Small-radius jets to all orders in QCD

  • Mrinal Dasgupta
  • Frédéric Dreyer
  • Gavin P. Salam
  • Gregory Soyez
Open Access
Regular Article - Theoretical Physics

Abstract

As hadron collider physics continues to push the boundaries of precision, it becomes increasingly important to have methods for predicting properties of jets across a broad range of jet radius values R, and in particular for small R. In this paper we resum all leading logarithmic terms, α s n  ln n R2, in the limit of small R, for a wide variety of observables. These include the inclusive jet spectrum, jet vetoes for Higgs physics and jet substructure tools. Some of the quantities that we consider are relevant also for heavy-ion collisions. Furthermore, we examine and comment on the underlying order-by-order convergence of the perturbative series for different R values. Our results indicate that small-R effects can be substantial. Phenomenological studies will appear in a forthcoming companion paper.

Keywords

QCD Phenomenology Jets 

Notes

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.

References

  1. [1]
    G.F. Sterman and S. Weinberg, Jets from Quantum Chromodynamics, Phys. Rev. Lett. 39 (1977) 1436 [INSPIRE].ADSCrossRefGoogle Scholar
  2. [2]
    S. Catani, Y.L. Dokshitzer, M.H. Seymour and B.R. Webber, Longitudinally invariant K t clustering algorithms for hadron hadron collisions, Nucl. Phys. B 406 (1993) 187 [INSPIRE].ADSCrossRefGoogle Scholar
  3. [3]
    ATLAS collaboration, Jet energy measurement and its systematic uncertainty in proton-proton collisions at \( \sqrt{s} \) = 7 TeV with the ATLAS detector, Eur. Phys. J. C 75 (2015) 17 [arXiv:1406.0076] [INSPIRE].ADSGoogle Scholar
  4. [4]
    CMS collaboration, Determination of Jet Energy Calibration and Transverse Momentum Resolution in CMS, 2011 JINST 6 P11002 [arXiv:1107.4277] [INSPIRE].
  5. [5]
    STAR collaboration, M. Ploskon, Inclusive cross section and correlations of fully reconstructed jets in \( \sqrt{s_{N\ N}} \) = 200-GEV Au+Au and p+p collisions, Nucl. Phys. A 830 (2009) 255C [arXiv:0908.1799] [INSPIRE].ADSGoogle Scholar
  6. [6]
    PHENIX collaboration, Y.-S. Lai, Direct jet reconstruction in p + p and Cu + Cu at PHENIX, arXiv:0911.3399 [INSPIRE].
  7. [7]
    ALICE collaboration, Measurement of charged jet suppression in Pb-Pb collisions at \( \sqrt{s_{N\ N}} \) = 2.76 TeV, JHEP 03 (2014) 013 [arXiv:1311.0633] [INSPIRE].ADSGoogle Scholar
  8. [8]
    ATLAS collaboration, Measurement of inclusive jet charged-particle fragmentation functions in Pb+Pb collisions at \( \sqrt{s_{N\ N}} \) = 2.76 TeV with the ATLAS detector, Phys. Lett. B 739 (2014) 320 [arXiv:1406.2979] [INSPIRE].ADSGoogle Scholar
  9. [9]
    CMS collaboration, Measurement of jet fragmentation in PbPb and pp collisions at \( \sqrt{s_{N\ N}} \) = 2.76 TeV, Phys. Rev. C 90 (2014) 024908 [arXiv:1406.0932] [INSPIRE].ADSGoogle Scholar
  10. [10]
    ALICE collaboration, Measurement of the inclusive differential jet cross section in pp collisions at \( \sqrt{s} \) = 2.76 TeV, Phys. Lett. B 722 (2013) 262 [arXiv:1301.3475] [INSPIRE].ADSGoogle Scholar
  11. [11]
    CMS collaboration, Measurement of the ratio of inclusive jet cross sections using the anti-k T algorithm with radius parameters R=0.5 and 0.7 in pp collisions at \( \sqrt{s} \) = 7 TeV, Phys. Rev. D 90 (2014) 072006 [arXiv:1406.0324] [INSPIRE].ADSGoogle Scholar
  12. [12]
    S. Eckweiler, Measurement of the inclusive jet cross-section in proton-proton collisions at \( \sqrt{s} \) = 7 TeV with the ATLAS detector, CERN-THESIS-2011-145.Google Scholar
  13. [13]
    G. Soyez, A Simple description of jet cross-section ratios, Phys. Lett. B 698 (2011) 59 [arXiv:1101.2665] [INSPIRE].ADSCrossRefGoogle Scholar
  14. [14]
    J.M. Butterworth, A.R. Davison, M. Rubin and G.P. Salam, Jet substructure as a new Higgs search channel at the LHC, Phys. Rev. Lett. 100 (2008) 242001 [arXiv:0802.2470] [INSPIRE].ADSCrossRefGoogle Scholar
  15. [15]
    D. Krohn, J. Thaler and L.-T. Wang, Jet Trimming, JHEP 02 (2010) 084 [arXiv:0912.1342] [INSPIRE].ADSCrossRefGoogle Scholar
  16. [16]
    B. Nachman, P. Nef, A. Schwartzman, M. Swiatlowski and C. Wanotayaroj, Jets from Jets: Re-clustering as a tool for large radius jet reconstruction and grooming at the LHC, JHEP 02 (2015) 075 [arXiv:1407.2922] [INSPIRE].ADSCrossRefGoogle Scholar
  17. [17]
    A. Abdesselam, E.B. Kuutmann, U. Bitenc, G. Brooijmans, J. Butterworth et al., Boosted objects: A Probe of beyond the Standard Model physics, Eur. Phys. J. C 71 (2011) 1661 [arXiv:1012.5412] [INSPIRE].ADSCrossRefGoogle Scholar
  18. [18]
    A. Altheimer, S. Arora, L. Asquith, G. Brooijmans, J. Butterworth et al., Jet Substructure at the Tevatron and LHC: New results, new tools, new benchmarks, J. Phys. G 39 (2012) 063001 [arXiv:1201.0008] [INSPIRE].ADSCrossRefGoogle Scholar
  19. [19]
    A. Altheimer, A. Arce, L. Asquith, J. Backus Mayes, E. Bergeaas Kuutmann et al., Boosted objects and jet substructure at the LHC. Report of BOOST2012, held at IFIC Valencia, 23rd-27th of July 2012, Eur. Phys. J. C 74 (2014) 2792 [arXiv:1311.2708] [INSPIRE].ADSCrossRefGoogle Scholar
  20. [20]
    T. Plehn and M. Spannowsky, Top Tagging, J. Phys. G 39 (2012) 083001 [arXiv:1112.4441] [INSPIRE].ADSCrossRefGoogle Scholar
  21. [21]
    F.J. Tackmann, J.R. Walsh and S. Zuberi, Resummation Properties of Jet Vetoes at the LHC, Phys. Rev. D 86 (2012) 053011 [arXiv:1206.4312] [INSPIRE].ADSGoogle Scholar
  22. [22]
    M.H. Seymour, Jet shapes in hadron collisions: Higher orders, resummation and hadronization, Nucl. Phys. B 513 (1998) 269 [hep-ph/9707338] [INSPIRE].ADSCrossRefGoogle Scholar
  23. [23]
    E. Gerwick, S. Schumann, B. Gripaios and B. Webber, QCD Jet Rates with the Inclusive Generalized kt Algorithms, JHEP 04 (2013) 089 [arXiv:1212.5235] [INSPIRE].ADSCrossRefGoogle Scholar
  24. [24]
    S. Catani, M. Fontannaz, J.P. Guillet and E. Pilon, Isolating Prompt Photons with Narrow Cones, JHEP 09 (2013) 007 [arXiv:1306.6498] [INSPIRE].ADSCrossRefGoogle Scholar
  25. [25]
    S. Alioli and J.R. Walsh, Jet Veto Clustering Logarithms Beyond Leading Order, JHEP 03 (2014) 119 [arXiv:1311.5234] [INSPIRE].ADSCrossRefGoogle Scholar
  26. [26]
    A. von Manteuffel, R.M. Schabinger and H.X. Zhu, The Complete Two-Loop Integrated Jet Thrust Distribution In Soft-Collinear Effective Theory, JHEP 03 (2014) 139 [arXiv:1309.3560] [INSPIRE].ADSCrossRefGoogle Scholar
  27. [27]
    S. Catani, Y.L. Dokshitzer, M. Olsson, G. Turnock and B.R. Webber, New clustering algorithm for multi - jet cross-sections in e + e annihilation, Phys. Lett. B 269 (1991) 432 [INSPIRE].ADSCrossRefGoogle Scholar
  28. [28]
    Y.L. Dokshitzer, G.D. Leder, S. Moretti and B.R. Webber, Better jet clustering algorithms, JHEP 08 (1997) 001 [hep-ph/9707323] [INSPIRE].ADSCrossRefGoogle Scholar
  29. [29]
    M. Wobisch and T. Wengler, Hadronization corrections to jet cross-sections in deep inelastic scattering, hep-ph/9907280 [INSPIRE].
  30. [30]
    M. Cacciari, G.P. Salam and G. Soyez, The Anti-k(t) jet clustering algorithm, JHEP 04 (2008) 063 [arXiv:0802.1189] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  31. [31]
    G.P. Salam and G. Soyez, A Practical Seedless Infrared-Safe Cone jet algorithm, JHEP 05 (2007) 086 [arXiv:0704.0292] [INSPIRE].ADSCrossRefGoogle Scholar
  32. [32]
    Y.L. Dokshitzer, V.A. Khoze, A.H. Mueller and S.I. Troian, Basics of perturbative QCD, Gif-sur-Yvette, France: Ed. Frontieres, 1991, pg. 274.Google Scholar
  33. [33]
    R.K. Ellis, W.J. Stirling and B.R. Webber, QCD and collider physics, Camb. Monogr. Part. Phys. Nucl. Phys. Cosmol. 8 (1996) 1 [INSPIRE].Google Scholar
  34. [34]
    H1 collaboration, A. Aktas et al., Measurement of inclusive jet production in deep-inelastic scattering at high Q 2 and determination of the strong coupling, Phys. Lett. B 653 (2007) 134 [arXiv:0706.3722] [INSPIRE].ADSGoogle Scholar
  35. [35]
    ZEUS collaboration, H. Abramowicz et al., Inclusive-jet cross sections in NC DIS at HERA and a comparison of the kT, anti-kT and SIScone jet algorithms, Phys. Lett. B 691 (2010) 127 [arXiv:1003.2923] [INSPIRE].ADSGoogle Scholar
  36. [36]
    CDF collaboration, T. Aaltonen et al., Measurement of the Inclusive Jet Cross Section at the Fermilab Tevatron pp Collider Using a Cone-Based Jet Algorithm, Phys. Rev. D 78 (2008) 052006 [Erratum ibid. D 79 (2009) 119902] [arXiv:0807.2204] [INSPIRE].
  37. [37]
    D0 collaboration, V.M. Abazov et al., Measurement of the inclusive jet cross section in \( p\overline{p} \) collisions at \( \sqrt{s} \) = 1.96 TeV, Phys. Rev. D 85 (2012) 052006 [arXiv:1110.3771] [INSPIRE].ADSGoogle Scholar
  38. [38]
    ATLAS collaboration, Measurement of the inclusive jet cross-section in proton-proton collisions at \( \sqrt{s} \) = 7 TeV using 4.5 fb −1 of data with the ATLAS detector, JHEP 02 (2015) 153 [arXiv:1410.8857] [INSPIRE].ADSGoogle Scholar
  39. [39]
    CMS collaboration, Measurements of differential jet cross sections in proton-proton collisions at \( \sqrt{s} \) = 7 TeV with the CMS detector, Phys. Rev. D 87 (2013) 112002 [arXiv:1212.6660] [INSPIRE].ADSGoogle Scholar
  40. [40]
    J. Currie, A. Gehrmann-De Ridder, E.W.N. Glover and J. Pires, NNLO QCD corrections to jet production at hadron colliders from gluon scattering, JHEP 01 (2014) 110 [arXiv:1310.3993] [INSPIRE].ADSCrossRefGoogle Scholar
  41. [41]
    R. Boughezal, F. Caola, K. Melnikov, F. Petriello and M. Schulze, Higgs boson production in association with a jet at next-to-next-to-leading order in perturbative QCD, JHEP 06 (2013) 072 [arXiv:1302.6216] [INSPIRE].ADSCrossRefGoogle Scholar
  42. [42]
    D. de Florian, P. Hinderer, A. Mukherjee, F. Ringer and W. Vogelsang, Approximate next-to-next-to-leading order corrections to hadronic jet production, Phys. Rev. Lett. 112 (2014) 082001 [arXiv:1310.7192] [INSPIRE].ADSCrossRefGoogle Scholar
  43. [43]
    M. Botje, QCDNUM: Fast QCD Evolution and Convolution, Comput. Phys. Commun. 182 (2011) 490 [arXiv:1005.1481] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  44. [44]
    A. Vogt, Efficient evolution of unpolarized and polarized parton distributions with QCD-PEGASUS, Comput. Phys. Commun. 170 (2005) 65 [hep-ph/0408244] [INSPIRE].ADSCrossRefGoogle Scholar
  45. [45]
    G.P. Salam and J. Rojo, A Higher Order Perturbative Parton Evolution Toolkit (HOPPET), Comput. Phys. Commun. 180 (2009) 120 [arXiv:0804.3755] [INSPIRE].ADSCrossRefGoogle Scholar
  46. [46]
    V. Bertone, S. Carrazza and J. Rojo, APFEL: A PDF Evolution Library with QED corrections, Comput. Phys. Commun. 185 (2014) 1647 [arXiv:1310.1394] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  47. [47]
    M. Cacciari, M. Dasgupta, F. Dreyer, G.P. Salam and G. Soyez, in preparation.Google Scholar
  48. [48]
    ATLAS collaboration, Measurement of the correlation of jets with high p T isolated prompt photons in lead-lead collisions at sqrts NN = 2.76 TeV with the ATLAS detector at the LHC, ATLAS-CONF-2012-121.
  49. [49]
    CMS collaboration, Studies of jet quenching using isolated-photon+jet correlations in PbPb and pp collisions at \( \sqrt{s_{NN}} \) = 2.76 TeV, Phys. Lett. B 718 (2013) 773 [arXiv:1205.0206] [INSPIRE].ADSGoogle Scholar
  50. [50]
    A. Banfi, G.P. Salam and G. Zanderighi, NLL+NNLO predictions for jet-veto efficiencies in Higgs-boson and Drell-Yan production, JHEP 06 (2012) 159 [arXiv:1203.5773] [INSPIRE].ADSCrossRefGoogle Scholar
  51. [51]
    A. Banfi, P.F. Monni, G.P. Salam and G. Zanderighi, Higgs and Z-boson production with a jet veto, Phys. Rev. Lett. 109 (2012) 202001 [arXiv:1206.4998] [INSPIRE].ADSCrossRefGoogle Scholar
  52. [52]
    T. Becher and M. Neubert, Factorization and NNLL Resummation for Higgs Production with a Jet Veto, JHEP 07 (2012) 108 [arXiv:1205.3806] [INSPIRE].ADSCrossRefGoogle Scholar
  53. [53]
    T. Becher, M. Neubert and L. Rothen, Factorization and N 3 LL p +NNLO predictions for the Higgs cross section with a jet veto, JHEP 10 (2013) 125 [arXiv:1307.0025] [INSPIRE].ADSCrossRefGoogle Scholar
  54. [54]
    I.W. Stewart, F.J. Tackmann, J.R. Walsh and S. Zuberi, Jet p T resummation in Higgs production at NNLL +NNLO, Phys. Rev. D 89 (2014) 054001 [arXiv:1307.1808] [INSPIRE].ADSGoogle Scholar
  55. [55]
    A. Banfi, P.F. Monni and G. Zanderighi, Quark masses in Higgs production with a jet veto, JHEP 01 (2014) 097 [arXiv:1308.4634] [INSPIRE].ADSCrossRefGoogle Scholar
  56. [56]
    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] [INSPIRE].
  57. [57]
    A. Banfi, G.P. Salam and G. Zanderighi, Infrared safe definition of jet flavor, Eur. Phys. J. C 47 (2006) 113 [hep-ph/0601139] [INSPIRE].ADSCrossRefGoogle Scholar
  58. [58]
    J. Gallicchio and M.D. Schwartz, Quark and Gluon Tagging at the LHC, Phys. Rev. Lett. 107 (2011) 172001 [arXiv:1106.3076] [INSPIRE].ADSCrossRefGoogle Scholar
  59. [59]
    J. Gallicchio and M.D. Schwartz, Quark and Gluon Jet Substructure, JHEP 04 (2013) 090 [arXiv:1211.7038] [INSPIRE].ADSCrossRefGoogle Scholar
  60. [60]
    A.J. Larkoski, G.P. Salam and J. Thaler, Energy Correlation Functions for Jet Substructure, JHEP 06 (2013) 108 [arXiv:1305.0007] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  61. [61]
    A.J. Larkoski, J. Thaler and W.J. Waalewijn, Gaining (Mutual) Information about Quark/Gluon Discrimination, JHEP 11 (2014) 129 [arXiv:1408.3122] [INSPIRE].ADSCrossRefGoogle Scholar
  62. [62]
    ATLAS collaboration, Light-quark and gluon jet discrimination in pp collisions at \( \sqrt{s} \) = 7 TeV with the ATLAS detector, Eur. Phys. J. C 74 (2014) 3023 [arXiv:1405.6583] [INSPIRE].ADSGoogle Scholar
  63. [63]
    CMS Collaboration, Performance of quark/gluon discrimination in 8 TeV pp data, CMS-PAS-JME-13-002.
  64. [64]
    M. Dasgupta and G.P. Salam, Resummation of nonglobal QCD observables, Phys. Lett. B 512 (2001) 323 [hep-ph/0104277] [INSPIRE].ADSMATHGoogle Scholar
  65. [65]
    Y. Delenda, R. Appleby, M. Dasgupta and A. Banfi, On QCD resummation with k(t) clustering, JHEP 12 (2006) 044 [hep-ph/0610242] [INSPIRE].ADSCrossRefGoogle Scholar
  66. [66]
    G.P. Korchemsky and G.F. Sterman, Nonperturbative corrections in resummed cross-sections, Nucl. Phys. B 437 (1995) 415 [hep-ph/9411211] [INSPIRE].ADSCrossRefGoogle Scholar
  67. [67]
    M. Dasgupta, L. Magnea and G.P. Salam, Non-perturbative QCD effects in jets at hadron colliders, JHEP 02 (2008) 055 [arXiv:0712.3014] [INSPIRE].ADSCrossRefGoogle Scholar
  68. [68]
    M. Dasgupta, A. Fregoso, S. Marzani and G.P. Salam, Towards an understanding of jet substructure, JHEP 09 (2013) 029 [arXiv:1307.0007] [INSPIRE].ADSCrossRefGoogle Scholar
  69. [69]
    M. Cacciari, G.P. Salam and G. Soyez, FastJet User Manual, Eur. Phys. J. C 72 (2012) 1896 [arXiv:1111.6097] [INSPIRE].ADSCrossRefGoogle Scholar

Copyright information

© The Author(s) 2015

Authors and Affiliations

  • Mrinal Dasgupta
    • 1
  • Frédéric Dreyer
    • 2
    • 3
  • Gavin P. Salam
    • 4
  • Gregory Soyez
    • 5
  1. 1.Consortium for Fundamental Physics, School of Physics & AstronomyUniversity of ManchesterManchesterUnited Kingdom
  2. 2.Sorbonne Universités, UPMC Univ Paris 06, UMR 7589, LPTHEParisFrance
  3. 3.CNRS, UMR 7589, LPTHEParisFrance
  4. 4.CERN, PH-THGeneva 23Switzerland
  5. 5.IPhT, CEA Saclay, CNRS URA 2306Gif-sur-YvetteFrance

Personalised recommendations