Hadron Collider (LHC), we have tremendously improved our knowledge of the fundamental interactions of elementary particles. Since (virtual) NLO EW corrections originate from both “genuine” EW corrections on top of the dominant LO contributions and QCD corrections on top of the subdominant ones, we provide additional terms for taking into account the logarithmic dependence of the former, as done in the original work of Denner and Pozzorini, and of the latter All these modifications concern the approximation of the matrix elements or, more precisely, the interference of tree-level and renormalised one-loop amplitudes leading to the ultra-violet (UV) finite virtual corrections. In a fully automated way, for several different processes, we compare exact results for virtual contributions obtained via MadLoop [18], one of the modules of MadGraph5_aMC@NLO, and via the new implementation of the modified algorithm of Denner and Pozzorini for calculating one-loop virtual Sudakov logarithms.
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