Skip to main content
Springer Nature Link
Account
Menu
Find a journal Publish with us Track your research
Search
Cart
  1. Home
  2. Journal of High Energy Physics
  3. Article

The automation of next-to-leading order electroweak calculations

  • Regular Article - Theoretical Physics
  • Open access
  • Published: 31 July 2018
  • Volume 2018, article number 185, (2018)
  • Cite this article
Download PDF

You have full access to this open access article

Journal of High Energy Physics Aims and scope Submit manuscript
The automation of next-to-leading order electroweak calculations
Download PDF
  • R. Frederix1,
  • S. Frixione2,
  • V. Hirschi3,
  • D. Pagani1,
  • H.-S. Shao4 &
  • …
  • M. Zaro5 

  • 904 Accesses

  • 163 Citations

  • 1 Altmetric

  • Explore all metrics

An Erratum to this article was published on 12 November 2021

This article has been updated

A preprint version of the article is available at arXiv.

Abstract

We present the key features relevant to the automated computation of all the leading- and next-to-leading order contributions to short-distance cross sections in a mixed-coupling expansion, with special emphasis on the first subleading NLO term in the QCD+EW scenario, commonly referred to as NLO EW corrections. We discuss, in particular, the FKS subtraction in the context of a mixed-coupling expansion; the extension of the FKS subtraction to processes that include final-state tagged particles, defined by means of fragmentation functions; and some properties of the complex mass scheme. We combine the present paper with the release of a new version of MadGraph5_aMC@NLO, capable of dealing with mixed-coupling expansions. We use the code to obtain illustrative inclusive and differential results for the 13-TeV LHC.

Article PDF

Download to read the full article text

Similar content being viewed by others

One-loop electroweak Sudakov logarithms: a revisitation and automation

Article Open access 18 February 2022

NLO electroweak automation and precise predictions for W + multijet production at the LHC

Article Open access 02 April 2015

Logarithmic EW corrections at one-loop

Article Open access 18 October 2024
Use our pre-submission checklist

Avoid common mistakes on your manuscript.

Change history

  • 12 November 2021

    An Erratum to this paper has been published: https://doi.org/10.1007/JHEP11(2021)085

References

  1. J.R. Andersen et al., Les Houches 2017: physics at TeV colliders Standard Model working group report, in 10th Les Houches Workshop on Physics at TeV Colliders (PhysTeV 2017), Les Houches, France, 5-23 June 2017 [arXiv:1803.07977] [INSPIRE].

  2. M. Kuroda, G. Moultaka and D. Schildknecht, Direct one loop renormalization of SU(2)L × U(1)Y four fermion processes and running coupling constants, Nucl. Phys. B 350 (1991) 25 [INSPIRE].

  3. G. Degrassi and A. Sirlin, Gauge invariant selfenergies and vertex parts of the Standard Model in the pinch technique framework, Phys. Rev. D 46 (1992) 3104 [INSPIRE].

    ADS  Google Scholar 

  4. P. Ciafaloni and D. Comelli, Sudakov enhancement of electroweak corrections, Phys. Lett. B 446 (1999) 278 [hep-ph/9809321] [INSPIRE].

  5. M. Ciafaloni, P. Ciafaloni and D. Comelli, Bloch-Nordsieck violating electroweak corrections to inclusive TeV scale hard processes, Phys. Rev. Lett. 84 (2000) 4810 [hep-ph/0001142] [INSPIRE].

  6. A. Denner and S. Pozzorini, One loop leading logarithms in electroweak radiative corrections. 1. Results, Eur. Phys. J. C 18 (2001) 461 [hep-ph/0010201] [INSPIRE].

  7. A. Denner and S. Pozzorini, One loop leading logarithms in electroweak radiative corrections. 2. Factorization of collinear singularities, Eur. Phys. J. C 21 (2001) 63 [hep-ph/0104127] [INSPIRE].

  8. S. Actis, A. Denner, L. Hofer, J.-N. Lang, A. Scharf and S. Uccirati, RECOLA: REcursive Computation of One-Loop Amplitudes, Comput. Phys. Commun. 214 (2017) 140 [arXiv:1605.01090] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  9. S. Actis, A. Denner, L. Hofer, A. Scharf and S. Uccirati, Recursive generation of one-loop amplitudes in the Standard Model, JHEP 04 (2013) 037 [arXiv:1211.6316] [INSPIRE].

    Article  ADS  Google Scholar 

  10. T. Gleisberg et al., Event generation with SHERPA 1.1, JHEP 02 (2009) 007 [arXiv:0811.4622] [INSPIRE].

  11. M. Schönherr, An automated subtraction of NLO EW infrared divergences, Eur. Phys. J. C 78 (2018) 119 [arXiv:1712.07975] [INSPIRE].

  12. F. Cascioli, P. Maierhofer and S. Pozzorini, Scattering amplitudes with open loops, Phys. Rev. Lett. 108 (2012) 111601 [arXiv:1111.5206] [INSPIRE].

    Article  ADS  Google Scholar 

  13. G. Cullen et al., Automated one-loop calculations with GoSam, Eur. Phys. J. C 72 (2012) 1889 [arXiv:1111.2034] [INSPIRE].

  14. G. Cullen et al., GoSam-2.0: a tool for automated one-loop calculations within the Standard Model and beyond, Eur. Phys. J. C 74 (2014) 3001 [arXiv:1404.7096] [INSPIRE].

  15. R. Frederix, T. Gehrmann and N. Greiner, Automation of the dipole subtraction method in MadGraph/MadEvent, JHEP 09 (2008) 122 [arXiv:0808.2128] [INSPIRE].

    Article  ADS  Google Scholar 

  16. T. Gehrmann and N. Greiner, Photon radiation with MadDipole, JHEP 12 (2010) 050 [arXiv:1011.0321] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  17. J. Alwall et al., The automated computation of tree-level and next-to-leading order differential cross sections and their matching to parton shower simulations, JHEP 07 (2014) 079 [arXiv:1405.0301] [INSPIRE].

    Article  ADS  Google Scholar 

  18. A. Denner, L. Hofer, A. Scharf and S. Uccirati, Electroweak corrections to lepton pair production in association with two hard jets at the LHC, JHEP 01 (2015) 094 [arXiv:1411.0916] [INSPIRE].

    Article  ADS  Google Scholar 

  19. A. Denner, R. Feger and A. Scharf, Irreducible background and interference effects for Higgs-boson production in association with a top-quark pair, JHEP 04 (2015) 008 [arXiv:1412.5290] [INSPIRE].

    Article  Google Scholar 

  20. A. Denner and R. Feger, NLO QCD corrections to off-shell top-antitop production with leptonic decays in association with a Higgs boson at the LHC, JHEP 11 (2015) 209 [arXiv:1506.07448] [INSPIRE].

    Article  ADS  Google Scholar 

  21. S. Kallweit, J.M. Lindert, P. Maierhöfer, S. Pozzorini and M. Schönherr, NLO electroweak automation and precise predictions for W + multijet production at the LHC, JHEP 04 (2015) 012 [arXiv:1412.5157] [INSPIRE].

  22. S. Frixione, V. Hirschi, D. Pagani, H.S. Shao and M. Zaro, Weak corrections to Higgs hadroproduction in association with a top-quark pair, JHEP 09 (2014) 065 [arXiv:1407.0823] [INSPIRE].

    Article  ADS  Google Scholar 

  23. M. Chiesa, N. Greiner and F. Tramontano, Automation of electroweak corrections for LHC processes, J. Phys. G 43 (2016) 013002 [arXiv:1507.08579] [INSPIRE].

  24. S. Kallweit, J.M. Lindert, P. Maierhofer, S. Pozzorini and M. Schönherr, NLO QCD + EW predictions for V + jets including off-shell vector-boson decays and multijet merging, JHEP 04 (2016) 021 [arXiv:1511.08692] [INSPIRE].

  25. S. Frixione, V. Hirschi, D. Pagani, H.S. Shao and M. Zaro, Electroweak and QCD corrections to top-pair hadroproduction in association with heavy bosons, JHEP 06 (2015) 184 [arXiv:1504.03446] [INSPIRE].

    Article  ADS  Google Scholar 

  26. B. Biedermann et al., Next-to-leading-order electroweak corrections to pp → W + W − → 4 leptons at the LHC, JHEP 06 (2016) 065 [arXiv:1605.03419] [INSPIRE].

  27. B. Biedermann, A. Denner, S. Dittmaier, L. Hofer and B. Jäger, Electroweak corrections to pp → μ + μ − e + e − + X at the LHC: a Higgs background study, Phys. Rev. Lett. 116 (2016) 161803 [arXiv:1601.07787] [INSPIRE].

  28. A. Denner and M. Pellen, NLO electroweak corrections to off-shell top-antitop production with leptonic decays at the LHC, JHEP 08 (2016) 155 [arXiv:1607.05571] [INSPIRE].

    Article  ADS  Google Scholar 

  29. B. Biedermann, A. Denner and M. Pellen, Large electroweak corrections to vector-boson scattering at the Large Hadron Collider, Phys. Rev. Lett. 118 (2017) 261801 [arXiv:1611.02951] [INSPIRE].

    Article  ADS  Google Scholar 

  30. B. Biedermann, A. Denner, S. Dittmaier, L. Hofer and B. Jager, Next-to-leading-order electroweak corrections to the production of four charged leptons at the LHC, JHEP 01 (2017) 033 [arXiv:1611.05338] [INSPIRE].

    Article  ADS  Google Scholar 

  31. A. Denner, J.-N. Lang, M. Pellen and S. Uccirati, Higgs production in association with off-shell top-antitop pairs at NLO EW and QCD at the LHC, JHEP 02 (2017) 053 [arXiv:1612.07138] [INSPIRE].

    Article  ADS  Google Scholar 

  32. R. Frederix, S. Frixione, V. Hirschi, D. Pagani, H.-S. Shao and M. Zaro, The complete NLO corrections to dijet hadroproduction, JHEP 04 (2017) 076 [arXiv:1612.06548] [INSPIRE].

    Article  ADS  Google Scholar 

  33. D. Pagani, I. Tsinikos and M. Zaro, The impact of the photon PDF and electroweak corrections on \( t\overline{t} \) distributions, Eur. Phys. J. C 76 (2016) 479 [arXiv:1606.01915] [INSPIRE].

  34. B. Biedermann, S. Bräuer, A. Denner, M. Pellen, S. Schumann and J.M. Thompson, Automation of NLO QCD and EW corrections with Sherpa and RECOLA, Eur. Phys. J. C 77 (2017) 492 [arXiv:1704.05783] [INSPIRE].

  35. S. Kallweit, J.M. Lindert, S. Pozzorini and M. Schönherr, NLO QCD + EW predictions for 2ℓ2ν diboson signatures at the LHC, JHEP 11 (2017) 120 [arXiv:1705.00598] [INSPIRE].

  36. B. Biedermann, A. Denner and M. Pellen, Complete NLO corrections to W + W + scattering and its irreducible background at the LHC, JHEP 10 (2017) 124 [arXiv:1708.00268] [INSPIRE].

  37. B. Biedermann, A. Denner and L. Hofer, Next-to-leading-order electroweak corrections to the production of three charged leptons plus missing energy at the LHC, JHEP 10 (2017) 043 [arXiv:1708.06938] [INSPIRE].

    Article  ADS  Google Scholar 

  38. M. Chiesa, N. Greiner, M. Schönherr and F. Tramontano, Electroweak corrections to diphoton plus jets, JHEP 10 (2017) 181 [arXiv:1706.09022] [INSPIRE].

    Article  ADS  Google Scholar 

  39. M. Czakon, D. Heymes, A. Mitov, D. Pagani, I. Tsinikos and M. Zaro, Top-pair production at the LHC through NNLO QCD and NLO EW, JHEP 10 (2017) 186 [arXiv:1705.04105] [INSPIRE].

    Article  ADS  Google Scholar 

  40. R. Frederix, D. Pagani and M. Zaro, Large NLO corrections in \( t\overline{t}{W}^{\pm } \) and \( t\overline{t}t\overline{t} \) hadroproduction from supposedly subleading EW contributions, JHEP 02 (2018) 031 [arXiv:1711.02116] [INSPIRE].

  41. C. Gütschow, J.M. Lindert and M. Schönherr, Multi-jet merged top-pair production including electroweak corrections, Eur. Phys. J. C 78 (2018) 317 [arXiv:1803.00950] [INSPIRE].

  42. M. Czakon, D. Heymes, A. Mitov, D. Pagani, I. Tsinikos and M. Zaro, Top-quark charge asymmetry at the LHC and Tevatron through NNLO QCD and NLO EW, Phys. Rev. D 98 (2018) 014003 [arXiv:1711.03945] [INSPIRE].

  43. F. Maltoni, D. Pagani, A. Shivaji and X. Zhao, Trilinear Higgs coupling determination via single-Higgs differential measurements at the LHC, Eur. Phys. J. C 77 (2017) 887 [arXiv:1709.08649] [INSPIRE].

  44. M.L. Mangano, T. Plehn, P. Reimitz, T. Schell and H.-S. Shao, Measuring the top Yukawa coupling at 100 TeV, J. Phys. G 43 (2016) 035001 [arXiv:1507.08169] [INSPIRE].

  45. V. Hirschi and O. Mattelaer, Automated event generation for loop-induced processes, JHEP 10 (2015) 146 [arXiv:1507.00020] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  46. S. Frixione, Z. Kunszt and A. Signer, Three jet cross-sections to next-to-leading order, Nucl. Phys. B 467 (1996) 399 [hep-ph/9512328] [INSPIRE].

  47. S. Frixione, A general approach to jet cross-sections in QCD, Nucl. Phys. B 507 (1997) 295 [hep-ph/9706545] [INSPIRE].

  48. A. Denner, S. Dittmaier, M. Roth and D. Wackeroth, Predictions for all processes e + e − → 4 fermions + γ, Nucl. Phys. B 560 (1999) 33 [hep-ph/9904472] [INSPIRE].

  49. A. Denner, S. Dittmaier, M. Roth and L.H. Wieders, Electroweak corrections to charged-current e + e − → 4 fermion processes: technical details and further results, Nucl. Phys. B 724 (2005) 247 [Erratum ibid. B 854 (2012) 504] [hep-ph/0505042] [INSPIRE].

  50. R. Frederix, S. Frixione, F. Maltoni and T. Stelzer, Automation of next-to-leading order computations in QCD: the FKS subtraction, JHEP 10 (2009) 003 [arXiv:0908.4272] [INSPIRE].

    Article  ADS  Google Scholar 

  51. R. Frederix, S. Frixione, A.S. Papanastasiou, S. Prestel and P. Torrielli, Off-shell single-top production at NLO matched to parton showers, JHEP 06 (2016) 027 [arXiv:1603.01178] [INSPIRE].

    Article  ADS  Google Scholar 

  52. G. Ossola, C.G. Papadopoulos and R. Pittau, Reducing full one-loop amplitudes to scalar integrals at the integrand level, Nucl. Phys. B 763 (2007) 147 [hep-ph/0609007] [INSPIRE].

  53. P. Mastrolia, E. Mirabella and T. Peraro, Integrand reduction of one-loop scattering amplitudes through Laurent series expansion, JHEP 06 (2012) 095 [Erratum ibid. 11 (2012) 128] [arXiv:1203.0291] [INSPIRE].

  54. G. Passarino and M.J.G. Veltman, One loop corrections for e + e − annihilation into μ + μ − in the Weinberg model, Nucl. Phys. B 160 (1979) 151 [INSPIRE].

  55. A.I. Davydychev, A simple formula for reducing Feynman diagrams to scalar integrals, Phys. Lett. B 263 (1991) 107 [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  56. A. Denner and S. Dittmaier, Reduction schemes for one-loop tensor integrals, Nucl. Phys. B 734 (2006) 62 [hep-ph/0509141] [INSPIRE].

  57. V. Hirschi, R. Frederix, S. Frixione, M.V. Garzelli, F. Maltoni and R. Pittau, Automation of one-loop QCD corrections, JHEP 05 (2011) 044 [arXiv:1103.0621] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  58. G. Ossola, C.G. Papadopoulos and R. Pittau, CutTools: a program implementing the OPP reduction method to compute one-loop amplitudes, JHEP 03 (2008) 042 [arXiv:0711.3596] [INSPIRE].

    Article  ADS  Google Scholar 

  59. T. Peraro, Ninja: automated integrand reduction via Laurent expansion for one-loop amplitudes, Comput. Phys. Commun. 185 (2014) 2771 [arXiv:1403.1229] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  60. V. Hirschi and T. Peraro, Tensor integrand reduction via Laurent expansion, JHEP 06 (2016) 060 [arXiv:1604.01363] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  61. H.-S. Shao, IREGI user manual, unpublished.

  62. A. Denner, S. Dittmaier and L. Hofer, Collier: a fortran-based Complex One-Loop LIbrary in Extended Regularizations, Comput. Phys. Commun. 212 (2017) 220 [arXiv:1604.06792] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  63. S. Frixione and B.R. Webber, Matching NLO QCD computations and parton shower simulations, JHEP 06 (2002) 029 [hep-ph/0204244] [INSPIRE].

  64. N.D. Christensen and C. Duhr, FeynRules — Feynman rules made easy, Comput. Phys. Commun. 180 (2009) 1614 [arXiv:0806.4194] [INSPIRE].

    Article  ADS  Google Scholar 

  65. N.D. Christensen et al., A comprehensive approach to new physics simulations, Eur. Phys. J. C 71 (2011) 1541 [arXiv:0906.2474] [INSPIRE].

  66. N.D. Christensen, C. Duhr, B. Fuks, J. Reuter and C. Speckner, Introducing an interface between WHIZARD and FeynRules, Eur. Phys. J. C 72 (2012) 1990 [arXiv:1010.3251] [INSPIRE].

  67. C. Duhr and B. Fuks, A superspace module for the FeynRules package, Comput. Phys. Commun. 182 (2011) 2404 [arXiv:1102.4191] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  68. A. Alloul, N.D. Christensen, C. Degrande, C. Duhr and B. Fuks, FeynRules 2.0 — a complete toolbox for tree-level phenomenology, Comput. Phys. Commun. 185 (2014) 2250 [arXiv:1310.1921] [INSPIRE].

  69. A. Alloul, J. D’Hondt, K. De Causmaecker, B. Fuks and M. Rausch de Traubenberg, Automated mass spectrum generation for new physics, Eur. Phys. J. C 73 (2013) 2325 [arXiv:1301.5932] [INSPIRE].

  70. C. Degrande, Automatic evaluation of UV and R 2 terms for beyond the Standard Model Lagrangians: a proof-of-principle, Comput. Phys. Commun. 197 (2015) 239 [arXiv:1406.3030] [INSPIRE].

  71. L.A. Harland-Lang, V.A. Khoze and M.G. Ryskin, Sudakov effects in photon-initiated processes, Phys. Lett. B 761 (2016) 20 [arXiv:1605.04935] [INSPIRE].

  72. B. Mele and P. Nason, The fragmentation function for heavy quarks in QCD, Nucl. Phys. B 361 (1991) 626 [Erratum ibid. B 921 (2017) 841] [INSPIRE].

  73. T. Sjöstrand et al., An introduction to PYTHIA 8.2, Comput. Phys. Commun. 191 (2015) 159 [arXiv:1410.3012] [INSPIRE].

  74. J. Bellm et al., HERWIG 7.0/HERWIG++ 3.0 release note, Eur. Phys. J. C 76 (2016) 196 [arXiv:1512.01178] [INSPIRE].

  75. S. Frixione, Colourful FKS subtraction, JHEP 09 (2011) 091 [arXiv:1106.0155] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  76. R. Frederix, S. Frixione, V. Hirschi, F. Maltoni, R. Pittau and P. Torrielli, Four-lepton production at hadron colliders: aMC@NLO predictions with theoretical uncertainties, JHEP 02 (2012) 099 [arXiv:1110.4738] [INSPIRE].

    Article  ADS  Google Scholar 

  77. R.K. Ellis, M.A. Furman, H.E. Haber and I. Hinchliffe, Large corrections to high p T hadron-hadron scattering in QCD, Nucl. Phys. B 173 (1980) 397 [INSPIRE].

  78. F. Aversa, P. Chiappetta, M. Greco and J.P. Guillet, QCD corrections to parton-parton scattering processes, Nucl. Phys. B 327 (1989) 105 [INSPIRE].

  79. R.G. Stuart, Gauge invariance, analyticity and physical observables at the Z 0 resonance, Phys. Lett. B 262 (1991) 113 [INSPIRE].

  80. R.G. Stuart, General renormalization of the gauge invariant perturbation expansion near the Z 0 resonance, Phys. Lett. B 272 (1991) 353 [INSPIRE].

  81. A. Sirlin, Observations concerning mass renormalization in the electroweak theory, Phys. Lett. B 267 (1991) 240 [INSPIRE].

  82. A. Sirlin, Theoretical considerations concerning the Z 0 mass, Phys. Rev. Lett. 67 (1991) 2127 [INSPIRE].

  83. G.F. Sterman, An introduction to quantum field theory, Cambridge University Press, Cambridge, U.K., (1993) [INSPIRE].

  84. A. Aeppli, F. Cuypers and G.J. van Oldenborgh, O(Γ) corrections to W pair production in e + e − and γγ collisions, Phys. Lett. B 314 (1993) 413 [hep-ph/9303236] [INSPIRE].

  85. A. Aeppli, G.J. van Oldenborgh and D. Wyler, Unstable particles in one loop calculations, Nucl. Phys. B 428 (1994) 126 [hep-ph/9312212] [INSPIRE].

  86. A.P. Chapovsky, V.A. Khoze, A. Signer and W.J. Stirling, Nonfactorizable corrections and effective field theories, Nucl. Phys. B 621 (2002) 257 [hep-ph/0108190] [INSPIRE].

  87. M. Beneke, A.P. Chapovsky, A. Signer and G. Zanderighi, Effective theory approach to unstable particle production, Phys. Rev. Lett. 93 (2004) 011602 [hep-ph/0312331] [INSPIRE].

  88. M. Beneke, A.P. Chapovsky, A. Signer and G. Zanderighi, Effective theory calculation of resonant high-energy scattering, Nucl. Phys. B 686 (2004) 205 [hep-ph/0401002] [INSPIRE].

  89. A. Denner, Techniques for calculation of electroweak radiative corrections at the one loop level and results for W physics at LEP-200, Fortsch. Phys. 41 (1993) 307 [arXiv:0709.1075] [INSPIRE].

  90. T. Bauer, J. Gegelia, G. Japaridze and S. Scherer, Complex-mass scheme and perturbative unitarity, Int. J. Mod. Phys. A 27 (2012) 1250178 [arXiv:1211.1684] [INSPIRE].

  91. A. Denner and J.-N. Lang, The complex-mass scheme and unitarity in perturbative quantum field theory, Eur. Phys. J. C 75 (2015) 377 [arXiv:1406.6280] [INSPIRE].

  92. G. ’t Hooft and M.J.G. Veltman, Scalar one loop integrals, Nucl. Phys. B 153 (1979) 365 [INSPIRE].

  93. R.K. Ellis and G. Zanderighi, Scalar one-loop integrals for QCD, JHEP 02 (2008) 002 [arXiv:0712.1851] [INSPIRE].

    Article  ADS  Google Scholar 

  94. G. Passarino, C. Sturm and S. Uccirati, Higgs pseudo-observables, second Riemann sheet and all that, Nucl. Phys. B 834 (2010) 77 [arXiv:1001.3360] [INSPIRE].

  95. M.J.G. Veltman, Unitarity and causality in a renormalizable field theory with unstable particles, Physica 29 (1963) 186 [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  96. P. Ciafaloni and D. Comelli, The importance of weak bosons emission at LHC, JHEP 09 (2006) 055 [hep-ph/0604070] [INSPIRE].

  97. U. Baur, Weak boson emission in hadron collider processes, Phys. Rev. D 75 (2007) 013005 [hep-ph/0611241] [INSPIRE].

  98. G. Bell, J.H. Kuhn and J. Rittinger, Electroweak Sudakov logarithms and real gauge-boson radiation in the TeV region, Eur. Phys. J. C 70 (2010) 659 [arXiv:1004.4117] [INSPIRE].

  99. W.J. Stirling and E. Vryonidou, Electroweak corrections and Bloch-Nordsieck violations in 2-to-2 processes at the LHC, JHEP 04 (2013) 155 [arXiv:1212.6537] [INSPIRE].

  100. M. Chiesa et al., Electroweak Sudakov corrections to new physics searches at the LHC, Phys. Rev. Lett. 111 (2013) 121801 [arXiv:1305.6837] [INSPIRE].

    Article  ADS  Google Scholar 

  101. J.R. Christiansen and T. Sjöstrand, Weak gauge boson radiation in parton showers, JHEP 04 (2014) 115 [arXiv:1401.5238] [INSPIRE].

    Article  ADS  Google Scholar 

  102. F. Krauss, P. Petrov, M. Schoenherr and M. Spannowsky, Measuring collinear W emissions inside jets, Phys. Rev. D 89 (2014) 114006 [arXiv:1403.4788] [INSPIRE].

  103. C.W. Bauer and N. Ferland, Resummation of electroweak Sudakov logarithms for real radiation, JHEP 09 (2016) 025 [arXiv:1601.07190] [INSPIRE].

    Article  ADS  Google Scholar 

  104. C. Degrande, C. Duhr, B. Fuks, D. Grellscheid, O. Mattelaer and T. Reiter, UFO — the Universal FeynRules Output, Comput. Phys. Commun. 183 (2012) 1201 [arXiv:1108.2040] [INSPIRE].

  105. Particle Data Group collaboration, C. Patrignani et al., Review of particle physics, Chin. Phys. C 40 (2016) 100001 [INSPIRE].

  106. B.A. Kniehl and A. Sirlin, Differences between the pole and on-shell masses and widths of the Higgs boson, Phys. Rev. Lett. 81 (1998) 1373 [hep-ph/9805390] [INSPIRE].

  107. B.A. Kniehl, C.P. Palisoc and A. Sirlin, Elimination of threshold singularities in the relation between on shell and pole widths, Phys. Rev. D 66 (2002) 057902 [hep-ph/0205304] [INSPIRE].

  108. P.A. Grassi, B.A. Kniehl and A. Sirlin, Width and partial widths of unstable particles in the light of the Nielsen identities, Phys. Rev. D 65 (2002) 085001 [hep-ph/0109228] [INSPIRE].

  109. J. Butterworth et al., PDF4LHC recommendations for LHC run II, J. Phys. G 43 (2016) 023001 [arXiv:1510.03865] [INSPIRE].

  110. A. Manohar, P. Nason, G.P. Salam and G. Zanderighi, How bright is the proton? A precise determination of the photon parton distribution function, Phys. Rev. Lett. 117 (2016) 242002 [arXiv:1607.04266] [INSPIRE].

    Article  ADS  Google Scholar 

  111. A. Buckley et al., LHAPDF6: parton density access in the LHC precision era, Eur. Phys. J. C 75 (2015) 132 [arXiv:1412.7420] [INSPIRE].

  112. M. Cacciari, G.P. Salam and G. Soyez, The anti-k t jet clustering algorithm, JHEP 04 (2008) 063 [arXiv:0802.1189] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  113. M. Cacciari, G.P. Salam and G. Soyez, FastJet user manual, Eur. Phys. J. C 72 (2012) 1896 [arXiv:1111.6097] [INSPIRE].

  114. A. van Hameren, OneLOop: for the evaluation of one-loop scalar functions, Comput. Phys. Commun. 182 (2011) 2427 [arXiv:1007.4716] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  115. S. Dittmaier and M. Krämer, Electroweak radiative corrections to W boson production at hadron colliders, Phys. Rev. D 65 (2002) 073007 [hep-ph/0109062] [INSPIRE].

  116. J.H. Kuhn, A. Kulesza, S. Pozzorini and M. Schulze, Electroweak corrections to hadronic production of W bosons at large transverse momenta, Nucl. Phys. B 797 (2008) 27 [arXiv:0708.0476] [INSPIRE].

  117. W. Hollik, T. Kasprzik and B.A. Kniehl, Electroweak corrections to W -boson hadroproduction at finite transverse momentum, Nucl. Phys. B 790 (2008) 138 [arXiv:0707.2553] [INSPIRE].

  118. A. Denner, S. Dittmaier, T. Kasprzik and A. Muck, Electroweak corrections to W + jet hadroproduction including leptonic W -boson decays, JHEP 08 (2009) 075 [arXiv:0906.1656] [INSPIRE].

  119. A. Denner, S. Dittmaier, T. Kasprzik and A. Mück, Electroweak corrections to monojet production at the LHC, Eur. Phys. J. C 73 (2013) 2297 [arXiv:1211.5078] [INSPIRE].

  120. J.R. Andersen et al., Les Houches 2015: physics at TeV colliders Standard Model working group report, in 9th Les Houches Workshop on Physics at TeV Colliders (PhysTeV 2015), Les Houches, France, 1-19 June 2015 [arXiv:1605.04692] [INSPIRE].

  121. S. Frixione, P. Nason and G. Ridolfi, Strong corrections to W Z production at hadron colliders, Nucl. Phys. B 383 (1992) 3 [INSPIRE].

  122. J.M. Butterworth, A.R. Davison, M. Rubin and G.P. Salam, Jet substructure as a new Higgs search channel at the LHC, Phys. Rev. Lett. 100 (2008) 242001 [arXiv:0802.2470] [INSPIRE].

    Article  ADS  Google Scholar 

  123. C.W. Bauer and B.O. Lange, Scale setting and resummation of logarithms in pp → V + jets, arXiv:0905.4739 [INSPIRE].

  124. M. Rubin, G.P. Salam and S. Sapeta, Giant QCD K-factors beyond NLO, JHEP 09 (2010) 084 [arXiv:1006.2144] [INSPIRE].

  125. U. Baur, O. Brein, W. Hollik, C. Schappacher and D. Wackeroth, Electroweak radiative corrections to neutral current Drell-Yan processes at hadron colliders, Phys. Rev. D 65 (2002) 033007 [hep-ph/0108274] [INSPIRE].

  126. S. Dittmaier and M. Huber, Radiative corrections to the neutral-current Drell-Yan process in the Standard Model and its minimal supersymmetric extension, JHEP 01 (2010) 060 [arXiv:0911.2329] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  127. J.H. Kuhn, A. Kulesza, S. Pozzorini and M. Schulze, One-loop weak corrections to hadronic production of Z bosons at large transverse momenta, Nucl. Phys. B 727 (2005) 368 [hep-ph/0507178] [INSPIRE].

  128. A. Denner, S. Dittmaier, T. Kasprzik and A. Muck, Electroweak corrections to dilepton + jet production at hadron colliders, JHEP 06 (2011) 069 [arXiv:1103.0914] [INSPIRE].

    Article  ADS  Google Scholar 

  129. W. Hollik, B.A. Kniehl, E.S. Scherbakova and O.L. Veretin, Electroweak corrections to Z-boson hadroproduction at finite transverse momentum, Nucl. Phys. B 900 (2015) 576 [arXiv:1504.07574] [INSPIRE].

  130. S. Gieseke, T. Kasprzik and J.H. Kühn, Vector-boson pair production and electroweak corrections in HERWIG++, Eur. Phys. J. C 74 (2014) 2988 [arXiv:1401.3964] [INSPIRE].

  131. M. Billóni, S. Dittmaier, B. Jäger and C. Speckner, Next-to-leading order electroweak corrections to pp → W + W − → 4 leptons at the LHC in double-pole approximation, JHEP 12 (2013) 043 [arXiv:1310.1564] [INSPIRE].

  132. S. Frixione, A next-to-leading order calculation of the cross-section for the production of W + W − pairs in hadronic collisions, Nucl. Phys. B 410 (1993) 280 [INSPIRE].

  133. J. Baglio, L.D. Ninh and M.M. Weber, Massive gauge boson pair production at the LHC: a next-to-leading order story, Phys. Rev. D 88 (2013) 113005 [arXiv:1307.4331] [INSPIRE].

  134. T. Gehrmann et al., W + W − production at hadron colliders in next to next to leading order QCD, Phys. Rev. Lett. 113 (2014) 212001 [arXiv:1408.5243] [INSPIRE].

  135. M.L. Ciccolini, S. Dittmaier and M. Krämer, Electroweak radiative corrections to associated WH and ZH production at hadron colliders, Phys. Rev. D 68 (2003) 073003 [hep-ph/0306234] [INSPIRE].

  136. A. Denner, S. Dittmaier, S. Kallweit and A. Muck, Electroweak corrections to Higgs-strahlung off W/Z bosons at the Tevatron and the LHC with HAWK, JHEP 03 (2012) 075 [arXiv:1112.5142] [INSPIRE].

  137. F. Granata, J.M. Lindert, C. Oleari and S. Pozzorini, NLO QCD + EW predictions for HV and HV + jet production including parton-shower effects, JHEP 09 (2017) 012 [arXiv:1706.03522] [INSPIRE].

  138. M. Ciccolini, A. Denner and S. Dittmaier, Strong and electroweak corrections to the production of Higgs + 2 jets via weak interactions at the LHC, Phys. Rev. Lett. 99 (2007) 161803 [arXiv:0707.0381] [INSPIRE].

  139. M. Ciccolini, A. Denner and S. Dittmaier, Electroweak and QCD corrections to Higgs production via vector-boson fusion at the LHC, Phys. Rev. D 77 (2008) 013002 [arXiv:0710.4749] [INSPIRE].

  140. D.T. Nhung, L.D. Ninh and M.M. Weber, NLO W W Z production at the LHC, in Proceedings, 9th Rencontres du Vietnam: windows on the universe, Quy Nhon, Vietnam, 11-17 August 2013, pg. 219 [arXiv:1310.6159] [INSPIRE].

  141. Y.-B. Shen, R.-Y. Zhang, W.-G. Ma, X.-Z. Li, Y. Zhang and L. Guo, NLO QCD + NLO EW corrections to W ZZ productions with leptonic decays at the LHC, JHEP 10 (2015) 186 [Erratum ibid. 10 (2016) 156] [arXiv:1507.03693] [INSPIRE].

  142. H. Wang, R.-Y. Zhang, W.-G. Ma, L. Guo, X.-Z. Li and S.-M. Wang, NLO QCD + EW corrections to ZZZ production with subsequent leptonic decays at the LHC, J. Phys. G 43 (2016) 115001 [arXiv:1610.05876] [INSPIRE].

  143. Y.-B. Shen, R.-Y. Zhang, W.-G. Ma, X.-Z. Li and L. Guo, NLO QCD and electroweak corrections to W W W production at the LHC, Phys. Rev. D 95 (2017) 073005 [arXiv:1605.00554] [INSPIRE].

  144. S. Dittmaier, A. Huss and G. Knippen, Next-to-leading-order QCD and electroweak corrections to W W W production at proton-proton colliders, JHEP 09 (2017) 034 [arXiv:1705.03722] [INSPIRE].

  145. S. Frixione, E. Laenen, P. Motylinski, B.R. Webber and C.D. White, Single-top hadroproduction in association with a W boson, JHEP 07 (2008) 029 [arXiv:0805.3067] [INSPIRE].

    Article  ADS  Google Scholar 

  146. C.D. White, S. Frixione, E. Laenen and F. Maltoni, Isolating W t production at the LHC, JHEP 11 (2009) 074 [arXiv:0908.0631] [INSPIRE].

  147. C. Weydert et al., Charged Higgs boson production in association with a top quark in MC@NLO, Eur. Phys. J. C 67 (2010) 617 [arXiv:0912.3430] [INSPIRE].

  148. E. Re, Single-top W t-channel production matched with parton showers using the POWHEG method, Eur. Phys. J. C 71 (2011) 1547 [arXiv:1009.2450] [INSPIRE].

  149. T. Binoth, D. Goncalves Netto, D. Lopez-Val, K. Mawatari, T. Plehn and I. Wigmore, Automized squark-neutralino production to next-to-leading order, Phys. Rev. D 84 (2011) 075005 [arXiv:1108.1250] [INSPIRE].

  150. D. Gonçalves-Netto, D. López-Val, K. Mawatari, T. Plehn and I. Wigmore, Automated squark and gluino production to next-to-leading order, Phys. Rev. D 87 (2013) 014002 [arXiv:1211.0286] [INSPIRE].

  151. R. Gavin et al., Matching squark pair production at NLO with parton showers, JHEP 10 (2013) 187 [arXiv:1305.4061] [INSPIRE].

    Article  ADS  Google Scholar 

  152. R. Gavin et al., Squark production and decay matched with parton showers at NLO, Eur. Phys. J. C 75 (2015) 29 [arXiv:1407.7971] [INSPIRE].

  153. F. Demartin, B. Maier, F. Maltoni, K. Mawatari and M. Zaro, tW H associated production at the LHC, Eur. Phys. J. C 77 (2017) 34 [arXiv:1607.05862] [INSPIRE].

  154. T.M.P. Tait, The tW − mode of single top production, Phys. Rev. D 61 (1999) 034001 [hep-ph/9909352] [INSPIRE].

  155. S. Zhu, Next-to-leading order QCD corrections to bg → tW − at CERN Large Hadron Collider, Phys. Lett. B 524 (2002) 283 [Erratum ibid. B 537 (2002) 351] [hep-ph/0109269] [INSPIRE].

  156. F. Cascioli, S. Kallweit, P. Maierhöfer and S. Pozzorini, A unified NLO description of top-pair and associated W t production, Eur. Phys. J. C 74 (2014) 2783 [arXiv:1312.0546] [INSPIRE].

  157. W. Beenakker, R. Hopker, M. Spira and P.M. Zerwas, Squark and gluino production at hadron colliders, Nucl. Phys. B 492 (1997) 51 [hep-ph/9610490] [INSPIRE].

  158. E.L. Berger, T. Han, J. Jiang and T. Plehn, Associated production of a top quark and a charged Higgs boson, Phys. Rev. D 71 (2005) 115012 [hep-ph/0312286] [INSPIRE].

  159. T.N. Dao, W. Hollik and D.N. Le, W ∓ H ± production and CP asymmetry at the LHC, Phys. Rev. D 83 (2011) 075003 [arXiv:1011.4820] [INSPIRE].

  160. W. Hollik, J.M. Lindert and D. Pagani, NLO corrections to squark-squark production and decay at the LHC, JHEP 03 (2013) 139 [arXiv:1207.1071] [INSPIRE].

    Article  ADS  Google Scholar 

  161. Y. Zhang, W.-G. Ma, R.-Y. Zhang, C. Chen and L. Guo, QCD NLO and EW NLO corrections to \( t\overline{t}H \) production with top quark decays at hadron collider, Phys. Lett. B 738 (2014) 1 [arXiv:1407.1110] [INSPIRE].

  162. S. Dittmaier, A. Huss and C. Speckner, Weak radiative corrections to dijet production at hadron colliders, JHEP 11 (2012) 095 [arXiv:1210.0438] [INSPIRE].

    Article  ADS  Google Scholar 

  163. M. Beccaria, G. Macorini, F.M. Renard and C. Verzegnassi, Single top production in the t-channel at LHC: a realistic test of electroweak models, Phys. Rev. D 74 (2006) 013008 [hep-ph/0605108] [INSPIRE].

  164. E. Mirabella, Electroweak corrections to t-channel single top production at the LHC, Nuovo Cim. B 123 (2008) 1111 [arXiv:0811.2051] [INSPIRE].

  165. D. Bardin, S. Bondarenko, L. Kalinovskaya, V. Kolesnikov and W. von Schlippe, Electroweak radiative corrections to single-top production, Eur. Phys. J. C 71 (2011) 1533 [arXiv:1008.1859] [INSPIRE].

  166. J.A. Dror, M. Farina, E. Salvioni and J. Serra, Strong tW scattering at the LHC, JHEP 01 (2016) 071 [arXiv:1511.03674] [INSPIRE].

  167. C. Degrande, R. Frederix, V. Hirschi, M. Ubiali, M. Wiesemann and M. Zaro, Accurate predictions for charged Higgs production: closing the m H ± ∼ m t window, Phys. Lett. B 772 (2017) 87 [arXiv:1607.05291] [INSPIRE].

  168. J. Alwall, M. Herquet, F. Maltoni, O. Mattelaer and T. Stelzer, MadGraph 5: going beyond, JHEP 06 (2011) 128 [arXiv:1106.0522] [INSPIRE].

  169. V. Bertone, S. Carrazza, D. Pagani and M. Zaro, On the impact of lepton PDFs, JHEP 11 (2015) 194 [arXiv:1508.07002] [INSPIRE].

    Article  ADS  Google Scholar 

  170. C.W. Bauer, N. Ferland and B.R. Webber, Standard Model parton distributions at very high energies, JHEP 08 (2017) 036 [arXiv:1703.08562] [INSPIRE].

    Article  ADS  Google Scholar 

  171. M. Jezabek and J.H. Kuhn, QCD corrections to semileptonic decays of heavy quarks, Nucl. Phys. B 314 (1989) 1 [INSPIRE].

  172. A. Denner and T. Sack, The top width, Nucl. Phys. B 358 (1991) 46 [INSPIRE].

  173. A. Czarnecki, QCD corrections to the decay t → W b in dimensional regularization, Phys. Lett. B 252 (1990) 467 [INSPIRE].

  174. C.S. Li, R.J. Oakes and T.C. Yuan, QCD corrections to t → W + b, Phys. Rev. D 43 (1991) 3759 [INSPIRE].

  175. J.-A. Liu and Y.-P. Yao, One loop radiative corrections to a heavy top decay in the Standard Model, Int. J. Mod. Phys. A 6 (1991) 4925 [INSPIRE].

  176. G. Eilam, R.R. Mendel, R. Migneron and A. Soni, Radiative corrections to top quark decay, Phys. Rev. Lett. 66 (1991) 3105 [INSPIRE].

    Article  ADS  Google Scholar 

  177. M. Jezabek and J.H. Kuhn, The top width: theoretical update, Phys. Rev. D 48 (1993) R1910 [Erratum ibid. D 49 (1994) 4970] [hep-ph/9302295] [INSPIRE].

  178. L. Basso, S. Dittmaier, A. Huss and L. Oggero, Techniques for the treatment of IR divergences in decay processes at NLO and application to the top-quark decay, Eur. Phys. J. C 76 (2016) 56 [arXiv:1507.04676] [INSPIRE].

  179. W.J. Marciano and A. Sirlin, Deviations from electron-muon universality in the leptonic decays of the intermediate bosons, Phys. Rev. D 8 (1973) 3612 [INSPIRE].

  180. D. Albert, W.J. Marciano, D. Wyler and Z. Parsa, Decays of intermediate vector bosons, radiative corrections and QCD jets, Nucl. Phys. B 166 (1980) 460 [INSPIRE].

  181. K. Inoue, A. Kakuto, H. Komatsu and S. Takeshita, Radiative corrections for W → e anti-neutrino decay in the Weinberg-Salam model with arbitrary number of generations, Prog. Theor. Phys. 64 (1980) 1008 [INSPIRE].

  182. T.H. Chang, K.J.F. Gaemers and W.L. van Neerven, QCD corrections to the mass and width of the intermediate vector bosons, Nucl. Phys. B 202 (1982) 407 [INSPIRE].

  183. M. Consoli, S. Lo Presti and L. Maiani, Higher order effects and the vector boson physical parameters, Nucl. Phys. B 223 (1983) 474 [INSPIRE].

  184. D. Yu. Bardin, S. Riemann and T. Riemann, Electroweak one loop corrections to the decay of the charged vector boson, Z. Phys. C 32 (1986) 121 [INSPIRE].

  185. A. Denner and T. Sack, The W boson width, Z. Phys. C 46 (1990) 653 [INSPIRE].

  186. M. Dine and J.R. Sapirstein, Higher order QCD corrections in e + e − annihilation, Phys. Rev. Lett. 43 (1979) 668 [INSPIRE].

  187. W. Celmaster and R.J. Gonsalves, An analytic calculation of higher order quantum chromodynamic corrections in e + e − annihilation, Phys. Rev. Lett. 44 (1980) 560 [INSPIRE].

  188. A. Czarnecki and J.H. Kuhn, Non factorizable QCD and electroweak corrections to the hadronic Z boson decay rate, Phys. Rev. Lett. 77 (1996) 3955 [hep-ph/9608366] [INSPIRE].

  189. A. Djouadi, J. Kalinowski and M. Spira, HDECAY: a program for Higgs boson decays in the Standard Model and its supersymmetric extension, Comput. Phys. Commun. 108 (1998) 56 [hep-ph/9704448] [INSPIRE].

  190. A. Djouadi, J. Kalinowski, M. Muehlleitner and M. Spira, HDECAY: twenty++ years after, arXiv:1801.09506 [INSPIRE].

  191. T. Hahn, Generating Feynman diagrams and amplitudes with FeynArts 3, Comput. Phys. Commun. 140 (2001) 418 [hep-ph/0012260] [INSPIRE].

Download references

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

Author information

Authors and Affiliations

  1. Physik Department T31, Technische Universität München, James-Franck-Str. 1, D-85748, Garching, Germany

    R. Frederix & D. Pagani

  2. INFN, Sezione di Genova, Via Dodecaneso 33, I-16146, Genoa, Italy

    S. Frixione

  3. Institute for Theoretical Physics, ETH Zürich, Wolfgang-Pauli-strasse 27, 8093, Zürich, Switzerland

    V. Hirschi

  4. Laboratoire de Physique Théorique et Hautes Energies (LPTHE), UMR 7589, Sorbonne Université et CNRS, 4 place Jussieu, 75252, Paris Cedex 05, France

    H.-S. Shao

  5. Nikhef, Science Park 105, NL-1098 XG, Amsterdam, The Netherlands

    M. Zaro

Authors
  1. R. Frederix
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. Frixione
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. V. Hirschi
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. D. Pagani
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. H.-S. Shao
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. M. Zaro
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. Frixione.

Additional information

ArXiv ePrint: 1804.10017

Rights and permissions

Open Access  This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.

The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Frederix, R., Frixione, S., Hirschi, V. et al. The automation of next-to-leading order electroweak calculations. J. High Energ. Phys. 2018, 185 (2018). https://doi.org/10.1007/JHEP07(2018)185

Download citation

  • Received: 07 May 2018

  • Accepted: 21 July 2018

  • Published: 31 July 2018

  • DOI: https://doi.org/10.1007/JHEP07(2018)185

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

Keywords

  • NLO Computations
Use our pre-submission checklist

Avoid common mistakes on your manuscript.

Advertisement

Search

Navigation

  • Find a journal
  • Publish with us
  • Track your research

Discover content

  • Journals A-Z
  • Books A-Z

Publish with us

  • Journal finder
  • Publish your research
  • Open access publishing

Products and services

  • Our products
  • Librarians
  • Societies
  • Partners and advertisers

Our imprints

  • Springer
  • Nature Portfolio
  • BMC
  • Palgrave Macmillan
  • Apress
  • Your US state privacy rights
  • Accessibility statement
  • Terms and conditions
  • Privacy policy
  • Help and support
  • Cancel contracts here

Not affiliated

Springer Nature

© 2024 Springer Nature