NLO EW Research Articles

Logarithmic EW corrections at one-loop

We present a fully automated implementation of next-to-leading order electroweak (NLO EW) corrections in the logarithmic approximation in OpenLoops. For energies above the electroweak scale NLO EW corrections are logarithmically enhanced and in tails of kinematic distributions of crucial LHC processes yield correction factors of several tens of percent. The implementation of the logarithmic Sudakov EW approximation in the amplitude generator OpenLoops is fully general, largely model independent, it supports the computation of EW corrections to resonant processes, and it is suitable for extensions to the two-loop NNLO EW level. The implementation is based on an efficient representation of the logarithmic approximation in terms of an effective vertex approach. Investigating a set of representative LHC processes we find excellent agreement between the logarithmic approximation and full one-loop results in observables where the assumptions of the EW Sudakov approximation are fulfilled.

NLO EW corrections to polarised W+W− production and decay at the LHC

In this letter we present results for next-to-leading-order electroweak corrections to doubly polarised W+W− production at the LHC in the fully leptonic decay channel. We model the production and the decay of two polarised W bosons in the double-pole approximation, including factorisable real and virtual electroweak corrections, and separating polarisation states at amplitude level. We obtain integrated and differential predictions for polarised signals in a realistic fiducial setup.

Precision phenomenology with fiducial cross sections in the triple-differential Drell-Yan process

The production of lepton pairs (Drell-Yan process) at the LHC is being measured to high precision, enabling the extraction of distributions that are triply differential in the di-lepton mass and rapidity as well as in the scattering angle described by the leptons. The measurements are performed for a fiducial phase space, defined by cuts on the individual lepton momenta and rapidities. Based on the ATLAS triple-differential Drell-Yan measurement at 8 TeV, we perform a detailed investigation of the phenomenology of this process based on state-of-the-art perturbative predictions in QCD and the electroweak theory. Our results demonstrate the highly non-trivial interplay between measurement variables and fiducial cuts, which leads to forbidden regions at Born level, and induces sensitivity on extra particle emissions from higher perturbative orders. We also investigate the sensitivity of the measurement on parton distributions and electroweak parameters. We derive Standard-Model theory predictions which combine NNLO QCD and NLO EW corrections and include partial N3LO QCD as well as higher-order EW corrections where appropriate. Our results will enable the use of the triple-differential Drell-Yan data in a precise experimental determination of the weak mixing angle.

NLO QCD and EW corrections to off-shell tZj production at the LHC

The production of a single top quark in association with a Z boson (tZj production) at the LHC is a relevant probe of the electroweak sector of the Standard Model as well as a window to possible new-physics effects. The growing experimental interest in performing differential measurements for this process demands an improved theoretical modelling in realistic fiducial regions. In this article we present an NLO-accurate tZj calculation that includes complete off-shell effects and spin correlations, combining QCD and electroweak radiative corrections to the LO signal. Integrated and differential cross sections are shown for a fiducial setup characterised by three charged leptons, two jets, and missing energy.

Angular coefficients in hbox {W}+hbox {j} production at the LHC with high precision

The extraction of the W-boson mass, a fundamental parameter of the Standard Model, from hadron-hadron collision requires precise theory predictions. In this regard, angular coefficients are crucial to model the dynamics of W-boson production. In this work, we provide, for the first time, angular coefficients at NNLO QCD + NLO EW accuracy for finite transverse momentum W-boson at the LHC. The corrections can reach up to 10% in certain regions of phase space. They are accompanied by a significant reduction of the scale uncertainty. This work should, besides providing reference values for theory-data comparison, provide state-of-the-art theory input for W-boson mass measurements.

NLO QCD and EW corrections to vector-boson scattering into W+W− at the LHC

We present the full next-to-leading-order electroweak and QCD corrections to vector-boson scattering into a pair of off-shell opposite-sign W bosons decaying into leptons of different flavour at the LHC. We include full leading-order predictions for the irreducible background. Explicitly, we investigate the process pp → e+νeμ− overline{nu} μjj + X at leading orders mathcal{O} (α6), mathcal{O} (αsα5), mathcal{O} ( {alpha}_{mathrm{s}}^2 α4), supplemented by the loop-induced mathcal{O} ( {alpha}_{mathrm{s}}^4 α4) contribution, and at next-to-leading orders mathcal{O} (α7)and mathcal{O} (αsα6) in two setups providing fiducial cross sections as well as differential distributions. We take full account of photon-induced next-to-leading-order contributions, which prove to be non negligible. With −11.4% and −6.7% in the two setups, the electroweak corrections are smaller than for other vector-boson-scattering processes. This can be traced back to the presence of the Higgs-boson resonance in the fiducial phase space, whose effects we analyse within an additional unphysical, but manifestly gauge-invariant setup. The QCD corrections amount to −5.1% and −21.6% in the two setups. The large size of the latter correction, compared to other vector-boson scattering processes, is explained by a very restrictive definition of its fiducial phase space.

Higher-order EW corrections in ZZ and ZZj production at the LHC

We consider the production of a pair of Z bosons at the LHC and study the inclusion of EW corrections in theoretical predictions at fixed order and based on multijet-merged parton-shower simulations. To this end we present exact NLO EW results for pp → e+e−μ+μ−, and, for the first time, for pp → e+e−μ+μ−j, and compare them to the EW virtual and NLL Sudakov approximation. We then match the exact NLO EW result to the resummed Sudakov logarithms to achieve an improved mathrm{NLO} mathrm{EW}+mathrm{NLL} {mathrm{EW}}_{mathrm{sud}}^{mathrm{exp}} result.Further, we discuss the inclusion of the above EW corrections in MePs@Nlo event simulations in the framework of the Sherpa event generator. We present detailed phenomenological predictions for inclusive ZZ and ZZj production taking into account the dominant EW corrections through the EW virtual approximation, as well as through (exponentiated) EW Sudakov logarithms.

One-loop electroweak Sudakov logarithms: a revisitation and automation

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.

On improving NLO merging for mathrm{t}overline{mathrm{t}}mathrm{W} production

We introduce an improvement to the FxFx matrix element merging procedure for pp → toverline{t}W production at NLO in QCD with one and/or two additional jets. The main modification is an improved treatment of jets that are not logarithmically enhanced in the low transverse-momentum regime. We provide predictions for the inclusive cross section and the toverline{t}W differential distributions including parton-shower effects. Taking also the NLO EW corrections into account, this results in the most-accurate predictions for this process to date. We further proceed to include the on-shell LO decays of the toverline{t}W including the tree-level spin correlations within the narrow-width approximation, focusing on the multi-lepton signatures studied at the LHC. We find a ∼30% increase over the NLO QCD prediction and large non-flat K-factors to differential distributions.

NLO EW and QCD corrections to polarized ZZ production in the four-charged-lepton channel at the LHC

Measuring the polarization of electroweak bosons at the LHC allows for important tests of the electroweak-symmetry-breaking mechanism that is realized in nature. Therefore, precise Standard Model predictions are needed for the production of polarized bosons in the presence of realistic kinematic selections. We formulate a method for the calculation of polarized cross-sections at NLO that relies on the pole approximation and the separation of polarized matrix elements at the amplitude level. In this framework, we compute NLO-accurate cross-sections for the production of two polarized Z bosons at the LHC, including for the first time NLO EW corrections and combining them with NLO QCD corrections and contributions from the gluon-induced process.

Combined NLO EW and QCD corrections to off-shell text {t} overline{text {t}}text {W} production at the LHC

The high luminosity that will be accumulated at the LHC will enable precise differential measurements of the hadronic production of a top–antitop-quark pair in association with a text {W} boson. Therefore, an accurate description of this process is needed for realistic final states. In this work we combine for the first time the NLO QCD and electroweak corrections to the full off-shell text {t} overline{text {t}}text {W} ^+ production at the LHC in the three-charged-lepton channel, including all spin correlations, non-resonant effects, and interferences. To this end, we have computed the NLO electroweak radiative corrections to the leading QCD order as well as the NLO QCD corrections to both the QCD and the electroweak leading orders.

Parton distributions from LHC, HERA, Tevatron and fixed target data: MSHT20 PDFs

We present the new MSHT20 set of parton distribution functions (PDFs) of the proton, determined from global analyses of the available hard scattering data. The PDFs are made available at NNLO, NLO, and LO, and supersede the MMHT14 sets. They are obtained using the same basic framework, but the parameterisation is now adapted and extended, and there are 32 pairs of eigenvector PDFs. We also include a large number of new data sets: from the final HERA combined data on total and heavy flavour structure functions, to final Tevatron data, and in particular a significant number of new LHC 7 and 8 TeV data sets on vector boson production, inclusive jets and top quark distributions. We include up to NNLO QCD corrections for all data sets that play a major role in the fit, and NLO EW corrections where relevant. We find that these updates have an important impact on the PDFs, and for the first time the NNLO fit is strongly favoured over the NLO, reflecting the wider range and in particular increased precision of data included in the fit. There are some changes to central values and a significant reduction in the uncertainties of the PDFs in many, though not all, cases. Nonetheless, the PDFs and the resulting predictions are generally within one standard deviation of the MMHT14 results. The major changes are the u-d valence quark difference at small x, due to the improved parameterisation and new precise data, the {bar{d}}, {bar{u}} difference at small x, due to a much improved parameterisation, and the strange quark PDF due to the effect of LHC W, Z data and inclusion of new NNLO corrections for dimuon production in neutrino DIS. We discuss the phenomenological impact of our results, and in general find reduced uncertainties in predictions for processes such as Higgs, top quark pair and W, Z production at post LHC Run-II energies.

NLO QCD and EW corrections to vector-boson scattering into ZZ at the LHC

We present the first calculation of the full next-to-leading-order electroweak and QCD corrections for vector-boson scattering (VBS) into a pair of Z bosons at the LHC. We consider specifically the process pp → e+e−μ+μ−jj + X at orders mathcal{O} (α7) and mathcal{O} (αsα6) and take all off-shell and interference contributions into account. Owing to the presence of enhanced Sudakov logarithms, the electroweak corrections amount to −16% of the leading-order electroweak fiducial cross section and induce significant shape distortions of differential distributions. The QCD corrections on the other hand are larger (+24%) than typical QCD corrections in VBS. This originates from considering the full computation including tri-boson contributions in a rather inclusive phase space. We also provide a leading-order analysis of all contributions to the cross section for pp → e+e−μ+μ−jj + X in a realistic setup.

Fixed-order and merged parton-shower predictions for WW and WWj production at the LHC including NLO QCD and EW corrections

First, we present a combined analysis of pp to {mu}^{+}{v}_{mu }{mathrm{e}}^{-}{overline{v}}_{mathrm{e}} and pp to {mu}^{+}{v}_{mu }{mathrm{e}}^{-}{overline{v}}_{mathrm{e}}mathrm{j} at next-to-leading order, including both QCD and electroweak corrections. Second, we provide all-order predictions for pp to {mu}^{+}{v}_{mu }{mathrm{e}}^{-}{overline{v}}_{mathrm{e}}+ jets using merged parton-shower simulations that also include approximate EW effects. A fully inclusive sample for WW production is compared to the fixed-order computations for exclusive zero- and one-jet selections. The various higher-order effects are studied in detail at the level of cross sections and differential distributions for realistic experimental set-ups. Our study confirms that merged predictions are significantly more stable than the fixed-order ones in particular regarding ratios between the two processes.

NLO QCD+NLO EW corrections to diboson production matched to parton shower

We present the matching of NLO QCD and NLO EW corrections to parton showers for vector-boson pair production at the LHC. We consider leptonic final states, including resonant and non-resonant diagrams, spin correlations and off-shell effects. Our results are obtained interfacing the Recola2-Collier one-loop provider with the POWHEG-BOX-RES framework. We discuss our implementation, we validate it at fixed order, and we show our final results matched to parton shower. A by-product of our work is also a general interface between Recola2-Collier and POWHEG-BOX-RES. This is the first time that EW and QCD corrections to diboson production are consistently matched to parton showers.

NLO QCD+EW predictions for tHj and tZj production at the LHC

In this work we calculate the cross sections for the hadroproduction of a single top quark or antiquark in association with a Higgs (tHj) or Z boson (tZj) at NLO QCD+EW accuracy. In the case of tZj production we consider both the case of the Z boson undecayed and the complete final state tℓ+ℓ−j, including off-shell and non-resonant effects. We perform our calculation in the five-flavour-scheme (5FS), without selecting any specific production channel (s-, t- or tW associated). Moreover, we provide a more realistic estimate of the theory uncertainty by carefully including the differences between the four-flavour-scheme (4FS) and 5FS predictions. The difficulties underlying this procedure in the presence of EW corrections are discussed in detail. We find that NLO EW corrections are in general within the NLO QCD theory uncertainties only if the flavour scheme uncertainty (4FS vs. 5FS) is taken into account. For the case of tℓ+ℓ−j production we also investigate differences between NLO QCD+EW predictions and NLO QCD predictions matched with a parton shower simulation including multiple photon emissions.

W+W− production at the LHC: NLO QCD corrections to the loop-induced gluon fusion channel

We compute the NLO QCD corrections to the loop-induced gluon fusion contribution in W+W− production at the LHC. We consider the full leptonic process pp→ℓ+ℓ′−νℓν¯ℓ′+X, by including resonant and non-resonant diagrams, spin correlations and off-shell effects. Quark–gluon partonic channels are included for the first time in the calculation, and our results are combined with NNLO predictions to the quark annihilation channel at the fully differential level. The computed corrections, which are formally of O(αS3), increase the NNLO cross section by only about 2%, but have an impact on the shapes of kinematical distributions, in part due to the jet veto, which is usually applied to reduce the top-quark background. Our results, supplemented with NLO EW effects, provide the most advanced fixed-order predictions available to date for this process, and are compared with differential ATLAS data at s=13TeV.

NNLO QCD + NLO EW with Matrix+OpenLoops: precise predictions for vector-boson pair production

We present the first combination of NNLO QCD and NLO EW corrections for vector-boson pair production at the LHC. We consider all final states with two, three and four charged leptons, including resonant and non-resonant diagrams, spin correlations and off-shell effects. Detailed predictions are discussed for three representative channels corresponding to W+W−, W±Z and Z Z production. Both QCD and EW corrections are very significant, and the details of their combination can play a crucial role to achieve the level of precision demanded by experimental analyses. In this context we point out nontrivial issues that arise at large transverse momenta, where the EW corrections are strongly enhanced by Sudakov logarithms and the QCD corrections can feature so-called giant K -factors. Our calculations have been carried out in the Matrix+OpenLoops framework and can be extended to the production of an arbitrary colour singlet in hadronic collisions, provided that the required two-loop QCD amplitudes are available. Combined NNLO QCD and NLO EW predictions for the full set of massive diboson processes will be made publicly available in the next release of Matrix and will be instrumental in advancing precision diboson studies and new-physics searches at the LHC and future hadron colliders.

Differential top quark pair production at the LHC: Challenges for PDF fits

We present the results of a PDF fit to differential top quark production within the MMHT framework. We in particular consider ATLAS data in the lepton + jet and dilepton channels and CMS data in the lepton + jet channel, at 8 TeV. While the fit quality to the ATLAS dilepton data is good, for the CMS case we see some issues in achieving a good fit quality for certain distributions. However, we focus on the ATLAS lepton + jet data, for which correlations of the statistical and systematic errors are provided across the four relevant distributions for PDF determination, namely p_T^t, M_{tt}, y_t and y_{tt}. We find severe difficulties in fitting these distributions simultaneously, with particular sensitivity to the precise degree of correlation taken between the dominant two-point MC uncertainties in the data. We investigate the effect of some reasonable decorrelation of these uncertainties, finding the impact on the fit quality to be significant and the resultant gluon not negligible. This is in particular found to be larger than the effect of including NNLO QCD and NLO EW corrections in the top quark pair production cross section on the fit, motivating a closer understanding of the physics underlying these errors sources and in particular the uncertainty on the degree of correlation in them.

Top-quark charge asymmetry at the LHC and Tevatron through NNLO QCD and NLO EW

We provide the most up-to-date predictions for the top-quark charge asymmetry A_C at the LHC with a centre-of-mass energy of 8 TeV. Our result is accurate at the NNLO level in the strong interactions and at the complete-NLO level in both the strong and electroweak interactions. We present results for the inclusive A_C, several differential asymmetries as well as the P_{T,tt} and M_{tt} cumulative asymmetries. Similarly to the Tevatron forward-backward asymmetry A_FB, both NNLO QCD and NLO EW corrections to A_C are found to be significant. The inclusion of higher-order corrections reduces the residual scale dependence in the predicted A_C. The pattern of higher-order corrections indicates good perturbative control over these observables. We conclude that at present there is nearly uniform agreement between Standard Model predictions and LHC measurements across all A_C-related observables. All previously published differential A_FB predictions at the Tevatron are updated to the same accuracy.