Electroweak Sudakov Logarithms Research Articles

Automated resummation of electroweak Sudakov logarithms in diboson production at future colliders

At energies that are large with respect to the electroweak scale, the electroweak corrections to scattering processes involve large logarithms that have to be resummed to obtain decent predictions. Soft-collinear effective theory (SCET) has been proposed as a suitable framework to allow for this resummation, while retaining non-logarithmic corrections in a consistent way. In this paper, we investigate the approximations needed to use this approach for the calculation of electroweak corrections to off-shell diboson production at high-energy colliders. Upon implementing the method into a Monte-Carlo integration code, we provide resummed predictions for cross sections and distributions at a 3TeV\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$3\\,\ ext {TeV} $$\\end{document} lepton collider and a 100TeV\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$100\\,\ ext {TeV} $$\\end{document} proton collider.

Improving NLO QCD event generators with high-energy EW corrections

AbstractIn this work we present a new method for the combination of electroweak (EW) corrections at high energies, the so-called EW Sudakov logarithms (EWSL), and next-to-leading-order QCD predictions matched to parton-shower simulations (NLO+PS). Our approach is based on a reweighting procedure of NLO+PS events. In particular, both events with and without an extra hard emission from matrix elements are consistently reweighted via the inclusion of the corresponding EWSL contribution. We describe the technical details and the implementation in the MadGraph5_aMC@NLO framework. Via a completely automated procedure, events at this level of accuracy can be obtained for a vast class of hadroproduction processes. As a byproduct we provide results for phenomenologically relevant physical distributions from top-quark pair and Higgs boson associated production ($$t {\bar{t}} H$$ t t ¯ H ) and from the associated production of three Z gauge bosons (ZZZ).

Electroweak resummation of neutralino dark-matter annihilation into high-energy photons

We consider the resummation of large electroweak Sudakov logarithms for the annihilation of neutralino DM with (TeV) mass to high-energy photons in the minimal supersymmetric standard model, extending previous work on the minimal wino and Higgsino models. We find that NLL resummation reduces the yield of photons by about 20% for Higgsino-dominated DM at masses around 1 TeV, and up to 45% for neutralinos with larger wino admixture at heavier masses near 3 TeV. This sizable effect is relevant when observations or exclusion limits are translated into MSSM parameter-space constraints.

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.

Automated evaluation of electroweak Sudakov logarithms in SHERPA

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.

Electroweak loops as a probe of new physics in toverline{t} production at the LHC

We calculate the \U0001d4aa(α) weak corrections to top quark pair production at the LHC and include anomalous electroweak interactions from dimension-six operators. The loop calculation and renormalization are consistently done within the Standard Model Effective Field Theory. Sensitivity to the involved operators is exposed through the virtual corrections, which receive enhancement from electroweak Sudakov logarithms. We investigate the prospects of using this feature for probing New Physics at the LHC that so far has only been studied in final states with on-shell sensitivity such as toverline{t} + Z or t → bW. We find that the large toverline{t} production rate and the excellent perturbative control allow compensating the loop suppression and yield remarkably strong constraints that are competitive with those from toverline{t} + Z.

Precise yield of high-energy photons from Higgsino dark matter annihilation

The impact of electroweak Sudakov logarithms on the endpoint of the photon spectrum for wino dark matter annihilation was studied intensively over the last several years. In this work, we extend these results to Higgsino dark matter {chi}_1^0 . We achieve NLL′ resummation accuracy for narrow and intermediate spectral energy resolutions, of order {m}_W^2/{m}_{chi } and mW, respectively. This is the most accurate prediction to date for the yield of high-energy γ-rays from {chi}_1^0{chi}_1^0 → γ + X annihilation for the energy resolutions realized by current and next-generation telescopes. We also discuss for the first time the effect of power corrections in mW/mχ in this context and argue why they are not sizeable.

Resummed photon spectrum from dark matter annihilation for intermediate and narrow energy resolution

The annihilation cross section of weakly interacting TeV scale dark matter particles χ0 into photons is affected by large quantum corrections due to electroweak Sudakov logarithms and the Sommerfeld effect. We extend our previous work on the resummation of the semi-inclusive photon energy spectrum in χ0χ0 → γ + X in the vicinity of the maximal photon energy Eγ = mχ with NLL’ accuracy from the case of narrow photon energy resolution {E}_{mathrm{res}}^{gamma } of order {m}_W^2/{m}_{chi } to intermediate resolution of order {E}_{mathrm{res}}^{gamma}sim {m}_W . We also provide details on the previous narrow resolution calculation. The two calculations, performed in different effective field theory set-ups for the wino dark matter model, are then shown to match well, providing an accurate representation up to energy resolutions of about 300 GeV.

Next-to-leading-order electroweak corrections to the production of three charged leptons plus missing energy at the LHC

The production of a neutral and a charged vector boson with subsequent decays into three charged leptons and a neutrino is a very important process for precision tests of the Standard Model of elementary particles and in searches for anomalous triple-gauge-boson couplings. In this article, the first computation of next-to-leading-order electroweak corrections to the production of the four-lepton final states μ+μ−e+νe, {mu}^{+}{mu}^{-}{mathrm{e}}^{-}{overline{nu}}_{mathrm{e}} , μ+μ−μ+νμ, and {mu}^{+}{mu}^{-}{mu}^{-}{overline{nu}}_{mu } at the Large Hadron Collider is presented. We use the complete matrix elements at leading and next-to-leading order, including all off-shell effects of intermediate massive vector bosons and virtual photons. The relative electroweak corrections to the fiducial cross sections from quark-induced partonic processes vary between −3% and −6%, depending significantly on the event selection. At the level of differential distributions, we observe large negative corrections of up to −30% in the high-energy tails of distributions originating from electroweak Sudakov logarithms. Photon-induced contributions at next-to-leading order raise the leading-order fiducial cross section by +2%. Interference effects in final states with equal-flavour leptons are at the permille level for the fiducial cross section, but can lead to sizeable effects in off-shell sensitive phase-space regions.

Resummation of electroweak Sudakov logarithms for real radiation

Using the known resummation of virtual corrections together with knowledge of the leading-log structure of real radiation in a parton shower, we derive analytic expressions for the resummed real radiation after they have been integrated over all of phase space. Performing a numerical analysis for both the 13 TeV LHC and a 100 TeV $pp$ collider, we show that resummation of the real corrections is at least as important as resummation of the virtual corrections, and that this resummation has a sizable effect for partonic center of mass energies exceeding $\sqrt{s} = {\cal O}$(few TeV). For partonic center of mass energies $\sqrt{s} \gtrsim$ 10 TeV, which can be reached at a 100 TeV collider, resummation becomes an O(1) effect and needs to be included even for rough estimates of the cross-sections.

Heavy dark matter annihilation from effective field theory.

We formulate an effective field theory description for SU(2)_{L} triplet fermionic dark matter by combining nonrelativistic dark matter with gauge bosons in the soft-collinear effective theory. For a given dark matter mass, the annihilation cross section to line photons is obtained with 5% precision by simultaneously including Sommerfeld enhancement and the resummation of electroweak Sudakov logarithms at next-to-leading logarithmic order. Using these results, we present more accurate and precise predictions for the gamma-ray line signal from annihilation, updating both existing constraints and the reach of future experiments.

Electroweak corrections to lepton pair production in association with two hard jets at the LHC

We compute the next-to-leading order corrections of $O(\alpha_s^2\alpha^3)$ to the hadronic production of two oppositely charged leptons and two hard jets, $p p \to j j l^- l^+$, using Recola and Collier. We include electroweak and QCD corrections at the given order and all off-shell effects. We provide detailed predictions for the LHC operating at 13 TeV and obtain per-cent-level corrections for the total cross section. For differential distributions we find significant non-uniform distortions in high-energy tails at the level of several ten per cent due to electroweak Sudakov logarithms and deformations at the level of a few per cent for angular variables.

Combining QCD and electroweak corrections to dilepton production in the framework of the FEWZ simulation code

We combine the next-to-next-to-leading order (NNLO) QCD corrections to lepton-pair production through the Drell-Yan mechanism with the next-to-leading order (NLO) electroweak corrections within the framework of the FEWZ simulation code. Control over both sources of higher-order contributions is necessary for measurements where percent-level theoretical predictions are crucial, and in phase-space regions where the NLO electroweak corrections grow large. The inclusion of both corrections in a single simulation code eliminates the need to separately incorporate such effects as final-state radiation and electroweak Sudakov logarithms when comparing many experimental results to theory. We recalculate the NLO electroweak corrections in the complex-mass scheme for both massless and massive final-state leptons, and modify the QCD corrections in the original FEWZ code to maintain consistency with the complex-mass scheme to the lowest order. We present phenomenological results for LHC studies that include both NNLO QCD and NLO electroweak corrections. In addition, we study several interesting kinematics features induced by experimental cuts in the distribution of photon radiation at the LHC.

Electroweak Sudakov logarithms and real gauge-boson radiation in the TeV region

Electroweak radiative corrections give rise to large negative, double-logarithmically enhanced corrections in the TeV region. These are partly compensated by real radiation and, moreover, affected by selecting isospin-noninvariant external states. We investigate the impact of real gauge boson radiation more quantitatively by considering different restricted final state configurations. We consider successively a massive abelian gauge theory, a spontaneously broken SU(2) theory and the electroweak Standard Model. We find that details of the choice of the phase space cuts, in particular whether a fraction of collinear and soft radiation is included, have a strong impact on the relative amount of real and virtual corrections.

Combination of electroweak and QCD corrections to single W production at the Fermilab Tevatron and the CERN LHC

Precision studies of the production of a high-transverse momentum lepton in association with missing energy at hadron colliders require that electroweak and QCD higher-order contributions are simultaneously taken into account in theoretical predictions and data analysis. Here we present a detailed phenomenological study of the impact of electroweak and strong contributions, as well as of their combination, to all the observables relevant for the various facets of the $p\smartpap \to {\rm lepton} + X$ physics programme at hadron colliders, including luminosity monitoring and Parton Distribution Functions constraint, $W$ precision physics and search for new physics signals. We provide a theoretical recipe to carefully combine electroweak and strong corrections, that are mandatory in view of the challenging experimental accuracy already reached at the Fermilab Tevatron and aimed at the CERN LHC, and discuss the uncertainty inherent the combination. We conclude that the theoretical accuracy of our calculation can be conservatively estimated to be about 2% for standard event selections at the Tevatron and the LHC, and about 5% in the very high $W$ transverse mass/lepton transverse momentum tails. We also provide arguments for a more aggressive error estimate (about 1% and 3%, respectively) and conclude that in order to attain a one per cent accuracy: 1) exact mixed ${\cal O}(\alpha \alpha_s)$ corrections should be computed in addition to the already available NNLO QCD contributions and two-loop electroweak Sudakov logarithms; 2) QCD and electroweak corrections should be coherently included into a single event generator.

Electroweak corrections using effective field theory: Applications to the CERN LHC

Electroweak Sudakov logarithms at high energy, of the form $(\ensuremath{\alpha}/{sin}^{2}{\ensuremath{\theta}}_{W}{)}^{n}{log}^{m}s/{M}_{Z,W}^{2}$, are summed using effective theory (EFT) methods. The exponentiation of Sudakov logarithms and factorization is discussed in the EFT formalism. Radiative corrections are computed to scattering processes in the standard model involving an arbitrary number of external particles. The computations include nonzero particle masses such as the $t$-quark mass, electroweak mixing effects which lead to unequal $W$ and $Z$ masses and a massless photon, and Higgs corrections proportional to the top-quark Yukawa coupling. The structure of the radiative corrections, and which terms are summed by the EFT renormalization group is discussed in detail. The omitted terms are smaller than 1%. We give numerical results for the corrections to dijet production, dilepton production, $t\overline{t}$ production, and squark pair production. The purely electroweak corrections are significant---about 15% at 1 TeV, increasing to 30% at 5 TeV, and they change both the scattering rate and angular distribution. The QCD corrections (which are well-known) are also computed with the EFT. They are much larger---about a factor of 4 at 1 TeV, increasing to a factor of 30 at 5 TeV. Mass effects are also significant; the $q\overline{q}\ensuremath{\rightarrow}t\overline{t}$ rate is enhanced relative to the light-quark production rate by 40%.

Electroweak corrections to high energy processes using effective field theory

Electroweak Sudakov logarithms at high energy, of the form $(\ensuremath{\alpha}/{sin}^{2}{\ensuremath{\theta}}_{W}{)}^{n}{log}^{m}s/{M}_{Z,W}^{2}$, are summed using effective theory methods. The corrections are computed to processes involving two external particles in the standard model. The results include nonzero particle masses, such as the $t$-quark mass, electroweak mixing effects which lead to unequal $W$ and $Z$ masses, and radiative Higgs corrections proportional to the Yukawa couplings. We show that the matching at the scale ${M}_{W,Z}$ has a term at most linear in $\mathrm{log}s/{\ensuremath{\mu}}^{2}$ to all orders. The effective theory formalism is compared with, and extends, previous work based on infrared evolution equations.

Supersymmetric scalar production in the electroweak Sudakov regime of lepton colliders

We consider the production of supersymmetric (SUSY) scalar pairs at lepton colliders, for c.m. energies much larger than the mass of the heaviest SUSY (real or virtual) particle involved in the process. In that energy regime, we derive the leading and subleading terms of the electroweak Sudakov logarithms in the MSSM, first working at one loop with physical states and then resumming to all orders with asymptotic expansions. We show that the first order of the resummed expression reproduces the physical one loop approximation, and compute systematically the possible effects on various observables both at one loop and to all orders. We discuss the regimes and the observables where the one loop approximation can or cannot be trusted, working in an energy range between 1 TeV and 4 TeV under a ``light'' SUSY mass assumption. As a by-product of our analysis, we propose a determination of the MSSM parameter $\mathrm{tan}\ensuremath{\beta}$ showing how a relative accuracy $\ensuremath{\simeq}25%$ can be easily achieved in the region $\mathrm{tan}\ensuremath{\beta}\ensuremath{\gtrsim}14,$ under reasonable experimental assumptions.

Electroweak two-loop Sudakov logarithms for on-shell fermions and bosons

We calculate the virtual electroweak Sudakov (double) logarithms at one- and two-loop level for arbitrary on-shell/on-resonance particles in the Standard Model. The associated Sudakov form factors apply in a universal way to arbitrary non-mass-suppressed electroweak processes at high energies, although this universality has to be interpreted with care. The actual calculation is performed in the temporal Coulomb gauge, where the relevant contributions from collinear-soft gauge-boson exchange are contained exclusively in the self-energies of the external on-shell/on-resonance particles. In view of the special status of the time-like components in this gauge, a careful analysis of the asymptotic states of the theory is required. From this analysis we derive an all-order version of the Goldstone-boson Equivalence Theorem without the need for finite compensation factors. By exploiting conditions obtained from non-renormalization requirements, which are a consequence of our choice of gauge, we show that the Sudakov corrections can be extracted through a combination of energy derivatives and projections by means of external sources. We observe that the Standard Model behaves dynamically like an unbroken theory in the Sudakov limit, in spite of the fact that the explicit particle masses are needed at the kinematical (phase-space) level while calculating the Sudakov form factors.

Resummation of Yukawa enhanced and subleading Sudakov logarithms in longitudinal gauge boson and Higgs boson production

Future colliders will probe the electroweak theory at energies much larger than the gauge boson masses. Large double (DL) and single (SL) logarithmic virtual electroweak Sudakov corrections lead to significant effects for observable cross sections. Recently, leading and subleading universal corrections for external fermions and transverse gauge boson lines were resummed by employing the infrared evolution equation method. The results were confirmed at the DL level by explicit two loop calculations with the physical Standard Model (SM) fields. Also for longitudinal degrees of freedom the approach was utilized for DL-corrections via the Goldstone boson equivalence theorem. In all cases, the electroweak Sudakov logarithms exponentiate. In this paper we extend the same approach to both Yukawa enhanced as well as subleading Sudakov corrections to longitudinal gauge boson and Higgs production. We use virtual contributions to splitting functions of the appropriate Goldstone bosons in the high energy regime and find that all universal subleading terms exponentiate. The approach is verified by employing a non-Abelian version of Gribov's factorization theorem and by explicit comparison with existing one loop calculations. As a side result, we obtain also all top-Yukawa enhanced subleading logarithms for chiral fermion production at high energies to all orders. In all cases, the size of the subleading contributions at the two loop level is non-negligible in the context of precision measurements at future linear colliders.