Skip to main content
SpringerLink
Log in

Direct photon production with effective field theory

  • Published:
Journal of High Energy Physics Aims and scope Submit manuscript

The production of hard photons in hadronic collisions is studied using Soft-Collinear Effective Theory (SCET). This is the first application of SCET to a physical, observable cross section involving energetic partons in more than two directions. A factorization formula is derived which involves a non-trivial interplay of the angular dependence in the hard and soft functions, both quark and gluon jet functions, and multiple partonic channels. The relevant hard, jet and soft functions are computed to one loop and their anomalous dimensions are determined to three loops. The final resummed inclusive direct photon distribution is valid to next-to-next-to-leading logarithmic order (NNLL), one order beyond previous work. The result is improved by including non-logarithmic terms and photon isolation cuts through matching, and compared to Tevatron data and to fixed order results at the Tevatron and the LHC. The resummed cross section has a significantly smaller theoretical uncertainty than the next-to-leading fixed-order result, particularly at high transverse momentum.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. P. Aurenche, A. Douiri, R. Baier, M. Fontannaz and D. Schiff, Prompt Photon Production at Large p T in QCD Beyond the Leading Order, Phys. Lett. B 140 (1984) 87 [SPIRES].

    ADS  Google Scholar 

  2. P. Aurenche, R. Baier, M. Fontannaz and D. Schiff, Prompt Photon Production at Large p T Scheme Invariant QCD Predictions and Comparison with Experiment, Nucl. Phys. B 297 (1988) 661 [SPIRES].

    Article  ADS  Google Scholar 

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

    ADS  Google Scholar 

  4. S. Catani, M. Fontannaz, J.P. Guillet and E. Pilon, Cross-section of isolated prompt photons in hadron hadron collisions, JHEP 05 (2002) 028 [hep-ph/0204023] [SPIRES].

    Article  ADS  Google Scholar 

  5. E. Laenen, G. Oderda and G. Sterman, Resummation of threshold corrections for single particle inclusive cross-sections, Phys. Lett. B 438 (1998) 173 [hep-ph/9806467] [SPIRES].

    ADS  Google Scholar 

  6. D. Appell, G. Sterman and P.B. Mackenzie, Soft gluons and the normalization of the Drell-Yan cross-section, Nucl. Phys. B 309 (1988) 259 [SPIRES].

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  8. S. Catani, M.L. Mangano, P. Nason, C. Oleari and W. Vogelsang, Sudakov resummation effects in prompt photon hadroproduction, JHEP 03 (1999) 025 [hep-ph/9903436] [SPIRES].

    Article  ADS  Google Scholar 

  9. N. Kidonakis and J.F. Owens, Soft-gluon resummation and NNLO corrections for direct photon production, Phys. Rev. D 61 (2000) 094004 [hep-ph/9912388] [SPIRES].

    ADS  Google Scholar 

  10. N. Kidonakis and J.F. Owens, Next-to-next-to-leading-order soft-gluon corrections in direct photon production, Int. J. Mod. Phys. A 19 (2004) 149 [hep-ph/0307352] [SPIRES].

    ADS  Google Scholar 

  11. C.W. Bauer, S. Fleming, D. Pirjol and I.W. Stewart, An effective field theory for collinear and soft gluons: Heavy to light decays, Phys. Rev. D 63 (2001) 114020 [hep-ph/0011336] [SPIRES].

    ADS  Google Scholar 

  12. C.W. Bauer, D. Pirjol and I.W. Stewart, Soft-Collinear Factorization in Effective Field Theory, Phys. Rev. D 65 (2002) 054022 [hep-ph/0109045] [SPIRES].

    ADS  Google Scholar 

  13. M. Beneke, A.P. Chapovsky, M. Diehl and T. Feldmann, Soft-collinear effective theory and heavy-to-light currents beyond leading power, Nucl. Phys. B 643 (2002) 431 [hep-ph/0206152] [SPIRES].

    Article  ADS  Google Scholar 

  14. C.W. Bauer, S. Fleming, D. Pirjol, I.Z. Rothstein and I.W. Stewart, Hard scattering factorization from effective field theory, Phys. Rev. D 66 (2002) 014017 [hep-ph/0202088] [SPIRES].

    ADS  Google Scholar 

  15. A.V. Manohar, Deep inelastic scattering as x → 1 using soft-collinear effective theory, Phys. Rev. D 68 (2003) 114019 [hep-ph/0309176] [SPIRES].

    ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  17. T. Becher, M. Neubert and B.D. Pecjak, Factorization and momentum-space resummation in deep- inelastic scattering, JHEP 01 (2007) 076 [hep-ph/0607228] [SPIRES].

    Article  ADS  Google Scholar 

  18. P.-y. Chen, A. Idilbi and X.-d. Ji, QCD factorization for deep-inelastic scattering at large Bjorken x B ≈ 1 − O(Λ QCD /Q), Nucl. Phys. B 763 (2007) 183 [hep-ph/0607003] [SPIRES].

    Article  ADS  Google Scholar 

  19. A. Idilbi and X.-d. Ji, Threshold resummation for Drell-Yan process in soft- collinear effective theory, Phys. Rev. D 72 (2005) 054016 [hep-ph/0501006] [SPIRES].

    ADS  Google Scholar 

  20. T. Becher, M. Neubert and G. Xu, Dynamical Threshold Enhancement and Resummation in Drell-Yan Production, JHEP 07 (2008) 030 [arXiv:0710.0680] [SPIRES].

    Article  ADS  Google Scholar 

  21. A. Idilbi, X.-d. Ji, J.-P. Ma and F. Yuan, Threshold resummation for Higgs production in effective field theory, Phys. Rev. D 73 (2006) 077501 [hep-ph/0509294] [SPIRES].

    ADS  Google Scholar 

  22. V. Ahrens, T. Becher, M. Neubert and L.L. Yang, Origin of the Large Perturbative Corrections to Higgs Production at Hadron Colliders, Phys. Rev. D 79 (2009) 033013 [arXiv:0808.3008] [SPIRES].

    ADS  Google Scholar 

  23. V. Ahrens, T. Becher, M. Neubert and L.L. Yang, Renormalization-Group Improved Prediction for Higgs Production at Hadron Colliders, Eur. Phys. J. C 62 (2009) 333 [arXiv:0809.4283] [SPIRES].

    Article  ADS  Google Scholar 

  24. C. Lee and G. Sterman, Momentum flow correlations from event shapes: Factorized soft gluons and soft-collinear effective theory, Phys. Rev. D 75 (2007) 014022 [hep-ph/0611061] [SPIRES].

    ADS  Google Scholar 

  25. S. Fleming, A.H. Hoang, S. Mantry and I.W. Stewart, Jets from massive unstable particles: top-mass determination, Phys. Rev. D 77 (2008) 074010 [hep-ph/0703207] [SPIRES].

    ADS  Google Scholar 

  26. M.D. Schwartz, Resummation and NLO Matching of Event Shapes with Effective Field Theory, Phys. Rev. D 77 (2008) 014026 [arXiv:0709.2709] [SPIRES].

    ADS  Google Scholar 

  27. C.W. Bauer, S.P. Fleming, C. Lee and G. 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] [SPIRES].

    ADS  Google Scholar 

  28. T. Becher and M.D. Schwartz, A Precise determination of α s from LEP thrust data using effective field theory, JHEP 07 (2008) 034 [arXiv:0803.0342] [SPIRES].

    Article  ADS  Google Scholar 

  29. A. Hornig, C. Lee and G. Ovanesyan, Effective Predictions of Event Shapes: Factorized, Resummed and Gapped Angularity Distributions, JHEP 05 (2009) 122 [arXiv:0901.3780] [SPIRES].

    Article  ADS  Google Scholar 

  30. J.-y. Chiu, F. Golf, R. Kelley and A.V. Manohar, Electroweak Corrections in High Energy Processes using Effective Field Theory, Phys. Rev. D 77 (2008) 053004 [arXiv:0712.0396] [SPIRES].

    ADS  Google Scholar 

  31. J.-y. Chiu, R. Kelley and A.V. Manohar, Electroweak Corrections using Effective Field Theory: Applications to the LHC, Phys. Rev. D 78 (2008) 073006 [arXiv:0806.1240] [SPIRES].

    ADS  Google Scholar 

  32. 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] [SPIRES].

    Google Scholar 

  33. D.E. Kaplan and M.D. Schwartz, Constraining Light Colored Particles with Event Shapes, Phys. Rev. Lett. 101 (2008) 022002 [arXiv:0804.2477] [SPIRES].

    Article  ADS  Google Scholar 

  34. C.W. Bauer and M.D. Schwartz, Improving jet distributions with effective field theory, Phys. Rev. Lett. 97 (2006) 142001 [hep-ph/0604065] [SPIRES].

    Article  ADS  Google Scholar 

  35. C.W. Bauer, A. Hornig and F.J. Tackmann, Factorization for generic jet production, Phys. Rev. D 79 (2009) 114013 [arXiv:0808.2191] [SPIRES].

    ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  38. T. Becher and M. Neubert, Infrared singularities of QCD amplitudes with massive partons, Phys. Rev. D 79 (2009) 125004 [arXiv:0904.1021] [SPIRES].

    ADS  Google Scholar 

  39. R.J. Hill and M. Neubert, Spectator interactions in soft-collinear effective theory, Nucl. Phys. B 657 (2003) 229 [hep-ph/0211018] [SPIRES].

    Article  ADS  Google Scholar 

  40. S. Fleming and A.K. Leibovich, The resummed photon spectrum in radiative Υ decays, Phys. Rev. Lett. 90 (2003) 032001 [hep-ph/0211303] [SPIRES].

    Article  ADS  Google Scholar 

  41. S. Fleming and A.K. Leibovich, The photon spectrum in Υ decays, Phys. Rev. D 67 (2003) 074035 [hep-ph/0212094] [SPIRES].

    ADS  Google Scholar 

  42. S. Fleming, A.K. Leibovich and T. Mehen, Resumming the color octet contribution to e + e − → J/ψ + X, Phys. Rev. D 68 (2003) 094011 [hep-ph/0306139] [SPIRES].

    ADS  Google Scholar 

  43. P.B. Arnold and M.H. Reno, The Complete Computation of High p T W and Z Production in 2nd Order QCD, Nucl. Phys. B 319 (1989) 37 [Erratum ibid. B 330 (1990) 284] [SPIRES].

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    ADS  Google Scholar 

  47. G. Sterman and M.E. Tejeda-Yeomans, Multi-loop amplitudes and resummation, Phys. Lett. B 552 (2003) 48 [hep-ph/0210130] [SPIRES].

    ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  49. S.M. Aybat, L.J. Dixon and G. Sterman, The two-loop soft anomalous dimension matrix and resummation at next-to-next-to leading pole, Phys. Rev. D 74 (2006) 074004 [hep-ph/0607309] [SPIRES].

    ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  51. L.J. Dixon, E. Gardi and L. Magnea, On soft singularities at three loops and beyond, arXiv:0910.3653 [SPIRES].

  52. S. Catani and M.H. Seymour, The Dipole Formalism for the Calculation of QCD Jet Cross Sections at Next-to-Leading Order, Phys. Lett. B 378 (1996) 287 [hep-ph/9602277] [SPIRES].

    ADS  Google Scholar 

  53. S. Catani and M.H. Seymour, A general algorithm for calculating jet cross sections in NLO QCD, Nucl. Phys. B 485 (1997) 291 [Erratum ibid. B 510 (1998) 503] [hep-ph/9605323] [SPIRES].

    Article  ADS  Google Scholar 

  54. F. De Fazio and M. Neubert, B → X u l \( \overline v \) l decay distributions to order α s , JHEP 06 (1999) 017 [hep-ph/9905351] [SPIRES].

    Article  Google Scholar 

  55. T. Becher and M. Neubert, Toward a NNLO calculation of the \( \overline B \) → X s + γ decay rate with a cut on photon energy. II: Two-loop result for the jet function, Phys. Lett. B 637 (2006) 251 [hep-ph/0603140] [SPIRES].

    ADS  Google Scholar 

  56. C.W. Bauer, C.-W. Chiang, S. Fleming, A.K. Leibovich and I. Low, Resumming the color-octet contribution to radiative Υ decay, Phys. Rev. D 64 (2001) 114014 [hep-ph/0106316] [SPIRES].

    ADS  Google Scholar 

  57. C.W. Bauer and M.D. Schwartz, Event generation from effective field theory, Phys. Rev. D 76 (2007) 074004 [hep-ph/0607296] [SPIRES].

    ADS  Google Scholar 

  58. M. Beneke and V.M. Braun, Power corrections and renormalons in Drell-Yan production, Nucl. Phys. B 454 (1995) 253 [hep-ph/9506452] [SPIRES].

    Article  ADS  Google Scholar 

  59. S. Catani, M.L. Mangano, P. Nason and L. Trentadue, The Resummation of Soft Gluon in Hadronic Collisions, Nucl. Phys. B 478 (1996) 273 [hep-ph/9604351] [SPIRES].

    Article  ADS  Google Scholar 

  60. D0 collaboration, V.M. Abazov et al., Measurement of the isolated photon cross section in \( p\overline p \) collisions at √s = 1.96 TeV, Phys. Lett. B 639 (2006) 151 [Erratum ibid. B 658 (2008) 285] [hep-ex/0511054] [SPIRES].

    ADS  Google Scholar 

  61. C. Deluca Silberberg, Measurement of the inclusive isolated prompt photon production cross section at the Tevatron using the CDF detector, FERMILAB-THESIS-2009-18, Apr 2009.

  62. CDF collaboration, T. Aaltonen et al., Measurement of the Inclusive Isolated Prompt Photon Cross Section in ppbar Collisions at √s = 1.96 TeV using the CDF Detector, Phys. Rev. D 80 (2009) 111106 [arXiv:0910.3623] [SPIRES].

    Google Scholar 

  63. A.D. Martin, W.J. Stirling, R.S. Thorne and G. Watt, Parton distributions for the LHC, Eur. Phys. J. C 63 (2009) 189 [arXiv:0901.0002] [SPIRES].

    Article  Google Scholar 

  64. I.W. Stewart, F.J. Tackmann and W.J. Waalewijn, Factorization at the LHC: From PDFs to Initial State Jets, arXiv:0910.0467 [SPIRES].

  65. T. van Ritbergen, J.A.M. Vermaseren and S.A. Larin, The four-loop β-function in quantum chromodynamics, Phys. Lett. B 400 (1997) 379 [hep-ph/9701390] [SPIRES].

    ADS  Google Scholar 

  66. M. Czakon, The four-loop QCD β-function and anomalous dimensions, Nucl. Phys. B 710 (2005) 485 [hep-ph/0411261] [SPIRES].

    Article  ADS  Google Scholar 

  67. S. Moch, J.A.M. Vermaseren and A. Vogt, The three-loop splitting functions in QCD: The non-singlet case, Nucl. Phys. B 688 (2004) 101 [hep-ph/0403192] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  68. A. Vogt, S. Moch and J.A.M. Vermaseren, The three-loop splitting functions in QCD: The singlet case, Nucl. Phys. B 691 (2004) 129 [hep-ph/0404111] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute for Theoretical Physics, University of Bern, Sidlerstrasse 5, 3012, Bern, Switzerland

    Thomas Becher

  2. Department of Physics, Harvard University, Cambridge, MA, 02138, U.S.A.

    Matthew D. Schwartz

Authors
  1. Thomas Becher
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Matthew D. Schwartz
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Thomas Becher.

Additional information

ArXiv ePrint: 0911.0681

Rights and permissions

Reprints and permissions

About this article

Cite this article

Becher, T., Schwartz, M.D. Direct photon production with effective field theory. J. High Energ. Phys. 2010, 40 (2010). https://doi.org/10.1007/JHEP02(2010)040

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP02(2010)040

Keywords

Search

Navigation