Skip to main content
SpringerLink
Account
Menu
Find a journal Publish with us
Search
Cart
  1. Home
  2. Journal of High Energy Physics
  3. Article

Leading-color two-loop amplitudes for four partons and a W boson in QCD

  • Regular Article - Theoretical Physics
  • Open access
  • Published: 07 April 2022
  • volume 2022, Article number: 42 (2022)
Download PDF

You have full access to this open access article

Journal of High Energy Physics Aims and scope Submit manuscript
Leading-color two-loop amplitudes for four partons and a W boson in QCD
Download PDF
  • S. Abreu  ORCID: orcid.org/0000-0002-5966-20121,2,3,
  • F. Febres Cordero  ORCID: orcid.org/0000-0002-1389-49504,
  • H. Ita  ORCID: orcid.org/0000-0002-7821-002X5,
  • M. Klinkert5,
  • B. Page1 &
  • …
  • V. Sotnikov  ORCID: orcid.org/0000-0002-7406-21386,7 

  • 234 Accesses

  • 20 Citations

  • 1 Altmetric

  • Explore all metrics

Cite this article

A preprint version of the article is available at arXiv.

Abstract

We present the leading-color two-loop QCD corrections for the scattering of four partons and a W boson, including its leptonic decay. The amplitudes are assembled from the planar two-loop helicity amplitudes for four partons and a vector boson decaying to a lepton pair, which are also used to determine the planar two-loop amplitudes for four partons and a Z/γ∗ boson with a leptonic decay. The analytic expressions are obtained by setting up a dedicated Ansatz and constraining the free parameters from numerical samples obtained within the framework of numerical unitarity. The large linear systems that must be solved to determine the analytic expressions are constructed to be in Vandermonde form. Such systems can be very efficiently solved, bypassing the bottleneck of Gaussian elimination. Our results are expressed in a basis of one-mass pentagon functions, which opens the possibility of their efficient numerical evaluation.

Article PDF

Download to read the full article text

Similar content being viewed by others

Planar two-loop five-parton amplitudes from numerical unitarity

Article Open access 20 November 2018

S. Abreu, F. Febres Cordero, … V. Sotnikov

Leading-color two-loop QCD corrections for three-photon production at hadron colliders

Article Open access 14 January 2021

S. Abreu, B. Page, … V. Sotnikov

Analytic form of the planar two-loop five-parton scattering amplitudes in QCD

Article Open access 16 May 2019

S. Abreu, J. Dormans, … V. Sotnikov

Use our pre-submission checklist

Avoid common mistakes on your manuscript.

References

  1. ATLAS collaboration, Measurements of the W production cross sections in association with jets with the ATLAS detector, Eur. Phys. J. C 75 (2015) 82 [arXiv:1409.8639] [INSPIRE].

  2. CMS collaboration, Measurement of the differential cross sections for the associated production of a W boson and jets in proton-proton collisions at \( \sqrt{s} \) = 13 TeV, Phys. Rev. D 96 (2017) 072005 [arXiv:1707.05979] [INSPIRE].

  3. J. M. Campbell, R. K. Ellis and D. L. Rainwater, Next-to-leading order QCD predictions for W + 2 jet and Z + 2 jet production at the CERN LHC, Phys. Rev. D 68 (2003) 094021 [hep-ph/0308195] [INSPIRE].

    ADS  Google Scholar 

  4. C. F. Berger et al., Next-to-leading order QCD predictions for W + 3-jet distributions at hadron colliders, Phys. Rev. D 80 (2009) 074036 [arXiv:0907.1984] [INSPIRE].

    ADS  Google Scholar 

  5. F. R. Anger, F. Febres Cordero, S. Höche and D. Maître, Weak vector boson production with many jets at the LHC \( \sqrt{s} \) = 13 TeV, Phys. Rev. D 97 (2018) 096010 [arXiv:1712.08621] [INSPIRE].

    ADS  Google Scholar 

  6. 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].

    ADS  Google Scholar 

  7. A. Tricoli, M. Schönherr and P. Azzurri, Vector bosons and jets in proton collisions, Rev. Mod. Phys. 93 (2021) 025007 [arXiv:2012.13967] [INSPIRE].

    ADS  Google Scholar 

  8. L. Di Giustino, S. J. Brodsky, S.-Q. Wang and X.-G. Wu, Infinite-order scale-setting using the principle of maximum conformality: a remarkably efficient method for eliminating renormalization scale ambiguities for perturbative QCD, Phys. Rev. D 102 (2020) 014015 [arXiv:2002.01789] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  9. M. Bonvini, Probabilistic definition of the perturbative theoretical uncertainty from missing higher orders, Eur. Phys. J. C 80 (2020) 989 [arXiv:2006.16293] [INSPIRE].

    ADS  Google Scholar 

  10. C. Duhr, A. Huss, A. Mazeliauskas and R. Szafron, An analysis of Bayesian estimates for missing higher orders in perturbative calculations, JHEP 09 (2021) 122 [arXiv:2106.04585] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  11. Z. Bern, L. J. Dixon and D. A. Kosower, One loop amplitudes for e+ e− to four partons, Nucl. Phys. B 513 (1998) 3 [hep-ph/9708239] [INSPIRE].

    ADS  Google Scholar 

  12. Z. Bern, L. J. Dixon, D. A. Kosower and S. Weinzierl, One loop amplitudes for e+ e− → \( \overline{q}q\overline{Q}Q \), Nucl. Phys. B 489 (1997) 3 [hep-ph/9610370] [INSPIRE].

    ADS  Google Scholar 

  13. E. W. N. Glover and D. J. Miller, The one loop QCD corrections for γ∗ → \( Q\overline{Q}q\overline{q} \), Phys. Lett. B 396 (1997) 257 [hep-ph/9609474] [INSPIRE].

    ADS  Google Scholar 

  14. J. M. Campbell, E. W. N. Glover and D. J. Miller, The one loop QCD corrections for γ∗ → \( q\overline{q} gg \), Phys. Lett. B 409 (1997) 503 [hep-ph/9706297] [INSPIRE].

    ADS  Google Scholar 

  15. H. B. Hartanto, S. Badger, C. Brønnum-Hansen and T. Peraro, A numerical evaluation of planar two-loop helicity amplitudes for a W -boson plus four partons, JHEP 09 (2019) 119 [arXiv:1906.11862] [INSPIRE].

    ADS  MATH  Google Scholar 

  16. S. Badger, H. B. Hartanto and S. Zoia, Two-loop QCD corrections to \( Wb\overline{b} \) production at hadron colliders, Phys. Rev. Lett. 127 (2021) 012001 [arXiv:2102.02516] [INSPIRE].

    ADS  Google Scholar 

  17. S. Badger, H. B. Hartanto, J. Kryś and S. Zoia, Two-loop leading-colour QCD helicity amplitudes for Higgs boson production in association with a bottom-quark pair at the LHC, JHEP 11 (2021) 012 [arXiv:2107.14733] [INSPIRE].

    ADS  Google Scholar 

  18. K. G. Chetyrkin and F. V. Tkachov, Integration by parts: the algorithm to calculate β-functions in 4 loops, Nucl. Phys. B 192 (1981) 159 [INSPIRE].

    ADS  Google Scholar 

  19. S. Laporta, High precision calculation of multiloop Feynman integrals by difference equations, Int. J. Mod. Phys. A 15 (2000) 5087 [hep-ph/0102033] [INSPIRE].

    ADS  MathSciNet  MATH  Google Scholar 

  20. J. Gluza, K. Kajda and D. A. Kosower, Towards a basis for planar two-loop integrals, Phys. Rev. D 83 (2011) 045012 [arXiv:1009.0472] [INSPIRE].

    ADS  Google Scholar 

  21. K. J. Larsen and Y. Zhang, Integration-by-parts reductions from unitarity cuts and algebraic geometry, Phys. Rev. D 93 (2016) 041701 [arXiv:1511.01071] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  22. H. Ita, Two-loop integrand decomposition into master integrals and surface terms, Phys. Rev. D 94 (2016) 116015 [arXiv:1510.05626] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  23. A. von Manteuffel and R. M. Schabinger, A novel approach to integration by parts reduction, Phys. Lett. B 744 (2015) 101 [arXiv:1406.4513] [INSPIRE].

    ADS  MathSciNet  MATH  Google Scholar 

  24. T. Peraro, Scattering amplitudes over finite fields and multivariate functional reconstruction, JHEP 12 (2016) 030 [arXiv:1608.01902] [INSPIRE].

    ADS  MathSciNet  MATH  Google Scholar 

  25. J. Klappert and F. Lange, Reconstructing rational functions with FireFly, Comput. Phys. Commun. 247 (2020) 106951 [arXiv:1904.00009] [INSPIRE].

    Google Scholar 

  26. J. Klappert, S. Y. Klein and F. Lange, Interpolation of dense and sparse rational functions and other improvements in FireFly, Comput. Phys. Commun. 264 (2021) 107968 [arXiv:2004.01463] [INSPIRE].

    MathSciNet  Google Scholar 

  27. T. Peraro, FiniteFlow: multivariate functional reconstruction using finite fields and dataflow graphs, JHEP 07 (2019) 031 [arXiv:1905.08019] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  28. S. Abreu, F. Febres Cordero, H. Ita, M. Jaquier, B. Page and M. Zeng, Two-loop four-gluon amplitudes from numerical unitarity, Phys. Rev. Lett. 119 (2017) 142001 [arXiv:1703.05273] [INSPIRE].

    ADS  Google Scholar 

  29. S. Abreu, F. Febres Cordero, H. Ita, B. Page and M. Zeng, Planar two-loop five-gluon amplitudes from numerical unitarity, Phys. Rev. D 97 (2018) 116014 [arXiv:1712.03946] [INSPIRE].

    ADS  Google Scholar 

  30. S. Abreu, J. Dormans, F. Febres Cordero, H. Ita and B. Page, Analytic form of planar two-loop five-gluon scattering amplitudes in QCD, Phys. Rev. Lett. 122 (2019) 082002 [arXiv:1812.04586] [INSPIRE].

    ADS  MATH  Google Scholar 

  31. A. V. Kotikov, Differential equations method: new technique for massive Feynman diagrams calculation, Phys. Lett. B 254 (1991) 158 [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  32. E. Remiddi, Differential equations for Feynman graph amplitudes, Nuovo Cim. A 110 (1997) 1435 [hep-th/9711188] [INSPIRE].

    ADS  Google Scholar 

  33. J. M. Henn, Multiloop integrals in dimensional regularization made simple, Phys. Rev. Lett. 110 (2013) 251601 [arXiv:1304.1806] [INSPIRE].

    ADS  Google Scholar 

  34. S. Abreu, B. Page and M. Zeng, Differential equations from unitarity cuts: nonplanar hexa-box integrals, JHEP 01 (2019) 006 [arXiv:1807.11522] [INSPIRE].

    ADS  MathSciNet  MATH  Google Scholar 

  35. C. G. Papadopoulos, D. Tommasini and C. Wever, The pentabox master integrals with the simplified differential equations approach, JHEP 04 (2016) 078 [arXiv:1511.09404] [INSPIRE].

    ADS  Google Scholar 

  36. S. Abreu, H. Ita, F. Moriello, B. Page, W. Tschernow and M. Zeng, Two-loop integrals for planar five-point one-mass processes, JHEP 11 (2020) 117 [arXiv:2005.04195] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  37. D. D. Canko, C. G. Papadopoulos and N. Syrrakos, Analytic representation of all planar two-loop five-point master integrals with one off-shell leg, JHEP 01 (2021) 199 [arXiv:2009.13917] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  38. S. Abreu, H. Ita, B. Page and W. Tschernow, Two-loop hexa-box integrals for non-planar five-point one-mass processes, arXiv:2107.14180 [INSPIRE].

  39. C. G. Papadopoulos and C. Wever, Internal reduction method for computing Feynman integrals, JHEP 02 (2020) 112 [arXiv:1910.06275] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  40. D. Chicherin, V. Sotnikov and S. Zoia, Pentagon functions for one-mass planar scattering amplitudes, JHEP 01 (2022) 096 [arXiv:2110.10111] [INSPIRE].

    ADS  MathSciNet  MATH  Google Scholar 

  41. F. Moriello, Generalised power series expansions for the elliptic planar families of Higgs + jet production at two loops, JHEP 01 (2020) 150 [arXiv:1907.13234] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  42. M. Hidding, DiffExp, a Mathematica package for computing Feynman integrals in terms of one-dimensional series expansions, Comput. Phys. Commun. 269 (2021) 108125 [arXiv:2006.05510] [INSPIRE].

    MathSciNet  Google Scholar 

  43. T. Gehrmann, J. M. Henn and N. A. Lo Presti, Pentagon functions for massless planar scattering amplitudes, JHEP 10 (2018) 103 [arXiv:1807.09812] [INSPIRE].

    ADS  MATH  Google Scholar 

  44. D. Chicherin and V. Sotnikov, Pentagon functions for scattering of five massless particles, JHEP 12 (2020) 167 [arXiv:2009.07803] [INSPIRE].

    ADS  MathSciNet  MATH  Google Scholar 

  45. S. Abreu et al., Caravel: a C++ framework for the computation of multi-loop amplitudes with numerical unitarity, Comput. Phys. Commun. 267 (2021) 108069 [arXiv:2009.11957] [INSPIRE].

    MathSciNet  Google Scholar 

  46. S. Catani, The singular behavior of QCD amplitudes at two loop order, Phys. Lett. B 427 (1998) 161 [hep-ph/9802439] [INSPIRE].

    ADS  Google Scholar 

  47. T. Becher and M. Neubert, Infrared singularities of scattering amplitudes in perturbative QCD, Phys. Rev. Lett. 102 (2009) 162001 [Erratum ibid. 111 (2013) 199905] [arXiv:0901.0722] [INSPIRE].

  48. E. Gardi and L. Magnea, Factorization constraints for soft anomalous dimensions in QCD scattering amplitudes, JHEP 03 (2009) 079 [arXiv:0901.1091] [INSPIRE].

    ADS  Google Scholar 

  49. Ancillary files associated to the article webpage, http://www.hep.fsu.edu/∼ffebres/W4partons.

  50. S. Abreu, F. Febres Cordero, H. Ita, B. Page and V. Sotnikov, Planar two-loop five-parton amplitudes from numerical unitarity, JHEP 11 (2018) 116 [arXiv:1809.09067] [INSPIRE].

    ADS  MathSciNet  MATH  Google Scholar 

  51. A. Broggio, C. Gnendiger, A. Signer, D. Stöckinger and A. Visconti, SCET approach to regularization-scheme dependence of QCD amplitudes, JHEP 01 (2016) 078 [arXiv:1506.05301] [INSPIRE].

    ADS  Google Scholar 

  52. S. Weinzierl, Does one need the O(ϵ)- and O(ϵ2)-terms of one-loop amplitudes in an NNLO calculation?, Phys. Rev. D 84 (2011) 074007 [arXiv:1107.5131] [INSPIRE].

    ADS  Google Scholar 

  53. R. M. Schabinger, A new algorithm for the generation of unitarity-compatible integration by parts relations, JHEP 01 (2012) 077 [arXiv:1111.4220] [INSPIRE].

    ADS  MathSciNet  MATH  Google Scholar 

  54. M. Klinkert, Two-loop five-point amplitudes for vector-bosons and partons in QCD, Ph.D. thesis, to appear (2021).

  55. A. Ochirov and B. Page, Full colour for loop amplitudes in Yang-Mills theory, JHEP 02 (2017) 100 [arXiv:1612.04366] [INSPIRE].

    ADS  MathSciNet  MATH  Google Scholar 

  56. A. Ochirov and B. Page, Multi-quark colour decompositions from unitarity, JHEP 10 (2019) 058 [arXiv:1908.02695] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  57. F. R. Anger and V. Sotnikov, On the dimensional regularization of QCD helicity amplitudes with quarks, arXiv:1803.11127 [INSPIRE].

  58. S. Abreu, J. Dormans, F. Febres Cordero, H. Ita, B. Page and V. Sotnikov, Analytic form of the planar two-loop five-parton scattering amplitudes in QCD, JHEP 05 (2019) 084 [arXiv:1904.00945] [INSPIRE].

    ADS  MathSciNet  MATH  Google Scholar 

  59. V. Sotnikov, Scattering amplitudes with the multi-loop numerical unitarity method, Ph.D. thesis, Freiburg U., Freiburg, Germany (2019).

  60. F. A. Berends and W. T. Giele, Recursive calculations for processes with n gluons, Nucl. Phys. B 306 (1988) 759 [INSPIRE].

    ADS  Google Scholar 

  61. A. Hodges, Eliminating spurious poles from gauge-theoretic amplitudes, JHEP 05 (2013) 135 [arXiv:0905.1473] [INSPIRE].

    ADS  MathSciNet  MATH  Google Scholar 

  62. A. B. Goncharov, M. Spradlin, C. Vergu and A. Volovich, Classical polylogarithms for amplitudes and Wilson loops, Phys. Rev. Lett. 105 (2010) 151605 [arXiv:1006.5703] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  63. C. Duhr, H. Gangl and J. R. Rhodes, From polygons and symbols to polylogarithmic functions, JHEP 10 (2012) 075 [arXiv:1110.0458] [INSPIRE].

    ADS  MathSciNet  MATH  Google Scholar 

  64. C. Duhr, Hopf algebras, coproducts and symbols: an application to Higgs boson amplitudes, JHEP 08 (2012) 043 [arXiv:1203.0454] [INSPIRE].

    ADS  MathSciNet  MATH  Google Scholar 

  65. M. Heller and A. von Manteuffel, MultivariateApart: generalized partial fractions, Comput. Phys. Commun. 271 (2022) 108174 [arXiv:2101.08283] [INSPIRE].

    MathSciNet  Google Scholar 

  66. C. Gnendiger et al., To d, or not to d: recent developments and comparisons of regularization schemes, Eur. Phys. J. C 77 (2017) 471 [arXiv:1705.01827] [INSPIRE].

    ADS  Google Scholar 

  67. K. Risager, A direct proof of the CSW rules, JHEP 12 (2005) 003 [hep-th/0508206] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  68. H. Elvang, D. Z. Freedman and M. Kiermaier, Proof of the MHV vertex expansion for all tree amplitudes in N = 4 SYM theory, JHEP 06 (2009) 068 [arXiv:0811.3624] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  69. B. Page, Sagex mathematica and maple schools: lectures on finite fields and large ansätze, https://indico.desy.de/event/28075/, January 2021.

  70. R. K. Ellis, W. T. Giele and Z. Kunszt, A numerical unitarity formalism for evaluating one-loop amplitudes, JHEP 03 (2008) 003 [arXiv:0708.2398] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  71. G. H. Hardy et al., An introduction to the theory of numbers, Oxford University Press, Oxford, U.K. (1979).

  72. W. H. Press, S. A. Teukolsky, W. T. Vetterling and B. P. Flannery, Numerical recipes: the art of scientific computing, third edition, Cambridge University Press, Cambridge, U.K. (2007).

  73. S. Abreu, L. J. Dixon, E. Herrmann, B. Page and M. Zeng, The two-loop five-point amplitude in N = 4 super-Yang-Mills theory, Phys. Rev. Lett. 122 (2019) 121603 [arXiv:1812.08941] [INSPIRE].

    ADS  Google Scholar 

  74. S. Abreu, L. J. Dixon, E. Herrmann, B. Page and M. Zeng, The two-loop five-point amplitude in N = 8 supergravity, JHEP 03 (2019) 123 [arXiv:1901.08563] [INSPIRE].

    ADS  MathSciNet  MATH  Google Scholar 

  75. M. Ben-Or and P. Tiwari, A deterministic algorithm for sparse multivariate polynomial interpolation, in Proceedings of the twentieth annual ACM symposium on theory of computing, (1988), p. 301.

  76. D. Chicherin, J. M. Henn and G. Papathanasiou, Cluster algebras for Feynman integrals, Phys. Rev. Lett. 126 (2021) 091603 [arXiv:2012.12285] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  77. A. V. Smirnov, Algorithm FIRE — Feynman Integral REduction, JHEP 10 (2008) 107 [arXiv:0807.3243] [INSPIRE].

    ADS  MATH  Google Scholar 

  78. A. V. Smirnov, FIRE5: a C++ implementation of Feynman Integral REduction, Comput. Phys. Commun. 189 (2015) 182 [arXiv:1408.2372] [INSPIRE].

    ADS  MATH  Google Scholar 

  79. C. F. Berger et al., An automated implementation of on-shell methods for one-loop amplitudes, Phys. Rev. D 78 (2008) 036003 [arXiv:0803.4180] [INSPIRE].

    ADS  Google Scholar 

  80. S. A. Larin, The renormalization of the axial anomaly in dimensional regularization, Phys. Lett. B 303 (1993) 113 [hep-ph/9302240] [INSPIRE].

    ADS  Google Scholar 

  81. S. Abreu, F. Febres Cordero, H. Ita, B. Page and V. Sotnikov, Leading-color two-loop QCD corrections for three-jet production at hadron colliders, JHEP 07 (2021) 095 [arXiv:2102.13609] [INSPIRE].

    ADS  Google Scholar 

  82. M. Czakon, A. Mitov and R. Poncelet, Next-to-next-to-leading order study of three-jet production at the LHC, Phys. Rev. Lett. 127 (2021) 152001 [arXiv:2106.05331] [INSPIRE].

    ADS  Google Scholar 

  83. D. Kreimer, The γ5 problem and anomalies: a Clifford algebra approach, Phys. Lett. B 237 (1990) 59 [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  84. J. G. Korner, D. Kreimer and K. Schilcher, A practicable γ5 scheme in dimensional regularization, Z. Phys. C 54 (1992) 503 [INSPIRE].

    ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Theoretical Physics Department, CERN, 1211, Geneva 23, Switzerland

    S. Abreu & B. Page

  2. Higgs Centre for Theoretical Physics, School of Physics and Astronomy, The University of Edinburgh, James Clerk Maxwell Building, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, Scotland, U.K.

    S. Abreu

  3. Mani L. Bhaumik Institute for Theoretical Physics, Department of Physics and Astronomy, UCLA, 430 Portola Plaza, Los Angeles, CA, 90095, USA

    S. Abreu

  4. Physics Department, Florida State University, 77 Chieftan Way, Tallahassee, FL, 32306, USA

    F. Febres Cordero

  5. Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, Hermann-Herder-Straße 3, D-79104, Freiburg, Germany

    H. Ita & M. Klinkert

  6. Max Planck Institute for Physics (Werner Heisenberg Institute), Föhringer Ring 6, D-80805, Munich, Germany

    V. Sotnikov

  7. Physik-Institut, University of Zurich, Winterthurerstrasse 190, 8057, Zurich, Switzerland

    V. Sotnikov

Authors
  1. S. Abreu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. F. Febres Cordero
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. H. Ita
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. M. Klinkert
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. B. Page
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. V. Sotnikov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. Sotnikov.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

ArXiv ePrint: 2110.07541

Rights and permissions

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.

Reprints and Permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Abreu, S., Cordero, F.F., Ita, H. et al. Leading-color two-loop amplitudes for four partons and a W boson in QCD. J. High Energ. Phys. 2022, 42 (2022). https://doi.org/10.1007/JHEP04(2022)042

Download citation

  • Received: 05 January 2022

  • Revised: 12 March 2022

  • Accepted: 15 March 2022

  • Published: 07 April 2022

  • DOI: https://doi.org/10.1007/JHEP04(2022)042

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

  • Higher-Order Perturbative Calculations
  • Scattering Amplitudes
  • Electroweak Precision Physics
Use our pre-submission checklist

Avoid common mistakes on your manuscript.

Advertisement

search

Navigation

  • Find a journal
  • Publish with us

Discover content

  • Journals A-Z
  • Books A-Z

Publish with us

  • 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

Not affiliated

Springer Nature

© 2023 Springer Nature