Skip to main content

Calculating Four-Loop Corrections in QCD

  • Chapter
  • First Online:
Anti-Differentiation and the Calculation of Feynman Amplitudes

Part of the book series: Texts & Monographs in Symbolic Computation ((TEXTSMONOGR))

  • 709 Accesses

Abstract

We review the current status of perturbative corrections in QCD at four loops for scattering processes with space- and time-like kinematics at colliders, with specific focus on deep-inelastic scattering and electron-positron annihilation. The calculations build on the parametric reduction of loop and phase space integrals up to four-loop order using computer algebra programs such as Form, designed for large scale computations.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 139.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 179.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 179.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. S. Moch, J.A.M. Vermaseren, A. Vogt, Nucl. Phys. B 688, 101 (2004). arXiv:hep-ph/0403192

    Article  Google Scholar 

  2. A. Vogt, S. Moch, J.A.M. Vermaseren, Nucl. Phys. B 691, 129 (2004). arXiv:hep-ph/0404111

    Article  Google Scholar 

  3. A. Mitov, S. Moch, A. Vogt, Phys. Lett. B 638, 61 (2006). arXiv:hep-ph/0604053

    Article  Google Scholar 

  4. S. Moch, A. Vogt, Phys. Lett. B 659, 290 (2008). arXiv:0709.3899

    Article  Google Scholar 

  5. A.A. Almasy, S. Moch, A. Vogt, Nucl. Phys. B 854, 133 (2012). arXiv:1107.2263

    Article  Google Scholar 

  6. H. Chen, T.-Z. Yang, H.X. Zhu, Y.J. Zhu, Chin. Phys. C 45, 043101 (2021). arXiv:2006.10534

    Article  Google Scholar 

  7. W.L. van Neerven, E.B. Zijlstra, Phys. Lett. B 272, 127 (1991)

    Article  Google Scholar 

  8. E.B. Zijlstra, W.L. van Neerven, Phys. Lett. B 273, 476 (1991)

    Article  Google Scholar 

  9. E.B. Zijlstra, W.L. van Neerven, Nucl. Phys. B 383, 525 (1992)

    Article  Google Scholar 

  10. S. Moch, J.A.M. Vermaseren, Nucl. Phys. B 573, 853 (2000). arXiv:hep-ph/9912355

    Article  Google Scholar 

  11. P.J. Rijken, W.L. van Neerven, Phys. Lett. B 386, 422 (1996). arXiv:hep-ph/9604436

    Article  Google Scholar 

  12. P.J. Rijken, W.L. van Neerven, Nucl. Phys. B 487, 233 (1997). arXiv:hep-ph/9609377

    Article  Google Scholar 

  13. P.J. Rijken, W.L. van Neerven, Phys. Lett. B 392, 207 (1997). arXiv:hep-ph/9609379

    Article  Google Scholar 

  14. A. Mitov, S.-O. Moch, Nucl. Phys. B 751, 18 (2006). arXiv:hep-ph/0604160

    Article  Google Scholar 

  15. A. Accardi et al., Eur. Phys. J. C 76, 471 (2016). arXiv:1603.08906

    Article  Google Scholar 

  16. D. Boer et al., (2011). arXiv:1108.1713

    Google Scholar 

  17. A. Accardi et al., Eur. Phys. J. A 52, 268 (2016). arXiv:1212.1701

    Article  Google Scholar 

  18. A. Blondel et al., Standard model theory for the FCC-ee Tera-Z stage, in Mini Workshop on Precision EW and QCD Calculations for the FCC Studies : Methods and Techniques, CERN Yellow Reports: Monographs Vol. 3/2019, Geneva, 2018, CERN. arXiv:1809.01830

    Google Scholar 

  19. T. van Ritbergen, J.A.M. Vermaseren, S.A. Larin, Phys. Lett. B 400, 379 (1997). arXiv:hep-ph/9701390

    Google Scholar 

  20. M. Czakon, Nucl. Phys. B 710, 485 (2005). arXiv:hep-ph/0411261

    Article  Google Scholar 

  21. P.A. Baikov, K.G. Chetyrkin, J.H. Kühn, Phys. Rev. Lett. 118, 082002 (2017). arXiv:1606.08659

    Article  Google Scholar 

  22. F. Herzog, B. Ruijl, T. Ueda, J.A.M. Vermaseren, A. Vogt, JHEP 02, 090 (2017). arXiv:1701.01404

    Article  Google Scholar 

  23. T. Luthe, A. Maier, P. Marquard, Y. Schroder, JHEP 10, 166 (2017). arXiv:1709.07718

    Article  Google Scholar 

  24. J.A.M. Vermaseren, A. Vogt, S. Moch, Nucl. Phys. B 724, 3 (2005). arXiv:hep-ph/0504242

    Article  Google Scholar 

  25. S. Moch, J.A.M. Vermaseren, A. Vogt, Nucl. Phys. B 813, 220 (2009). arXiv:0812.4168

    Article  Google Scholar 

  26. B. Ruijl, T. Ueda, J.A.M. Vermaseren, J. Davies, A. Vogt, PoS LL2016, 071 (2016). arXiv:1605.08408

    Google Scholar 

  27. G. Das, S.-O. Moch, A. Vogt, JHEP 03, 116 (2020). arXiv:1912.12920

    Article  Google Scholar 

  28. S. Moch, B. Ruijl, T. Ueda, J.A.M. Vermaseren, A. Vogt, JHEP 10, 041 (2017). arXiv:1707.08315

    Article  Google Scholar 

  29. S. Moch, B. Ruijl, T. Ueda, J.A.M. Vermaseren, A. Vogt, Phys. Lett. B 782, 627 (2018). arXiv:1805.09638

    Article  Google Scholar 

  30. J. Davies, A. Vogt, B. Ruijl, T. Ueda, J.A.M. Vermaseren, Nucl. Phys. B 915, 335 (2017). arXiv:1610.07477

    Article  Google Scholar 

  31. F. Herzog et al., Phys. Lett. B 790, 436 (2019). arXiv:1812.11818

    Article  Google Scholar 

  32. A.J. Buras, Rev. Mod. Phys. 52, 199 (1980)

    Article  Google Scholar 

  33. P. Nogueira, J. Comput. Phys. 105, 279 (1993)

    Article  MathSciNet  Google Scholar 

  34. T. van Ritbergen, A.N. Schellekens, J.A.M. Vermaseren, Int. J. Mod. Phys. A 14, 41 (1999). arXiv:hep-ph/9802376

    Google Scholar 

  35. G. ’t Hooft, M.J.G. Veltman, Nucl. Phys. B 44, 189 (1972)

    Google Scholar 

  36. C.G. Bollini, J.J. Giambiagi, Nuovo Cim. B 12, 20 (1972)

    Article  Google Scholar 

  37. F.V. Tkachov, Phys. Lett. B 100, 65 (1981)

    Article  MathSciNet  Google Scholar 

  38. K.G. Chetyrkin, F.V. Tkachov, Nucl. Phys. B 192, 159 (1981)

    Article  Google Scholar 

  39. B. Ruijl, T. Ueda, J.A.M. Vermaseren, Comput. Phys. Commun. 253, 107198 (2020). arXiv:1704.06650

    Article  MathSciNet  Google Scholar 

  40. V. Magerya, A. Pikelner, JHEP 12, 026 (2019). arXiv:1910.07522

    Article  Google Scholar 

  41. P.A. Baikov, K.G. Chetyrkin, Nucl. Phys. B 837, 186 (2010). arXiv:1004.1153

    Article  Google Scholar 

  42. R.N. Lee, A.V. Smirnov, V.A. Smirnov, Nucl. Phys. B 856, 95 (2012). arXiv:1108.0732

    Article  Google Scholar 

  43. J.A.M. Vermaseren, (2000). arXiv:math-ph/0010025

    Google Scholar 

  44. J. Kuipers, T. Ueda, J.A.M. Vermaseren, J. Vollinga, Comput. Phys. Commun. 184, 1453 (2013). arXiv:1203.6543

    Article  Google Scholar 

  45. B. Ruijl, T. Ueda, J. Vermaseren, (2017). arXiv:1707.06453

    Google Scholar 

  46. M. Tentyukov, J.A.M. Vermaseren, Comput. Phys. Commun. 181, 1419 (2010). arXiv:hep-ph/0702279

    Article  Google Scholar 

  47. V.N. Velizhanin, Nucl. Phys. B 864, 113 (2012). arXiv:1203.1022

    Article  Google Scholar 

  48. J.A.M. Vermaseren, Int. J. Mod. Phys. A 14, 2037 (1999). arXiv:hep-ph/9806280

    Article  MathSciNet  Google Scholar 

  49. J. Blümlein, S. Kurth, Phys. Rev. D 60, 014018 (1999). arXiv:hep-ph/9810241

    Article  Google Scholar 

  50. A.K. Lenstra, H.W. Lenstra, L. Lovász, Mathematische Annalen 261, 515 (1982)

    Article  MathSciNet  Google Scholar 

  51. K. Matthews, (unpublished), summarized in [52]; see pp. 16/17

  52. J.H. Silverman, Des. Codes Cryptography 20, 5 (2000)

    Article  MathSciNet  Google Scholar 

  53. http://www.numbertheory.org/calc/krm_calc.html

  54. F. Herzog, B. Ruijl, JHEP 05, 037 (2017). arXiv:1703.03776

    Article  Google Scholar 

  55. K.G. Chetyrkin, F.V. Tkachov, Phys. Lett. B 114, 340 (1982)

    Article  Google Scholar 

  56. K.G. Chetyrkin, V.A. Smirnov, Phys. Lett. B 144, 419 (1984)

    Article  Google Scholar 

  57. K.G. Chetyrkin, (2017). arXiv:1701.08627

    Google Scholar 

  58. P. Nason, B.R. Webber, Nucl. Phys. B 421, 473 (1994) [Erratum: Nucl. Phys.B 480, 755 (1996)]

    Google Scholar 

  59. A. Gehrmann-De Ridder, T. Gehrmann, G. Heinrich, Nucl. Phys. B 682, 265 (2004). arXiv:hep-ph/0311276

    Article  Google Scholar 

  60. C. Anastasiou, K. Melnikov, Nucl. Phys. B 646, 220 (2002). arXiv:hep-ph/0207004

    Article  Google Scholar 

  61. O. Gituliar, V. Magerya, A. Pikelner, JHEP 06, 099 (2018). arXiv:1803.09084

    Article  Google Scholar 

  62. G. Heinrich, T. Huber, D. Maitre, Phys. Lett. B 662, 344 (2008). arXiv:0711.3590

    Article  Google Scholar 

  63. G. Heinrich, T. Huber, D.A. Kosower, V.A. Smirnov, Phys. Lett. B 678, 359 (2009). arXiv:0902.3512

    Article  Google Scholar 

  64. R.N. Lee, A.V. Smirnov, V.A. Smirnov, JHEP 04, 020 (2010). arXiv:1001.2887

    Article  Google Scholar 

  65. O.V. Tarasov, Phys. Rev. D 54, 6479 (1996). arXiv:hep-th/9606018

    Article  MathSciNet  Google Scholar 

  66. O.V. Tarasov, Nucl. Phys. B Proc. Suppl. 89, 237 (2000). arXiv:hep-ph/0102271

    Article  Google Scholar 

  67. R.N. Lee, Nucl. Phys. B 830, 474 (2010). arXiv:0911.0252

    Article  Google Scholar 

  68. R.N. Lee, K.T. Mingulov, (2017). arXiv:1712.05173

    Google Scholar 

  69. J. Blümlein, D.J. Broadhurst, J.A.M. Vermaseren, Comput. Phys. Commun. 181, 582 (2010). arXiv:0907.2557

    Article  Google Scholar 

  70. H.R.P. Ferguson, D.H. Bailey, S. Arno, Math. Comput. 68, 351 (1999)

    Article  Google Scholar 

  71. R.E. Cutkosky, J. Math. Phys. 1, 429 (1960)

    Article  Google Scholar 

  72. G. ’t Hooft, M.J.G. Veltman, NATO Sci. Ser. B 4, 177 (1974)

    Google Scholar 

  73. O. Gituliar, JHEP 02, 017 (2016). arXiv:1512.02045

    Article  Google Scholar 

  74. O. Gituliar, S. Moch, Acta Phys. Polon. B 46, 1279 (2015). arXiv:1505.02901

    Article  MathSciNet  Google Scholar 

  75. V. Magerya, (2021). PhD thesis (Universität Hamburg)

    Google Scholar 

  76. A.V. Kotikov, Phys. Lett. B 254, 158 (1991)

    Article  MathSciNet  Google Scholar 

  77. A.V. Kotikov, Phys. Lett. B 267, 123 (1991) [Erratum: Phys. Lett. B 295, 409–409 (1992)]

    Google Scholar 

  78. J.M. Henn, Phys. Rev. Lett. 110, 251601 (2013). arXiv:1304.1806

    Article  Google Scholar 

  79. R.N. Lee, JHEP 04, 108 (2015). arXiv:1411.0911

    Article  Google Scholar 

  80. R.N. Lee, A.A. Pomeransky, (2017). arXiv:1707.07856

    Google Scholar 

  81. O. Gituliar, V. Magerya, Comput. Phys. Commun. 219, 329 (2017). arXiv:1701.04269

    Article  MathSciNet  Google Scholar 

  82. O. Gituliar, V. Magerya, PoS LL2016, 030 (2016). arXiv:1607.00759

    Google Scholar 

  83. https://github.com/magv/fuchsia.cpp

Download references

Acknowledgements

S.M. is support by Deutsche Forschungsgemeinschaft (DFG) through the Research Unit FOR 2926, “Next Generation pQCD for Hadron Structure: Preparing for the EIC”, project MO 1801/5-1.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Sven-Olaf Moch .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2021 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Moch, SO., Magerya, V. (2021). Calculating Four-Loop Corrections in QCD. In: Blümlein, J., Schneider, C. (eds) Anti-Differentiation and the Calculation of Feynman Amplitudes. Texts & Monographs in Symbolic Computation. Springer, Cham. https://doi.org/10.1007/978-3-030-80219-6_14

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-80219-6_14

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-80218-9

  • Online ISBN: 978-3-030-80219-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics