Skip to main content

n-Jet Processes and IR Divergences of Gauge Theory Amplitudes

  • Chapter
  • First Online:
Introduction to Soft-Collinear Effective Theory

Part of the book series: Lecture Notes in Physics ((LNP,volume 896))

  • 1105 Accesses

Abstract

So far, we have only considered processes which involve large energy flows in two directions, such as the Sudakov form factor or the inclusive Drell-Yan cross section. However, many processes involve multiple directions of large energy flow. These include collider processes with several jets of energetic particles in the final state. In this section, we will discuss the effective theory relevant for observables which involve n directions of large energy flow.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 49.99
Price excludes VAT (USA)
  • Compact, lightweight 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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. T. Becher, M. Neubert, Infrared singularities of scattering amplitudes in perturbative QCD. Phys. Rev. Lett. 102, 162001 (2009). [arXiv:0901.0722]

    ADS  Google Scholar 

  2. T. Becher, M. Neubert, On the structure of infrared singularities of gauge-theory amplitudes. JHEP 06, 081 (2009). [arXiv:0903.1126]

    ADS  MathSciNet  Google Scholar 

  3. V. Ahrens, M. Neubert, L. Vernazza, Structure of infrared singularities of Gauge-theory amplitudes at three and four loops. JHEP 1209, 138 (2012). [arXiv:1208.4847]

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  5. L.J. Dixon, E. Gardi, L. Magnea, On soft singularities at three loops and beyond. JHEP 02, 081 (2010). [arXiv:0910.3653]

    ADS  MathSciNet  Google Scholar 

  6. V. Del Duca, C. Duhr, E. Gardi, L. Magnea, C.D. White, The Infrared structure of gauge theory amplitudes in the high-energy limit. JHEP 1112, 021 (2011). [arXiv:1109.3581]

    ADS  Google Scholar 

  7. V. Del Duca, C. Duhr, E. Gardi, L. Magnea, C.D. White, Infrared singularities and the high-energy limit. PoS RADCOR2011, 038 (2011). [arXiv:1201.2841]

  8. T. Becher, M. Neubert, Infrared singularities of QCD amplitudes with massive partons. Phys. Rev. D79, 125004 (2009). [arXiv:0904.1021] (Erratum-ibid.D80:109901, 2009)

  9. A. Bassetto, M. Ciafaloni, G. Marchesini, Jet structure and infrared sensitive quantities in perturbative QCD. Phys. Rep. 100, 201–272 (1983)

    ADS  Google Scholar 

  10. S. Catani, M.H. Seymour, The dipole formalism for the calculation of QCD jet cross sections at next-to-leading order. Phys. Lett. B378, 287–301 (1996). [hep-ph/9602277]

  11. A. Sen, Asymptotic behavior of the wide angle on-shell quark scattering amplitudes in nonabelian gauge theories. Phys. Rev. D28, 860 (1983)

    ADS  Google Scholar 

  12. N. Kidonakis, G. Oderda, G.F. Sterman, Evolution of color exchange in QCD hard scattering. Nucl. Phys. B531, 365–402 (1998). [hep-ph/9803241]

  13. S.M. Aybat, L.J. Dixon, G.F. Sterman, The two-loop anomalous dimension matrix for soft gluon exchange. Phys. Rev. Lett. 97, 072001 (2006). [hep-ph/0606254]

  14. S.M. Aybat, L.J. Dixon, G.F. Sterman, The two-loop soft anomalous dimension matrix and resummation at next-to-next-to leading pole. Phys. Rev. D74, 074004 (2006). [hep-ph/0607309]

  15. S. Moch, J.A.M. Vermaseren, A. Vogt, Three-loop results for quark and gluon form factors. Phys. Lett. B625, 245–252 (2005). [hep-ph/0508055]

  16. L.W. Garland, T. Gehrmann, E.W.N. Glover, A. Koukoutsakis, E. Remiddi, The two-loop QCD matrix element for \(e^{+}e^{-}\rightarrow 3\) jets. Nucl. Phys. B627, 107–188 (2002). [hep-ph/0112081]

  17. L.W. Garland, T. Gehrmann, E.W.N. Glover, A. Koukoutsakis, E. Remiddi, Two-loop QCD helicity amplitudes for \(e^{+}e^{-}\rightarrow 3\) jets. Nucl. Phys. B642, 227–262 (2002). [hep-ph/0206067]

  18. C. Anastasiou, E.N. Glover, C. Oleari, M. Tejeda-Yeomans, Two-loop QCD corrections to the scattering of massless distinct quarks. Nucl. Phys. B601, 318–340 (2001). [hep-ph/0010212]

  19. C. Anastasiou, E.N. Glover, C. Oleari, M. Tejeda-Yeomans, Two loop QCD corrections to massless identical quark scattering. Nucl. Phys. B601, 341–360 (2001). [hep-ph/0011094]

  20. C. Anastasiou, E.N. Glover, C. Oleari, M. Tejeda-Yeomans, Two loop QCD corrections to massless quark gluon scattering. Nucl. Phys. B605, 486–516 (2001). [hep-ph/0101304]

  21. Z. Bern, A. De Freitas, L.J. Dixon, Two loop helicity amplitudes for gluon-gluon scattering in QCD and supersymmetric Yang-Mills theory. JHEP 0203, 018 (2002). [hep-ph/0201161]

  22. Z. Bern, A. De Freitas, L.J. Dixon, Two loop helicity amplitudes for quark gluon scattering in QCD and gluino gluon scattering in supersymmetric Yang-Mills theory. JHEP 0306, 028 (2003). [hep-ph/0304168]

  23. Z. Bern, L.J. Dixon, V.A. Smirnov, Iteration of planar amplitudes in maximally supersymmetric Yang-Mills theory at three loops and beyond. Phys. Rev. D72, 085001 (2005). [hep-th/0505205]

    ADS  MathSciNet  Google Scholar 

  24. S. Caron-Huot, When does the gluon reggeize? [arXiv:1309.6521]

  25. J.G.M. Gatheral, Exponentiation of the Eikonal cross-sections in nonabelian gauge theories. Phys. Lett. B133, 90 (1983)

    ADS  MathSciNet  Google Scholar 

  26. J. Frenkel, J.C. Taylor, Nonabelian Eikonal exponentiation. Nucl. Phys. B246, 231 (1984)

    ADS  Google Scholar 

  27. A. Mitov, G. Sterman, I. Sung, Diagrammatic exponentiation for products of Wilson lines. Phys. Rev. D82, 096010 (2010). [arXiv:1008.0099]

    ADS  Google Scholar 

  28. E. Gardi, E. Laenen, G. Stavenga, C.D. White, Webs in multiparton scattering using the replica trick. JHEP 1011, 155 (2010). [arXiv:1008.0098]

    ADS  Google Scholar 

  29. E. Gardi, C.D. White, General properties of multiparton webs: proofs from combinatorics. JHEP 1103, 079 (2011). [arXiv:1102.0756]

    ADS  MathSciNet  Google Scholar 

  30. E. Gardi, J.M. Smillie, C.D. White, On the renormalization of multiparton webs. JHEP 1109, 114 (2011). [arXiv:1108.1357]

    ADS  Google Scholar 

  31. F.A. Berends, W.T. Giele, Recursive calculations for processes with n gluons. Nucl. Phys. B306, 759 (1988)

    ADS  Google Scholar 

  32. M.L. Mangano, S.J. Parke, Multi-Parton Amplitudes in gauge theories. Phys. Rep. 200, 301–367 (1991). [hep-th/0509223]

    ADS  Google Scholar 

  33. Z. Bern, G. Chalmers, Factorization in one loop gauge theory. Nucl. Phys. B447, 465–518 (1995). [hep-ph/9503236]

  34. D.A. Kosower, All-order collinear behavior in gauge theories. Nucl. Phys. B552, 319–336 (1999). [hep-ph/9901201]

  35. S. Catani, D. de Florian, G. Rodrigo, The triple collinear limit of one-loop QCD amplitudes. Phys. Lett. B586, 323–331 (2004). [hep-ph/0312067]

  36. V. Del Duca, C. Duhr, E. Gardi, L. Magnea, C.D. White, An infrared approach to reggeization. Phys. Rev. D85, 071104 (2012). [arXiv:1108.5947]

    ADS  Google Scholar 

  37. I. Balitsky, L. Lipatov, V.S. Fadin, Regge processes in non-abelian gauge theories (in russian), in Proceedings of Physics of Elementary Particles, Leningrad 1979, 1979, pp. 109–149

    Google Scholar 

  38. V. Fadin, R. Fiore, M. Kozlov, A. Reznichenko, Proof of the multi-Regge form of QCD amplitudes with gluon exchanges in the NLA. Phys. Lett. B639, 74–81 (2006). [hep-ph/0602006]

  39. A. Bogdan, V. Fadin, A proof of the reggeized form of amplitudes with quark exchanges. Nucl. Phys. B740, 36–57 (2006). [hep-ph/0601117]

  40. V. Del Duca, E.N. Glover, The high-energy limit of QCD at two loops. JHEP 0110, 035 (2001). [hep-ph/0109028]

  41. Z. Bern, J.J.M. Carrasco, L.J. Dixon, H. Johansson, R. Roiban, Manifest ultraviolet behavior for the three-loop four- point amplitude of N = 8 supergravity. Phys. Rev. D78, 105019 (2008) [arXiv:0808.4112]

    ADS  Google Scholar 

  42. S. Moch, J.A.M. Vermaseren, A. Vogt, The three-loop splitting functions in QCD: The non-singlet case. Nucl. Phys. B688, 101–134 (2004). [hep-ph/0403192]

  43. A. Armoni, Anomalous dimensions from a spinning D5−brane. JHEP 11, 009 (2006). [hep-th/0608026]

    ADS  MathSciNet  Google Scholar 

  44. L.F. Alday, J.M. Maldacena, Gluon scattering amplitudes at strong coupling. JHEP 06, 064 (2007). [arXiv:0705.0303]

    ADS  MathSciNet  Google Scholar 

  45. L.F. Alday, J.M. Maldacena, Comments on operators with large spin. JHEP 11, 019 (2007). [arXiv:0708.0672]

    ADS  MathSciNet  Google Scholar 

  46. A. Grozin, J.M. Henn, G.P. Korchemsky, P. Marquard, The three-loop cusp anomalous dimension in QCD. [arXiv:1409.0023]

  47. T. van Ritbergen, A. Schellekens, J. Vermaseren, Group theory factors for Feynman diagrams. Int. J. Mod. Phys. A14, 41–96 (1999). [hep-ph/9802376]

  48. S. Badger, E.N. Glover, Two loop splitting functions in QCD. JHEP 0407, 040 (2004). [hep-ph/0405236]

  49. I. Feige, M.D. Schwartz, Hard-soft-collinear factorization to all orders. [arXiv:1403.6472]

  50. D.R. Yennie, S.C. Frautschi, H. Suura, The infrared divergence phenomena and high-energy processes. Ann. Phys. 13, 379–452 (1961)

    ADS  Google Scholar 

  51. S. Weinberg, Infrared photons and gravitons. Phys. Rev. 140, B516–B524 (1965)

    ADS  MathSciNet  Google Scholar 

  52. M. Neubert, Heavy quark symmetry. Phys. Rep. 245, 259–396 (1994). [hep-ph/9306320]

  53. A. Mitov, G.F. Sterman, I. Sung, The massive soft anomalous dimension matrix at two loops. Phys. Rev. D79, 094015 (2009). [arXiv:0903.3241]

    ADS  Google Scholar 

  54. A. Ferroglia, M. Neubert, B.D. Pecjak, L.L. Yang, Two-loop divergences of scattering amplitudes with massive partons. Phys. Rev. Lett. 103, 201601 (2009). [arXiv:0907.4791]

    ADS  Google Scholar 

  55. A. Ferroglia, M. Neubert, B.D. Pecjak, L.L. Yang, Two-loop divergences of massive scattering amplitudes in non-abelian gauge theories. JHEP 11, 062 (2009). [arXiv:0908.3676]

    ADS  Google Scholar 

  56. A. Mitov, S. Moch, The singular behavior of massive QCD amplitudes. JHEP 05, 001 (2007). [hep-ph/0612149]

  57. T. Becher, K. Melnikov, Two-loop QED corrections to Bhabha scattering. JHEP 06, 084 (2007). [arXiv:0704.3582]

    ADS  Google Scholar 

  58. V. Ahrens, A. Ferroglia, M. Neubert, B.D. Pecjak, L.L. Yang, Threshold expansion at order α s 4 for the t-tbar invariant mass distribution at hadron colliders. Phys. Lett. B687, 331–337 (2010). [arXiv:0912.3375]

    ADS  Google Scholar 

  59. V. Ahrens, A. Ferroglia, M. Neubert, B.D. Pecjak, L.L. Yang, Renormalization-group improved predictions for top-quark pair production at hadron colliders. JHEP 09, 097 (2010). [arXiv:1003.5827]

    ADS  Google Scholar 

  60. V. Ahrens, A. Ferroglia, M. Neubert, B.D. Pecjak, L.-L. Yang, RG-improved single-particle inclusive cross sections and forward-backward asymmetry in \(t\bar{t}\) production at hadron colliders. JHEP 09, 070 (2011). [arXiv:1103.0550]

    ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Becher, T., Broggio, A., Ferroglia, A. (2015). n-Jet Processes and IR Divergences of Gauge Theory Amplitudes. In: Introduction to Soft-Collinear Effective Theory. Lecture Notes in Physics, vol 896. Springer, Cham. https://doi.org/10.1007/978-3-319-14848-9_8

Download citation

Publish with us

Policies and ethics