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

Next-to-leading power threshold effects for inclusive and exclusive processes with final state jets

  • Regular Article - Theoretical Physics
  • Open access
  • Published: 18 March 2020
  • Volume 2020, article number 106, (2020)
  • Cite this article
Download PDF

You have full access to this open access article

Journal of High Energy Physics Aims and scope Submit manuscript
Next-to-leading power threshold effects for inclusive and exclusive processes with final state jets
Download PDF
  • Melissa van Beekveld1,2,
  • Wim Beenakker1,3,
  • Eric Laenen2,3,4 &
  • …
  • Chris D. White5 

  • 411 Accesses

  • 24 Citations

  • 1 Altmetric

  • Explore all metrics

A preprint version of the article is available at arXiv.

Abstract

It is well known that cross-sections in perturbative QCD receive large corrections from soft and collinear radiation, which can be resummed to all orders in the coupling. Whether or not the universal properties of this radiation can be extended to next-to-leading power (NLP) in the threshold expansion has been the subject of much recent study. In particular, universal forms for next-to-leading order (NLO) cross-sections have been obtained for general colour-singlet production processes by considering only the emission of gluons. In this paper, we extend such formulae to processes containing final state jets, and show that the dominant NLP terms at NLO can be obtained using a similar prescription to the colour-singlet case. We furthermore consider the emission of soft quarks, which also leads to a class of universal NLP contributions at NLO. We illustrate our results using three different processes at NLO: deep-inelastic scattering, hadroproduction via electron-positron annihilation and prompt photon production.

Article PDF

Download to read the full article text

Similar content being viewed by others

NNLO QCD corrections to jet production in deep inelastic scattering

Article Open access 05 July 2017

Isolated photon production in association with a jet pair through next-to-next-to-leading order in QCD

Article Open access 12 October 2023

Infrared sensitivity of single jet inclusive production at hadron colliders

Article Open access 25 October 2018
Use our pre-submission checklist

Avoid common mistakes on your manuscript.

References

  1. G. Parisi, Summing large perturbative corrections in QCD, Phys. Lett. 90B (1980) 295 [INSPIRE].

    Article  ADS  Google Scholar 

  2. G. Curci and M. Greco, Large infrared corrections in QCD processes, Phys. Lett. 92B (1980) 175 [INSPIRE].

    Article  ADS  Google Scholar 

  3. G.F. Sterman, Summation of large corrections to short distance hadronic cross-sections, Nucl. Phys. B 281 (1987) 310 [INSPIRE].

    Article  ADS  Google Scholar 

  4. S. Catani and L. Trentadue, Resummation of the QCD perturbative series for hard processes, Nucl. Phys. B 327 (1989) 323 [INSPIRE].

    Article  ADS  Google Scholar 

  5. S. Catani and L. Trentadue, Comment on QCD exponentiation at large x, Nucl. Phys. B 353 (1991) 183 [INSPIRE].

    Article  ADS  Google Scholar 

  6. J.G.M. Gatheral, Exponentiation of eikonal cross-sections in nonabelian gauge theories, Phys. Lett. 133B (1983) 90 [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  7. J. Frenkel and J.C. Taylor, Nonabelian eikonal exponentiation, Nucl. Phys. B 246 (1984) 231 [INSPIRE].

    Article  ADS  Google Scholar 

  8. G. Sterman, Infrared divergences in perturbative QCD. AIP Conf. Proc. 74 (1981) 22.

    Article  ADS  Google Scholar 

  9. G.P. Korchemsky and G. Marchesini, Structure function for large x and renormalization of Wilson loop, Nucl. Phys. B 406 (1993) 225 [hep-ph/9210281] [INSPIRE].

  10. G.P. Korchemsky and G. Marchesini, Resummation of large infrared corrections using Wilson loops, Phys. Lett. B 313 (1993) 433 [INSPIRE].

    Article  ADS  Google Scholar 

  11. S. Forte and G. Ridolfi, Renormalization group approach to soft gluon resummation, Nucl. Phys. B 650 (2003) 229 [hep-ph/0209154] [INSPIRE].

  12. H. Contopanagos, E. Laenen and G.F. Sterman, Sudakov factorization and resummation, Nucl. Phys. B 484 (1997) 303 [hep-ph/9604313] [INSPIRE].

  13. T. Becher and M. Neubert, Threshold resummation in momentum space from effective field theory, Phys. Rev. Lett. 97 (2006) 082001 [hep-ph/0605050] [INSPIRE].

  14. M.D. Schwartz, Resummation and NLO matching of event shapes with effective field theory, Phys. Rev. D 77 (2008) 014026 [arXiv:0709.2709] [INSPIRE].

  15. C.W. Bauer, S.P. Fleming, C. Lee and G.F. Sterman, Factorization of e+ e− event shape distributions with hadronic final states in soft collinear effective theory, Phys. Rev. D 78 (2008) 034027 [arXiv:0801.4569] [INSPIRE].

  16. J.-y. Chiu, A. Fuhrer, R. Kelley and A.V. Manohar, Factorization structure of gauge theory amplitudes and application to hard scattering processes at the LHC, Phys. Rev. D 80 (2009) 094013 [arXiv:0909.0012] [INSPIRE].

  17. M. Krämer, E. Laenen and M. Spira, Soft gluon radiation in Higgs boson production at the LHC, Nucl. Phys. B 511 (1998) 523 [hep-ph/9611272] [INSPIRE].

  18. F. Herzog and B. Mistlberger, The soft-virtual Higgs cross-section at N3 LO and the convergence of the threshold expansion, in Proceedings, 49th Rencontres de Moriond on QCD and High Energy Interactions: La Thuile, Italy, March 22–29, 2014, pp. 57–60, 2014, arXiv:1405.5685 [INSPIRE].

  19. I. Moult, L. Rothen, I.W. Stewart, F.J. Tackmann and H.X. Zhu, Subleading power corrections for N-jettiness subtractions, Phys. Rev. D 95 (2017) 074023 [arXiv:1612.00450] [INSPIRE].

  20. R. Boughezal, X. Liu and F. Petriello, Power corrections in the N-jettiness subtraction scheme, JHEP 03 (2017) 160 [arXiv:1612.02911] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  21. I. Moult, L. Rothen, I.W. Stewart, F.J. Tackmann and H.X. Zhu, N -jettiness subtractions for gg → H at subleading power, Phys. Rev. D 97 (2018) 014013 [arXiv:1710.03227] [INSPIRE].

  22. R. Boughezal, A. Isgrò and F. Petriello, Next-to-leading-logarithmic power corrections for N -jettiness subtraction in color-singlet production, Phys. Rev. D 97 (2018) 076006 [arXiv:1802.00456] [INSPIRE].

  23. M.A. Ebert, I. Moult, I.W. Stewart, F.J. Tackmann, G. Vita and H.X. Zhu, Power Corrections for N-Jettiness Subtractions at 𝒪(αs), JHEP 12 (2018) 084 [arXiv:1807.10764] [INSPIRE].

    Article  ADS  Google Scholar 

  24. M.A. Ebert, I. Moult, I.W. Stewart, F.J. Tackmann, G. Vita and H.X. Zhu, Subleading power rapidity divergences and power corrections for qT , JHEP 04 (2019) 123 [arXiv:1812.08189] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  25. F.E. Low, Bremsstrahlung of very low-energy quanta in elementary particle collisions, Phys. Rev. 110 (1958) 974 [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  26. T.H. Burnett and N.M. Kroll, Extension of the low soft photon theorem, Phys. Rev. Lett. 20 (1968) 86 [INSPIRE].

    Article  ADS  Google Scholar 

  27. V. Del Duca, High-energy bremsstrahlung theorems for soft photons, Nucl. Phys. B 345 (1990) 369 [INSPIRE].

    Article  ADS  Google Scholar 

  28. E. Laenen, G. Stavenga and C.D. White, Path integral approach to eikonal and next-to-eikonal exponentiation, JHEP 03 (2009) 054 [arXiv:0811.2067] [INSPIRE].

    Article  ADS  Google Scholar 

  29. E. Laenen, L. Magnea, G. Stavenga and C.D. White, Next-to-eikonal corrections to soft gluon radiation: a diagrammatic approach, JHEP 01 (2011) 141 [arXiv:1010.1860] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  30. G. Soar, S. Moch, J.A.M. Vermaseren and A. Vogt, On Higgs-exchange DIS, physical evolution kernels and fourth-order splitting functions at large x, Nucl. Phys. B 832 (2010) 152 [arXiv:0912.0369] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  31. S. Moch and A. Vogt, On non-singlet physical evolution kernels and large-x coefficient functions in perturbative QCD, JHEP 11 (2009) 099 [arXiv:0909.2124] [INSPIRE].

    Article  ADS  Google Scholar 

  32. S. Moch and A. Vogt, Threshold resummation of the structure function FL , JHEP 04 (2009) 081 [arXiv:0902.2342] [INSPIRE].

    Article  ADS  Google Scholar 

  33. D. de Florian, J. Mazzitelli, S. Moch and A. Vogt, Approximate N3 LO Higgs-boson production cross section using physical-kernel constraints, JHEP 10 (2014) 176 [arXiv:1408.6277] [INSPIRE].

    Article  ADS  Google Scholar 

  34. N.A. Lo Presti, A.A. Almasy and A. Vogt, Leading large-x logarithms of the quark & gluon contributions to inclusive Higgs-boson and lepton-pair production, Phys. Lett. B 737 (2014) 120 [arXiv:1407.1553] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  35. E. Laenen, L. Magnea and G. Stavenga, On next-to-eikonal corrections to threshold resummation for the Drell-Yan and DIS cross sections, Phys. Lett. B 669 (2008) 173 [arXiv:0807.4412] [INSPIRE].

    Article  ADS  Google Scholar 

  36. G. Grunberg, Threshold resummation to any order in (1-x), arXiv:0710.5693 [INSPIRE].

  37. G. Grunberg and V. Ravindran, On threshold resummation beyond leading 1-x order, JHEP 10 (2009) 055 [arXiv:0902.2702] [INSPIRE].

    Article  ADS  Google Scholar 

  38. G. Grunberg, Large-x structure of physical evolution kernels in Deep Inelastic Scattering, Phys. Lett. B 687 (2010) 405 [arXiv:0911.4471] [INSPIRE].

    Article  ADS  Google Scholar 

  39. F. Cachazo and A. Strominger, Evidence for a new soft graviton theorem, arXiv:1404.4091 [INSPIRE].

  40. E. Casali, Soft sub-leading divergences in Yang-Mills amplitudes, JHEP 08 (2014) 077 [arXiv:1404.5551] [INSPIRE].

    Article  ADS  Google Scholar 

  41. C.D. White, Factorization properties of soft graviton amplitudes, JHEP 05 (2011) 060 [arXiv:1103.2981] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  42. H. Gervais, Soft photon theorem for high energy amplitudes in Yukawa and scalar theories, Phys. Rev. D 95 (2017) 125009 [arXiv:1704.00806] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  43. H. Gervais, Soft graviton emission at high and low energies in Yukawa and scalar theories, Phys. Rev. D 96 (2017) 065007 [arXiv:1706.03453] [INSPIRE].

  44. H. Gervais, Soft radiation theorems at all loop order in quantum field theory, Ph.D. thesis, SUNY, Stony Brook, U.S.A. (4 August 2017).

  45. D. Bonocore, E. Laenen, L. Magnea, S. Melville, L. Vernazza and C.D. White, A factorization approach to next-to-leading-power threshold logarithms, JHEP 06 (2015) 008 [arXiv:1503.05156] [INSPIRE].

    Article  ADS  Google Scholar 

  46. D. Bonocore, E. Laenen, L. Magnea, L. Vernazza and C.D. White, Non-abelian factorisation for next-to-leading-power threshold logarithms, JHEP 12 (2016) 121 [arXiv:1610.06842] [INSPIRE].

    Article  ADS  Google Scholar 

  47. M. Beneke, F. Campanario, T. Mannel and B.D. Pecjak, Power corrections to \( \overline{B}\to {X}_ul\overline{v}\left({X}_s\gamma \right) \) decay spectra in the ‘shape-function’ region, JHEP 06 (2005) 071 [hep-ph/0411395] [INSPIRE].

  48. A.J. Larkoski, D. Neill and I.W. Stewart, Soft theorems from effective field theory, JHEP 06 (2015) 077 [arXiv:1412.3108] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  49. D.W. Kolodrubetz, I. Moult and I.W. Stewart, Building blocks for subleading helicity operators, JHEP 05 (2016) 139 [arXiv:1601.02607] [INSPIRE].

    Article  ADS  Google Scholar 

  50. I. Moult, I.W. Stewart and G. Vita, A subleading operator basis and matching for gg → H, JHEP 07 (2017) 067 [arXiv:1703.03408] [INSPIRE].

    Article  ADS  Google Scholar 

  51. I. Feige, D.W. Kolodrubetz, I. Moult and I.W. Stewart, A complete basis of helicity operators for subleading factorization, JHEP 11 (2017) 142 [arXiv:1703.03411] [INSPIRE].

    Article  ADS  Google Scholar 

  52. C.-H. Chang, I.W. Stewart and G. Vita, A subleading power operator basis for the scalar quark current, JHEP 04 (2018) 041 [arXiv:1712.04343] [INSPIRE].

    Article  ADS  Google Scholar 

  53. M. Beneke, M. Garny, R. Szafron and J. Wang, Anomalous dimension of subleading-power N-jet operators, JHEP 03 (2018) 001 [arXiv:1712.04416] [INSPIRE].

    Article  ADS  Google Scholar 

  54. R. Goerke and M. Luke, Power Counting and Modes in SCET, JHEP 02 (2018) 147 [arXiv:1711.09136] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  55. R. Goerke and M. Inglis-Whalen, Renormalization of dijet operators at order 1/Q2 in soft-collinear effective theory, JHEP 05 (2018) 023 [arXiv:1711.09147] [INSPIRE].

    Article  ADS  Google Scholar 

  56. M. Beneke, M. Garny, R. Szafron and J. Wang, Anomalous dimension of subleading-power N -jet operators. Part II, JHEP 11 (2018) 112 [arXiv:1808.04742] [INSPIRE].

  57. M. Beneke, A. Broggio, M. Garny, S. Jaskiewicz, R. Szafron, L. Vernazza et al., Leading-logarithmic threshold resummation of the Drell-Yan process at next-to-leading power, JHEP 03 (2019) 043 [arXiv:1809.10631] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  58. I. Moult, I.W. Stewart, G. Vita and H.X. Zhu, First Subleading Power Resummation for Event Shapes, JHEP 08 (2018) 013 [arXiv:1804.04665] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  59. N. Bahjat-Abbas, D. Bonocore, J. Sinninghe Damsté, E. Laenen, L. Magnea, L. Vernazza et al., Diagrammatic resummation of leading-logarithmic threshold effects at next-to-leading power, JHEP 11 (2019) 002 [arXiv:1905.13710] [INSPIRE].

    Article  ADS  Google Scholar 

  60. V. Del Duca, E. Laenen, L. Magnea, L. Vernazza and C.D. White, Universality of next-to-leading power threshold effects for colourless final states in hadronic collisions, JHEP 11 (2017) 057 [arXiv:1706.04018] [INSPIRE].

    Article  ADS  Google Scholar 

  61. D. Bonocore, E. Laenen, L. Magnea, L. Vernazza and C.D. White, The method of regions and next-to-soft corrections in Drell-Yan production, Phys. Lett. B 742 (2015) 375 [arXiv:1410.6406] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  62. N. Bahjat-Abbas, J. Sinninghe Damsté, L. Vernazza and C.D. White, On next-to-leading power threshold corrections in Drell-Yan production at N3 LO, JHEP 10 (2018) 144 [arXiv:1807.09246] [INSPIRE].

    Article  ADS  Google Scholar 

  63. S. Alte, M. König and M. Neubert, Effective Field Theory after a New-Physics Discovery, JHEP 08 (2018) 095 [arXiv:1806.01278] [INSPIRE].

    Article  ADS  Google Scholar 

  64. M. Beneke and V.A. Smirnov, Asymptotic expansion of Feynman integrals near threshold, Nucl. Phys. B 522 (1998) 321 [hep-ph/9711391] [INSPIRE].

  65. C.D. White, Diagrammatic insights into next-to-soft corrections, Phys. Lett. B 737 (2014) 216 [arXiv:1406.7184] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  66. Z. Bern, S. Davies, P. Di Vecchia and J. Nohle, Low-energy behavior of gluons and gravitons from gauge invariance, Phys. Rev. D 90 (2014) 084035 [arXiv:1406.6987] [INSPIRE].

  67. J. Broedel, M. de Leeuw, J. Plefka and M. Rosso, Constraining subleading soft gluon and graviton theorems, Phys. Rev. D 90 (2014) 065024 [arXiv:1406.6574] [INSPIRE].

  68. S. Weinberg, Infrared photons and gravitons, Phys. Rev. 140 (1965) B516 [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  69. E.B. Zijlstra and W.L. van Neerven, Second order QCD corrections to deep inelastic scattering, Nucl. Phys. Proc. Suppl. B 29 (1992) 131.

    Article  ADS  Google Scholar 

  70. E.B. Zijlstra and W.L. van Neerven, Order \( {\alpha}_s^2 \) QCD corrections to the deep inelastic proton structure functions F2 and FL , Nucl. Phys. B 383 (1992) 525 [INSPIRE].

    Article  ADS  Google Scholar 

  71. P.J. Rijken and W.L. van Neerven, Higher order QCD corrections to the transverse and longitudinal fragmentation functions in electron-positron annihilation, Nucl. Phys. B 487 (1997) 233 [hep-ph/9609377] [INSPIRE].

  72. L.E. Gordon and W. Vogelsang, Polarized and unpolarized prompt photon production beyond the leading order, Phys. Rev. D 48 (1993) 3136 [INSPIRE].

    ADS  Google Scholar 

  73. S. Catani, M.L. Mangano and P. Nason, Sudakov resummation for prompt photon production in hadron collisions, JHEP 07 (1998) 024 [hep-ph/9806484] [INSPIRE].

  74. A. Bhattacharya, I. Moult, I.W. Stewart and G. Vita, Helicity Methods for High Multiplicity Subleading Soft and Collinear Limits, JHEP 05 (2019) 192 [arXiv:1812.06950] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  75. I. Moult, I.W. Stewart and G. Vita, Subleading Power Factorization with Radiative Functions, JHEP 11 (2019) 153 [arXiv:1905.07411] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

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. Theoretical High Energy Physics, Radboud University, Nijmegen, Heyendaalseweg 135, 6525, AJ, Nijmegen, The Netherlands

    Melissa van Beekveld & Wim Beenakker

  2. Nikhef, Science Park 105, 1098, XG, Amsterdam, The Netherlands

    Melissa van Beekveld & Eric Laenen

  3. Institute of Physics, University of Amsterdam, Science Park 904, 1018, XE, Amsterdam, The Netherlands

    Wim Beenakker & Eric Laenen

  4. ITF, Utrecht University, Leuvenlaan 4, 3584, CE, Utrecht, The Netherlands

    Eric Laenen

  5. Centre for Research in String Theory, School of Physics and Astronomy, Queen Mary University of London, 327 Mile End Road, London, E1 4NS, UK

    Chris D. White

Authors
  1. Melissa van Beekveld
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Wim Beenakker
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Eric Laenen
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Chris D. White
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Melissa van Beekveld.

Additional information

ArXiv ePrint: 1905.08741

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

van Beekveld, M., Beenakker, W., Laenen, E. et al. Next-to-leading power threshold effects for inclusive and exclusive processes with final state jets. J. High Energ. Phys. 2020, 106 (2020). https://doi.org/10.1007/JHEP03(2020)106

Download citation

  • Received: 05 June 2019

  • Revised: 22 January 2020

  • Accepted: 10 February 2020

  • Published: 18 March 2020

  • DOI: https://doi.org/10.1007/JHEP03(2020)106

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

  • Resummation
  • Perturbative QCD
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