Skip to main content
Log in

Towards W \( b\overline b \) + j at NLO with an automatized approach to one-loop computations

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

Abstract

We present results for the Os) virtual corrections to qgW \( b\overline b {q^{\prime }} \) obtained with a new automatized approach to the evaluation of one-loop amplitudes in terms of Feynman diagrams. Together with the Os) corrections to \( q{\overline q^{\prime }} \)W \( b\overline b g \), which can be obtained from our results by crossing symmetry, this represents the bulk of the next-to-leading order virtual QCD corrections to W \( b\overline b \) + j and W b + j hadronic production, calculated in a fixed-flavor scheme with four light flavors. Furthermore, these corrections represent a well defined and independent subset of the 1-loop amplitudes needed for the NNLO calculation of W \( b\overline b \). Our approach was tested against several existing results for NLO amplitudes including selected Os) one-loop corrections to W + 3 j hadronic production. We discuss the efficiency of our method both with respect to evaluation time and numerical stability.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. CDF collaboration, T. Aaltonen et al., First measurement of the b-jet cross section in events with a W boson in \( p\overline p \) collisions at \( \sqrt {s} = 1.96\;TeV \), Phys. Rev. Lett. 104 (2010) 131801 [arXiv:0909.1505] [INSPIRE].

    Article  ADS  Google Scholar 

  2. D0 collaboration, V. Abazov et al., A search for W \( b\overline b \) and W H production in \( p\overline p \) collisions at \( \sqrt {s} = 1.96\;TeV \), Phys. Rev. Lett. 94 (2005) 091802 [hep-ex/0410062] [INSPIRE].

    Article  ADS  Google Scholar 

  3. ATLAS collaboration, G. Aad et al., Measurement of the cross section for the production of a W boson in association with b-jets in pp collisions at \( \sqrt {s} = 7\;TeV \) with the ATLAS detector, Phys. Lett. B 707 (2012) 418 [arXiv:1109.1470] [INSPIRE].

    Article  ADS  Google Scholar 

  4. J.M. Campbell, R.K. Ellis, F. Maltoni and S. Willenbrock, Production of a W boson and two jets with one b quark tag, Phys. Rev. D 75 (2007) 054015 [hep-ph/0611348] [INSPIRE].

    ADS  Google Scholar 

  5. 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].

    Article  ADS  Google Scholar 

  6. 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].

    Article  ADS  Google Scholar 

  7. R.K. Ellis and S. Veseli, Strong radiative corrections to W \( b\overline b \) production in pp collisions, Phys. Rev. D 60 (1999) 011501 [hep-ph/9810489] [INSPIRE].

    ADS  Google Scholar 

  8. J.M. Campbell and R.K. Ellis, Next-to-leading order corrections to W + 2 jet and Z + 2 jet production at hadron colliders, Phys. Rev. D 65 (2002) 113007 [hep-ph/0202176] [INSPIRE].

    ADS  Google Scholar 

  9. 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 

  10. F. Febres Cordero, L. Reina and D. Wackeroth, NLO QCD corrections to W boson production with a massive b-quark jet pair at the Tevatron pp collider, Phys. Rev. D 74 (2006) 034007 [hep-ph/0606102] [INSPIRE].

    ADS  Google Scholar 

  11. F. Febres Cordero, Next-to-leading-order corrections to weak boson production with a massive quark jet pair at hadron colliders, arXiv:0809.3829 [INSPIRE].

  12. F. Febres Cordero, L. Reina and D. Wackeroth, W- and Z-boson production with a massive bottom-quark pair at the Large Hadron Collider, Phys. Rev. D 80 (2009) 034015 [arXiv:0906.1923] [INSPIRE].

    ADS  Google Scholar 

  13. S. Badger, J.M. Campbell and R. Ellis, QCD corrections to the hadronic production of a heavy quark pair and a W -boson including decay correlations, JHEP 03 (2011) 027 [arXiv:1011.6647] [INSPIRE].

    Article  ADS  Google Scholar 

  14. J.M. Campbell et al., Associated production of a W boson and one b jet, Phys. Rev. D 79 (2009) 034023 [arXiv:0809.3003] [INSPIRE].

    ADS  Google Scholar 

  15. F. Febres Cordero, L. Reina and D. Wackeroth, Associated production of a W or Z boson with bottom quarks at the Tevatron and the LHC, PoS(RADCOR2009)055 [arXiv:1001.3362] [INSPIRE].

  16. J. Campbell, F. Caola, F. Febres Cordero, L. Reina and D. Wackeroth, NLO QCD predictions for W + 1 jet and W + 2 jet production with at least one b jet at the 7 TeV LHC, Phys. Rev. D 86 (2012) 034021 [arXiv:1107.3714] [INSPIRE].

    ADS  Google Scholar 

  17. C. Oleari and L. Reina, W \( b\overline b \) production in POWHEG, JHEP 08 (2011) 061 [Erratum ibid. 1111 (2011)040] [arXiv:1105.4488] [INSPIRE].

    Article  ADS  Google Scholar 

  18. R. Frederix et al., W and Z/γ∗ boson production in association with a bottom-antibottom pair, JHEP 09 (2011) 061 [arXiv:1106.6019] [INSPIRE].

    Article  ADS  Google Scholar 

  19. T. Gleisberg et al., Event generation with SHERPA 1.1, JHEP 02 (2009) 007 [arXiv:0811.4622] [INSPIRE].

    Article  ADS  Google Scholar 

  20. P. Nason, A new method for combining NLO QCD with shower Monte Carlo algorithms, JHEP 11 (2004) 040 [hep-ph/0409146] [INSPIRE].

    Article  ADS  Google Scholar 

  21. S. Frixione, P. Nason and C. Oleari, Matching NLO QCD computations with parton shower simulations: the POWHEG method, JHEP 11 (2007) 070 [arXiv:0709.2092] [INSPIRE].

    Article  ADS  Google Scholar 

  22. S. Frixione and B.R. Webber, Matching NLO QCD computations and parton shower simulations, JHEP 06 (2002) 029 [hep-ph/0204244] [INSPIRE].

    Article  ADS  Google Scholar 

  23. C. Berger et al., Precise Predictions for W + 4 jet production at the Large Hadron Collider, Phys. Rev. Lett. 106 (2011) 092001 [arXiv:1009.2338] [INSPIRE].

    Article  ADS  Google Scholar 

  24. H. Ita et al., Precise predictions for Z + 4 jets at hadron colliders, Phys. Rev. D 85 (2012) 031501 [arXiv:1108.2229] [INSPIRE].

    ADS  Google Scholar 

  25. Z. Bern et al., Four-jet production at the Large Hadron Collider at next-to-leading order in QCD, Phys. Rev. Lett. 109 (2012) 042001 [arXiv:1112.3940] [INSPIRE].

    Article  ADS  Google Scholar 

  26. C. Berger et al., Next-to-leading order QCD predictions for Z, γ + 3-jet distributions at the Tevatron, Phys. Rev. D 82 (2010) 074002 [arXiv:1004.1659] [INSPIRE].

    ADS  Google Scholar 

  27. C. Berger et al., Precise predictions for W + 3 jet production at hadron colliders, Phys. Rev. Lett. 102 (2009) 222001 [arXiv:0902.2760] [INSPIRE].

    Article  ADS  Google Scholar 

  28. C. 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 

  29. R.K. Ellis, W. Giele, Z. Kunszt, K. Melnikov and G. Zanderighi, One-loop amplitudes for W + 3 jet production in hadron collisions, JHEP 01 (2009) 012 [arXiv:0810.2762] [INSPIRE].

    Article  ADS  Google Scholar 

  30. R.K. Ellis, K. Melnikov and G. Zanderighi, W + 3 jet production at the Tevatron, Phys. Rev. D 80 (2009) 094002 [arXiv:0906.1445] [INSPIRE].

    ADS  Google Scholar 

  31. K. Melnikov and G. Zanderighi, W + 3 jet production at the LHC as a signal or background, Phys. Rev. D 81 (2010) 074025 [arXiv:0910.3671] [INSPIRE].

    ADS  Google Scholar 

  32. F. Campanario, C. Englert, M. Rauch and D. Zeppenfeld, Precise predictions for Wγγ + jet production at hadron colliders, Phys. Lett. B 704 (2011) 515 [arXiv:1106.4009] [INSPIRE].

    Article  ADS  Google Scholar 

  33. F. Campanario, Towards ppV V jj at NLO QCD: bosonic contributions to triple vector boson production plus jet, JHEP 10 (2011) 070 [arXiv:1105.0920] [INSPIRE].

    Article  ADS  Google Scholar 

  34. G. Bevilacqua, M. Czakon, C. Papadopoulos and M. Worek, Dominant QCD backgrounds in Higgs boson analyses at the LHC: a study of pp\( t\overline t \) + 2 jets at next-to-leading order, Phys. Rev. Lett. 104 (2010) 162002 [arXiv:1002.4009] [INSPIRE].

    Article  ADS  Google Scholar 

  35. G. Bevilacqua, M. Czakon, C. Papadopoulos and M. Worek, Hadronic top-quark pair production in association with two jets at next-to-leading order QCD, Phys. Rev. D 84 (2011) 114017 [arXiv:1108.2851] [INSPIRE].

    ADS  Google Scholar 

  36. A. Bredenstein, A. Denner, S. Dittmaier and S. Pozzorini, NLO QCD corrections to \( t\overline t b\overline b \) production at the LHC: 1. quark-antiquark annihilation, JHEP 08 (2008) 108 [arXiv:0807.1248] [INSPIRE].

    Article  ADS  Google Scholar 

  37. A. Bredenstein, A. Denner, S. Dittmaier and S. Pozzorini, NLO QCD corrections to pp\( t\overline t b\overline b \) + X at the LHC, Phys. Rev. Lett. 103 (2009) 012002 [arXiv:0905.0110] [INSPIRE].

    Article  ADS  Google Scholar 

  38. A. Bredenstein, A. Denner, S. Dittmaier and S. Pozzorini, NLO QCD corrections to top anti-top bottom anti-bottom production at the LHC: 2. Full hadronic results, JHEP 03 (2010) 021 [arXiv:1001.4006] [INSPIRE].

    Article  ADS  Google Scholar 

  39. G. Bevilacqua, M. Czakon, C. Papadopoulos, R. Pittau and M. Worek, Assault on the NLO wishlist: pp\( t\overline t b\overline b \), JHEP 09 (2009) 109 [arXiv:0907.4723] [INSPIRE].

    Article  ADS  Google Scholar 

  40. T. Binoth et al., Next-to-leading order QCD corrections to pp\( b\overline b b\overline b \) + X at the LHC: the quark induced case, Phys. Lett. B 685 (2010) 293 [arXiv:0910.4379] [INSPIRE].

    Article  ADS  Google Scholar 

  41. T. Melia, K. Melnikov, R. Rontsch and G. Zanderighi, Next-to-leading order QCD predictions for W + W + jj production at the LHC, JHEP 12 (2010) 053 [arXiv:1007.5313] [INSPIRE].

    Article  ADS  Google Scholar 

  42. T. Melia, K. Melnikov, R. Rontsch and G. Zanderighi, NLO QCD corrections for W + W pair production in association with two jets at hadron colliders, Phys. Rev. D 83 (2011) 114043 [arXiv:1104.2327] [INSPIRE].

    ADS  Google Scholar 

  43. A. Denner, S. Dittmaier, S. Kallweit and S. Pozzorini, NLO QCD corrections to W W bb production at hadron colliders, Phys. Rev. Lett. 106 (2011) 052001 [arXiv:1012.3975] [INSPIRE].

    Article  ADS  Google Scholar 

  44. G. Bevilacqua, M. Czakon, A. van Hameren, C.G. Papadopoulos and M. Worek, Complete off-shell effects in top quark pair hadroproduction with leptonic decay at next-to-leading order, JHEP 02 (2011) 083 [arXiv:1012.4230] [INSPIRE].

    Article  ADS  Google Scholar 

  45. Z. Bern, L.J. Dixon and D.A. Kosower, On-shell methods in perturbative QCD, Annals Phys. 322 (2007) 1587 [arXiv:0704.2798] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  46. R.K. Ellis, Z. Kunszt, K. Melnikov and G. Zanderighi, One-loop calculations in quantum field theory: from Feynman diagrams to unitarity cuts, arXiv:1105.4319 [INSPIRE].

  47. C. 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 

  48. G. Ossola, C.G. Papadopoulos and R. Pittau, CutTools: a program implementing the OPP reduction method to compute one-loop amplitudes, JHEP 03 (2008) 042 [arXiv:0711.3596] [INSPIRE].

    Article  ADS  Google Scholar 

  49. G. Bevilacqua et al., HELAC-NLO, arXiv:1110.1499 [INSPIRE].

  50. W.T. Giele and G. Zanderighi, On the numerical evaluation of one-loop amplitudes: the gluonic case, JHEP 06 (2008) 038 [arXiv:0805.2152] [INSPIRE].

    Article  ADS  Google Scholar 

  51. V. Hirschi et al., Automation of one-loop QCD corrections, JHEP 05 (2011) 044 [arXiv:1103.0621] [INSPIRE].

    Article  ADS  Google Scholar 

  52. G. Cullen et al., Automated one-loop calculations with GoSam, Eur. Phys. J. C 72 (2012) 1889 [arXiv:1111.2034] [INSPIRE].

    Article  ADS  Google Scholar 

  53. A. Denner, S. Dittmaier, M. Roth and L. Wieders, Electroweak corrections to charged-current e + e → 4 fermion processes: technical details and further results, Nucl. Phys. B 724 (2005) 247 [Erratum ibid. B 854 (2012) 504–507] [hep-ph/0505042] [INSPIRE].

    Article  ADS  Google Scholar 

  54. A. Denner, S. Dittmaier, M. Roth and L. Wieders, Complete electroweak O(α) corrections to charged-current e + e → 4 fermion processes, Phys. Lett. B 612 (2005) 223 [Erratum ibid. B 704 (2011)667-668] [hep-ph/0502063] [INSPIRE].

    Article  ADS  Google Scholar 

  55. T. Schutzmeier, SME reductions in automated NLO computations with NLOX, in preparation.

  56. G. Passarino and M. Veltman, One loop corrections for e + e annihilation into μ + μ in the Weinberg model, Nucl. Phys. B 160 (1979) 151 [INSPIRE].

    Article  ADS  Google Scholar 

  57. A. Denner and S. Dittmaier, Reduction schemes for one-loop tensor integrals, Nucl. Phys. B 734 (2006) 62 [hep-ph/0509141] [INSPIRE].

    Article  ADS  Google Scholar 

  58. D.H. Bailey, http://crd.lbl.gov/˜dhbailey/mpdist/.

  59. T. Diakonidis et al., A complete reduction of one-loop tensor 5 and 6-point integrals, Phys. Rev. D 80 (2009) 036003 [arXiv:0812.2134] [INSPIRE].

    Google Scholar 

  60. T. Diakonidis et al., On the tensor reduction of one-loop pentagons and hexagons, Nucl. Phys. Proc. Suppl. 183 (2008) 109 [arXiv:0807.2984] [INSPIRE].

    Article  ADS  Google Scholar 

  61. R.K. Ellis and G. Zanderighi, Scalar one-loop integrals for QCD, JHEP 02 (2008) 002 [arXiv:0712.1851] [INSPIRE].

    Article  ADS  Google Scholar 

  62. T. Hahn and M. Pérez-Victoria, Automatized one loop calculations in four-dimensions and D-dimensions, Comput. Phys. Commun. 118 (1999) 153 [hep-ph/9807565] [INSPIRE].

    Article  ADS  Google Scholar 

  63. C. Berger et al., One-loop multi-parton amplitudes with a vector boson for the LHC, arXiv:0808.0941 [INSPIRE].

  64. H. Hartanto, L. Reina and T. Schutzmeier, in preparation.

  65. A. Denner and S. Dittmaier, Reduction of one loop tensor five point integrals, Nucl. Phys. B 658 (2003) 175 [hep-ph/0212259] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Laura Reina.

Additional information

ArXiv ePrint: 1110.4438

Rights and permissions

Reprints and permissions

About this article

Cite this article

Reina, L., Schutzmeier, T. Towards W \( b\overline b \) + j at NLO with an automatized approach to one-loop computations. J. High Energ. Phys. 2012, 119 (2012). https://doi.org/10.1007/JHEP09(2012)119

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP09(2012)119

Keywords

Navigation