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We present the new version of OpenLoops, an automated generator of tree and one-loop scattering amplitudes based on the open-loop recursion. One main novelty of OpenLoops 2 is the extension of the original algorithm from NLO QCD to the full Standard Model, including electroweak (EW) corrections from gauge, Higgs and Yukawa interactions. In this context, among several new features, we discuss the systematic bookkeeping of QCD-EW interferences, a flexible implementation of the complex-mass scheme for processes with on-shell and off-shell unstable particles, a special treatment of on-shell and off-shell external photons, and efficient scale variations. The other main novelty is the implementation of the recently proposed on-the-fly reduction algorithm, which supersedes the usage of external reduction libraries for the calculation of tree-loop interferences. This new algorithm is equipped with an automated system that avoids Gram-determinant instabilities through analytic methods in combination with a new hybrid-precision approach based on a highly targeted usage of quadruple precision with minimal CPU overhead. The resulting significant speed and stability improvements are especially relevant for challenging NLO multi-leg calculations and for NNLO applications. only little user intervention. Moreover, OpenLoops is used as a building block of Matrix [50] for the calculation of NNLO QCD observables. In this context, the automation of EW corrections in OpenLoops 2 opens the door to ubiquitous NLO QCD+NLO EW simulations in Sherpa [51, 52] and NNLO QCD+NLO EW calculations in Matrix [53].The OpenLoops 2 code is publicly available on the Hepforge webpage https://openloops.hepforge.org and via the Git repository https://gitlab.com/openloops/OpenLoops. It consists of a processindependent base code and a process library that covers several hundred partonic processes, including essentially all relevant processes at the LHC. The desired processes can be easily accessed through an automated download mechanism. The set of available processes is continuously extended, and possible missing processes can be promptly generated by the authors upon request.The paper is organised as follows. Section 2 presents the structure of the original open-loop recursion and the new on-the-fly reduction algorithm. Numerical instabilities and the new hybrid-precision system are discussed in detail. Section 3 deals with general aspects of NLO calculations and their automation in OpenLoops. This includes the bookkeeping of towers of terms of variable order α p s α q , the treatment of input parameters, optimal couplings for external photons, the renormalisation of the SM at O(α s ) and O(α), the on-shell and complex-mass schemes, and the I-operator. Section 4 provides instructions on how to use the program, starting from installation and process selection, and including the various interfaces for the calculation of matrix elements, colour/spin correlators, and tree amplitudes in colour space. Technical benchmarks concerning the speed and numerical sta...

We present a fully automated implementation of next-to-leading order electroweak (NLO EW) corrections in the OpenLoops matrix-element generator combined with the Sherpa and Munich Monte Carlo frameworks. The process-independent character of the implemented algorithms opens the door to NLO QCD+EW simulations for a vast range of Standard Model processes, up to high particle multiplicity, at current and future colliders. As a first application, we present NLO QCD+EW predictions for the production of positively charged on-shell W bosons in association with up to three jets at the Large Hadron Collider. At the TeV energy scale, due to the presence of large Sudakov logarithms, EW corrections reach the 20-40% level and play an important role for searches of physics beyond the Standard Model. The dependence of NLO EW effects on the jet multiplicity is investigated in detail, and we find that W + multijet final states feature genuinely different EW effects as compared to the case of W + 1 jet.

We present next-to-leading order (NLO) predictions including QCD and electroweak (EW) corrections for the production and decay of off-shell electroweak vector bosons in association with up to two jets at the 13 TeV LHC. All possible dilepton final states with zero, one or two charged leptons that can arise from off-shell W and Z bosons or photons are considered. All predictions are obtained using the automated implementation of NLO QCD+EW corrections in the OpenLoops matrix-element generator combined with the Munich and Sherpa Monte Carlo frameworks. Electroweak corrections play an especially important role in the context of BSM searches, due to the presence of large EW Sudakov logarithms at the TeV scale. In this kinematic regime, important observables such as the jet transverse momentum or the total transverse energy are strongly sensitive to multijet emissions. As a result, fixed-order NLO QCD+EW predictions are plagued by huge QCD corrections and poor theoretical precision. To remedy this problem we present an approximate method that allows for a simple and reliable implementation of NLO EW corrections in the MePs@Nlo multijet merging framework. Using this general approach we present an inclusive simulation of vector-boson production in association with jets that guarantees NLO QCD+EW accuracy in all phase-space regions involving up to two resolved jets.

We present a Monte Carlo generator that implements significant theoretical improvements in the simulation of top-quark pair production and decay at the LHC. Spin correlations and off-shell effects in top-decay chains are described in terms of exact matrix elements for pp → + ν l −ν l bb at order α 4 α 2 S plus full NLO QCD corrections, where the leptons and l belong to different families, and b quarks are massive. Thus, the contributions from tt and W t single-top production, plus contributions without top resonances and all relevant quantum interferences between different channels are fully included. Matrix elements are matched to the Pythia8 parton shower using a recently proposed method that allows for a consistent treatment of resonances in the POWHEG framework. These theoretical improvements are especially important for the interpretation of precision measurements of the top-quark mass, for single-top analyses in the W t channel, and for tt and W t backgrounds in the presence of jet vetoes or cuts that enhance off-shell effects. The new generator is based on a process-independent interface of the OpenLoops amplitude generator with the POWHEG-BOX framework.