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Mixed NNLO QCD x electroweak corrections of O(N_f \alpha_s \alpha) to single-W/Z production at the LHC
High Energy Physics - Phenomenology · Submitted 4 Sep 2020
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim While the corrections, which are implemented in the Monte Carlo program RADY, are negligible for observables that are dominated by resonant W/Z bosons, they affect invariant-mass distributions at the level of up to 2% for invariant masses of >500 GeV and are, thus, phenomenologically relevant.
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First results on the radiative corrections of order O(N_f\alpha_s\alpha) are presented for the off-shell production of W or Z bosons at the LHC, where N_f is the number of fermion flavours. These corrections comprise all diagrams at O(\alpha_s\alpha) with closed fermion loops, form a gauge-invariant part of the next-to-next-to-leading-order corrections of mixed QCD x electroweak type, and are the ones that concern the issue of mass renormalization of the W and Z resonances. The occurring irreducible two-loop diagrams, which involve only self-energy insertions, are calculated with current standard techniques, and explicit analytical results on the electroweak gauge-boson self-energies at O(\alpha_s\alpha) are given. Moreover, the generalization of the complex-mass scheme for a gauge-invariant treatment of the W/Z resonances is described for the order O(\alpha_s\alpha). While the corrections, which are implemented in the Monte Carlo program RADY, are negligible for observables that are dominated by resonant W/Z bosons, they affect invariant-mass distributions at the level of up to 2% for invariant masses of >500 GeV and are, thus, phenomenologically relevant. The impact on transverse-momentum distributions is similar, taking into account that leading-order predictions to those distributions underestimate the spectrum.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | First results on the radiative corrections of order O(N_f\alpha_s\alpha) are presented for the off-shell production of W or Z bosons at the LHC, where N_f is the number of fermion flavours. | contribution 0.95 | 0.93 | 0.15 | asserted 1.00 |
| s1 | These corrections comprise all diagrams at O(\alpha_s\alpha) with closed fermion loops, form a gauge-invariant part of the next-to-next-to-leading-order corrections of mixed QCD x electroweak type, and are the ones that concern the issue of mass renormalization of the W and Z resonances. | contribution 0.79 | 0.65 | 0.09 | asserted 1.00 |
| s2 | The occurring irreducible two-loop diagrams, which involve only self-energy insertions, are calculated with current standard techniques, and explicit analytical results on the electroweak gauge-boson self-energies at O(\alpha_s\alpha) are given. | method 0.87 | 0.93 | 0.06 | asserted 1.00 |
| s3 | Moreover, the generalization of the complex-mass scheme for a gauge-invariant treatment of the W/Z resonances is described for the order O(\alpha_s\alpha). | method 0.72 | 0.80 | 0.07 | asserted 0.99 |
| s4 | While the corrections, which are implemented in the Monte Carlo program RADY, are negligible for observables that are dominated by resonant W/Z bosons, they affect invariant-mass distributions at the level of up to 2% for invariant masses of >500 GeV and are, thus, phenomenologically relevant. | result 0.87 | 0.92 | 0.55 | asserted 1.00 |
| s5 | The impact on transverse-momentum distributions is similar, taking into account that leading-order predictions to those distributions underestimate the spectrum. | result 0.81 | 0.77 | 0.11 | asserted 0.98 |
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Original abstract
First results on the radiative corrections of order O(N_f\alpha_s\alpha) are presented for the off-shell production of W or Z bosons at the LHC, where N_f is the number of fermion flavours. These corrections comprise all diagrams at O(\alpha_s\alpha) with closed fermion loops, form a gauge-invariant part of the next-to-next-to-leading-order corrections of mixed QCD x electroweak type, and are the ones that concern the issue of mass renormalization of the W and Z resonances. The occurring irreducible two-loop diagrams, which involve only self-energy insertions, are calculated with current standard techniques, and explicit analytical results on the electroweak gauge-boson self-energies at O(\alpha_s\alpha) are given. Moreover, the generalization of the complex-mass scheme for a gauge-invariant treatment of the W/Z resonances is described for the order O(\alpha_s\alpha). While the corrections, which are implemented in the Monte Carlo program RADY, are negligible for observables that are dominated by resonant W/Z bosons, they affect invariant-mass distributions at the level of up to 2% for invariant masses of >500 GeV and are, thus, phenomenologically relevant. The impact on transverse-momentum distributions is similar, taking into account that leading-order predictions to those distributions underestimate the spectrum.
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References
How the literature uses it
21 arXiv papers cite this in 26 sentences
Papers citing it · 14 sentences without a confident label
Uses its method or tool 1 paper
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We also employ the complex-mass scheme [ref] and its extension to $(αα_s)$ corrections as described in Ref. [ref] .
Mixed QCD-electroweak corrections to dilepton production at the LHC in the high invariant mass region · Phenomenological results · 0.94
Compares with it 1 paper
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We have performed an independent calculation and checked our analytic results against those in Refs. [ref] .
Mixed QCD-electroweak corrections to dilepton production at the LHC in the high invariant mass region · Virtual corrections · 1.00
Cites it as background 10 papers
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The theoretical description of Drell-Yan differential distributions relies on perturbation theory in the Standard Model couplings, which is available to next-to-leading order () in the theory [ref] , next-to-next-to-leading order () in [ref] , and with mixed + corrections [ref] .
Precision phenomenology with fiducial cross sections in the triple-differential Drell-Yan process · Introduction · 0.97
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More recently, the $𝒪(α)$ corrections to the full off-shell Drell–Yan processes have been attacked by several groups, starting with the $𝒪(N_fα)$ corrections to the charged- and neutral-current channels which are enhanced by the number $N_f$ of fermion flavours [ref] .
Mixed NNLO QCD $\times$ electroweak corrections to single-Z production in pole approximation: differential distributions and forward-backward asymmetry · Introduction · 0.92
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The mixed NNLO contributions of $O(α_s α)$ have been evaluated in pole approximation for neutral and charged current DY [ref] while the complete corrections of $O(N_f α_s α)$ have been presented in Ref. [ref] .
On electroweak corrections to neutral current Drell-Yan with the POWHEG BOX · Introduction · 0.96
What it cites · 20 sentences without a confident label
Builds on 3 papers
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To solve this problem, we describe the generalization of the complex-mass scheme [ref] (see also Denner:2019vbn), which is a standard method for a gauge-invariant treatment of resonances at NLO, for the application to W/Z resonances at $O(α)$.
Electroweak corrections to charged-current e+e- --> 4 fermion processes - technical details and further results · Introduction · 0.89
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The $O(α)$ contribution $Δr_(α)$ to $Δr$ is entirely given by the fermion-loop contributions to the gauge-boson self-energies and, thus, follows from the $O(α)$ result [ref] for $Δr$ with the corresponding substitution for the self-energies, [equation] where we have used eq:SiAZ-WI.
Electroweak Radiative Corrections for Collider Physics · Electroweak input-parameter scheme · 0.82
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The $O(α)$ contribution $Δr_(α)$ to $Δr$ is entirely given by the fermion-loop contributions to the gauge-boson self-energies and, thus, follows from the $O(α)$ result [ref] for $Δr$ with the corresponding substitution for the self-energies, [equation] where we have used eq:SiAZ-WI.
Techniques for the calculation of electroweak radiative corrections at the one-loop level and results for W-physics at LEP200 · Electroweak input-parameter scheme · 0.82
Uses the method or tool of 15 papers
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The master integrals in $D = 4-2$ dimensions are solved by deriving differential equations in Henn's canonical form [ref] and subsequent integration to obtain the results as a Laurent expansion in $ϵ$ in terms of generalized polylogarithms up to weight three.
Lectures on differential equations for Feynman integrals · Introduction · 1.00
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The master integrals in $D = 4-2$ dimensions are solved by deriving differential equations in Henn's canonical form [ref] and subsequent integration to obtain the results as a Laurent expansion in $ϵ$ in terms of generalized polylogarithms up to weight three.
Multiloop integrals in dimensional regularization made simple · Introduction · 1.00
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Infrared singularities are handled with standard QCD dipole subtraction [ref] .
A General Algorithm for Calculating Jet Cross Sections in NLO QCD · Survey of diagrams and structure of the calculation · 1.00
Cites as support 2 papers
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As already expected from the size of the renormalization constants given in table:vert_ct, from the results on $O(α)$ corrections for stable W/Z bosons, and from the results in pole approximation [ref] , the impact of $O(N_fα)$ corrections is at the level of permille, and thus phenomenologically unimportant, in all regions where resonant W/Z bosons dominate the cross section.
Dominant mixed QCD-electroweak $\mathcal{O}(\alpha_s\alpha)$ corrections to Drell-Yan processes in the resonance region · Corrections to differential distributions · 0.96
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Already the NLO EW corrections to this channel turn out to be phenomenologically irrelevant [ref] , so that we do not include the $γγ$ channel in our calculation of $O(N_fα)$ corrections in the following, but restrict our calculation to $qq̅^(')$ annihilation.
Radiative corrections to the neutral-current Drell-Yan process in the Standard Model and its minimal supersymmetric extension · Survey of diagrams and structure of the calculation · 0.97
Cites as background 38 papers
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Inclusive results for the mixed QCD–EW corrections to on-shell Z production were calculated in [ref] and fully differential results in Delto:2019ewv,Buccioni:2020cfi,Cieri:2020ikq.
NNLO QCD$\times$EW corrections to Z production in the $q\bar{q}$ channel · Introduction · 0.80
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Inclusive results for the mixed QCD–EW corrections to on-shell Z production were calculated in [ref] and fully differential results in Delto:2019ewv,Buccioni:2020cfi,Cieri:2020ikq.
NNLO QCD$\times$EW corrections to on-shell $Z$ production · Introduction · 0.80
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Fixed-order QCD calculations for inclusive and differential observables are available up to next-to-next-to-leading (NNLO) order [ref] supplemented by threshold effects that have been studied up to next-to-next-to-next-to-leading order ($N^3LO$) accuracy [ref] and by resummed large logarithms occurring due to soft-gluon emissions at small transverse momentum [ref] .
Vector boson production at hadron colliders: a fully exclusive QCD calculation at NNLO · Introduction · 0.91
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