Automated evaluation of electroweak Sudakov logarithms in SHERPA
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Regular Article - Theoretical Physics
Automated evaluation of electroweak Sudakov logarithms in SHERPA Enrico Bothmann1, Davide Napoletano2,a 1 2
Institut für Theoretische Physik, Georg-August-Universität, Göttingen, 37077 Göttingen, Germany Università degli Studi di Milano-Bicocca and INFN, Piazza della Scienza 3, 20126 Milan, Italy
Received: 6 July 2020 / Accepted: 23 October 2020 © The Author(s) 2020
Abstract We present an automated implementation for the calculation of one-loop double and single Sudakov logarithms stemming from electroweak radiative corrections within the SHERPA event generation framework, based on the derivation in Denner and Pozzorini (Eur Phys J C 18:461– 480, 2001). At high energies, these logarithms constitute the leading contributions to the full NLO electroweak corrections. As examples, we show applications for relevant processes at both the LHC and future hadron colliders, namely on-shell W boson pair production, EW-induced dijet production and electron–positron production in association with four jets, providing the first estimate of EW corrections at this multiplicity.
1 Introduction In perturbative electroweak (EW) theory, higher-order corrections include, among other contributions, emissions of virtual and real gauge bosons and are known to have a large effect in the hard tail of observables at the LHC and future colliders [2]. In contrast to massless gauge theories, where real emission terms are necessary to regulate infrared divergences, in EW theory the weak gauge bosons are massive and therefore provide a natural lower scale cut-off, such that finite logarithms appear instead. Moreover, since the emission of an additional weak boson leads to an experimentally different signature with respect to the Born process, virtual logarithms are of physical significance without the inclusion of real radiation terms. The structure of such logarithmic contributions, referred to as Sudakov logarithms [3], and their factorisation properties were derived in full generality by Denner and Pozzorini [1,4– 8] at leading and next-to-leading logarithmic accuracy at both one- and two-loop order in the EW coupling expansion. In a e-mail:
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addition, the full set of next-to-next-to-next-to-leading logarithms was calculated at two-loop order in [9] for fourfermion processes. Moreover, Denner and Pozzorini have shown that in the high-energy scattering limit, at least at oneloop order, these logarithmic corrections can be factored as a sum over pairs of external legs in an otherwise processindependent way, hence providing a straightforward algorithm for computing them for any given process. The highenergy limit requires all invariants formed by pairs of particles to be large compared to the scale set by the weak gauge boson masses. In this sense we expect effects due to electroweak corrections in general, and to Sudakov logarithms in particular, to give rise to large effects in the hard tail of observables that have the dimensio
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