Advertisement

Journal of High Energy Physics

, 2012:117 | Cite as

Abelian non-global logarithms from soft gluon clustering

  • Randall Kelley
  • Jonathan R. Walsh
  • Saba Zuberi
Article

Abstract

Most recombination-style jet algorithms cluster soft gluons in a complex way. This leads to previously identified correlations in the soft gluon phase space and introduces logarithmic corrections to jet cross sections, which are known as clustering logarithms. The leading Abelian clustering logarithms occur at least at next-to leading logarithm (NLL) in the exponent of the distribution. Using the framework of Soft Collinear Effective Theory (SCET), we show that new clustering effects contributing at NLL arise at each order. While numerical resummation of clustering logs is possible, it is unlikely that they can be analytically resummed to NLL. Clustering logarithms make the anti-kT algorithm theoretically preferred, for which they are power suppressed. They can arise in Abelian and non-Abelian terms, and we calculate the Abelian clustering logarithms at O\( \left( {\alpha_s^2} \right) \) for the jet mass distribution using the Cambridge/Aachen and kT algorithms, including jet radius dependence, which extends previous results. We find that clustering logarithms can be naturally thought of as a class of non-global logarithms, which have traditionally been tied to non-Abelian correlations in soft gluon emission.

Keywords

Jets 

References

  1. [1]
    G.F. Sterman, Partons, factorization and resummation, TASI 95, hep-ph/9606312 [INSPIRE].
  2. [2]
    H. Contopanagos, E. Laenen and G.F. Sterman, Sudakov factorization and resummation, Nucl. Phys. B 484 (1997) 303 [hep-ph/9604313] [INSPIRE].ADSCrossRefGoogle Scholar
  3. [3]
    C.W. Bauer, S. Fleming and M.E. Luke, Summing Sudakov logarithms in B → X s γ in effective field theory, Phys. Rev. D 63 (2000) 014006 [hep-ph/0005275] [INSPIRE].ADSGoogle Scholar
  4. [4]
    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] [INSPIRE].ADSGoogle Scholar
  5. [5]
    C.W. Bauer and I.W. Stewart, Invariant operators in collinear effective theory, Phys. Lett. B 516 (2001)134 [hep-ph/0107001] [INSPIRE].ADSCrossRefGoogle Scholar
  6. [6]
    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] [INSPIRE].ADSGoogle Scholar
  7. [7]
    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] [INSPIRE].ADSGoogle Scholar
  8. [8]
    M. Dasgupta and G. Salam, Resummation of nonglobal QCD observables, Phys. Lett. B 512 (2001)323 [hep-ph/0104277] [INSPIRE].ADSGoogle Scholar
  9. [9]
    M. Dasgupta and G.P. Salam, Accounting for coherence in interjet E(t) flow: a case study, JHEP 03 (2002) 017 [hep-ph/0203009] [INSPIRE].ADSCrossRefGoogle Scholar
  10. [10]
    A. Banfi and M. Dasgupta, Problems in resumming interjet energy flows with k t clustering, Phys. Lett. B 628 (2005) 49 [hep-ph/0508159] [INSPIRE].ADSCrossRefGoogle Scholar
  11. [11]
    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
  12. [12]
    K. Khelifa-Kerfa, Non-global logs and clustering impact on jet mass with a jet veto distribution, JHEP 02 (2012) 072 [arXiv:1111.2016] [INSPIRE].ADSCrossRefGoogle Scholar
  13. [13]
    S. Catani, Y.L. Dokshitzer, M. Olsson, G. Turnock and B. Webber, New clustering algorithm for multi-jet cross-sections in e + e annihilation, Phys. Lett. B 269 (1991) 432 [INSPIRE].ADSCrossRefGoogle Scholar
  14. [14]
    S. Catani, Y.L. Dokshitzer, M. Seymour and B. Webber, Longitudinally invariant k t clustering algorithms for hadron hadron collisions, Nucl. Phys. B 406 (1993) 187 [INSPIRE].ADSCrossRefGoogle Scholar
  15. [15]
    S.D. Ellis and D.E. Soper, Successive combination jet algorithm for hadron collisions, Phys. Rev. D 48 (1993) 3160 [hep-ph/9305266] [INSPIRE].ADSGoogle Scholar
  16. [16]
    Y.L. Dokshitzer, G. Leder, S. Moretti and B. Webber, Better jet clustering algorithms, JHEP 08 (1997) 001 [hep-ph/9707323] [INSPIRE].ADSCrossRefGoogle Scholar
  17. [17]
    M. Cacciari, G.P. Salam and G. Soyez, The anti-k t jet clustering algorithm, JHEP 04 (2008) 063 [arXiv:0802.1189] [INSPIRE].ADSCrossRefGoogle Scholar
  18. [18]
    I.W. Stewart, F.J. Tackmann and W.J. Waalewijn, N-jettiness: an inclusive event shape to veto jets, Phys. Rev. Lett. 105 (2010) 092002 [arXiv:1004.2489] [INSPIRE].ADSCrossRefGoogle Scholar
  19. [19]
    R. Kelley, M.D. Schwartz and H.X. Zhu, Resummation of jet mass with and without a jet veto, arXiv:1102.0561 [INSPIRE].
  20. [20]
    S. Catani and M. 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] [INSPIRE].ADSCrossRefGoogle Scholar
  21. [21]
    S. Catani and M. Seymour, A general algorithm for calculating jet cross-sections in NLO QCD, Nucl. Phys. B 485 (1997) 291 [Erratum ibid. B 510 (1998) 503–504] [hep-ph/9605323] [INSPIRE].ADSCrossRefGoogle Scholar
  22. [22]
    R. Kelley, J.R. Walsh and S. Zuberi, Disentangling clustering effects in jet algorithms, arXiv:1203.2923 [INSPIRE].
  23. [23]
    R. Appleby and M. Seymour, Nonglobal logarithms in interjet energy flow with kt clustering requirement, JHEP 12 (2002) 063 [hep-ph/0211426] [INSPIRE].ADSCrossRefGoogle Scholar
  24. [24]
    R. Appleby and M. Seymour, The resummation of interjet energy flow for gaps between jets processes at HERA, JHEP 09 (2003) 056 [hep-ph/0308086] [INSPIRE].ADSCrossRefGoogle Scholar
  25. [25]
    S.D. Ellis, A. Hornig, C. Lee, C.K. Vermilion and J.R. Walsh, Consistent factorization of jet observables in exclusive multijet cross-sections, Phys. Lett. B 689 (2010) 82 [arXiv:0912.0262] [INSPIRE].ADSCrossRefGoogle Scholar
  26. [26]
    S.D. Ellis, C.K. Vermilion, J.R. Walsh, A. Hornig and C. Lee, Jet shapes and jet algorithms in SCET, JHEP 11 (2010) 101 [arXiv:1001.0014] [INSPIRE].ADSCrossRefGoogle Scholar
  27. [27]
    W.M.Y. Cheung, M. Luke and S. Zuberi, Phase space and jet definitions in SCET, Phys. Rev. D 80 (2009) 114021 [arXiv:0910.2479] [INSPIRE].ADSGoogle Scholar
  28. [28]
    A. Banfi, M. Dasgupta, K. Khelifa-Kerfa and S. Marzani, Non-global logarithms and jet algorithms in high-p T jet shapes, JHEP 08 (2010) 064 [arXiv:1004.3483] [INSPIRE].ADSCrossRefGoogle Scholar
  29. [29]
    R. Kelley, M.D. Schwartz, R.M. Schabinger and H.X. Zhu, The two-loop hemisphere soft function, Phys. Rev. D 84 (2011) 045022 [arXiv:1105.3676] [INSPIRE].ADSGoogle Scholar
  30. [30]
    A. Hornig, C. Lee, J.R. Walsh and S. Zuberi, Double non-global logarithms in-N-out of jets, JHEP 01 (2012) 149 [arXiv:1110.0004] [INSPIRE].ADSCrossRefGoogle Scholar
  31. [31]
    R. Kelley, M.D. Schwartz, R.M. Schabinger and H.X. Zhu, Jet mass with a jet veto at two loops and the universality of non-global structure, arXiv:1112.3343 [INSPIRE].
  32. [32]
    M.D. Schwartz, Resummation and NLO matching of event shapes with effective field theory, Phys. Rev. D 77 (2008) 014026 [arXiv:0709.2709] [INSPIRE].ADSGoogle Scholar
  33. [33]
    S. Fleming, A.H. Hoang, S. Mantry and I.W. Stewart, Top jets in the peak region: factorization analysis with NLL resummation, Phys. Rev. D 77 (2008) 114003 [arXiv:0711.2079] [INSPIRE].ADSGoogle Scholar
  34. [34]
    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].ADSGoogle Scholar
  35. [35]
    T.T. Jouttenus, Jet function with a jet algorithm in SCET, Phys. Rev. D 81 (2010) 094017 [arXiv:0912.5509] [INSPIRE].ADSGoogle Scholar
  36. [36]
    J.R. Walsh and S. Zuberi, Factorization constraints on jet substructure, arXiv:1110.5333 [INSPIRE].
  37. [37]
    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] [INSPIRE].ADSCrossRefGoogle Scholar
  38. [38]
    Z. Ligeti, I.W. Stewart and F.J. Tackmann, Treating the b quark distribution function with reliable uncertainties, Phys. Rev. D 78 (2008) 114014 [arXiv:0807.1926] [INSPIRE].ADSGoogle Scholar
  39. [39]
    A. Hornig, C. Lee, I.W. Stewart, J.R. Walsh and S. Zuberi, Non-global structure of the O \( \left( {\alpha_s^2} \right) \) dijet soft function, JHEP 08 (2011) 054 [arXiv:1105.4628] [INSPIRE].ADSCrossRefGoogle Scholar
  40. [40]
    C.W. Bauer, N.D. Dunn and A. Hornig, Subtractions for SCET soft functions, arXiv:1102.4899 [INSPIRE].
  41. [41]
    R. Kelley, J.R. Walsh and S. Zuberi, Disentangling clustering effects in jet algorithms, arXiv:1203.2923 [INSPIRE].
  42. [42]
    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] [INSPIRE].ADSCrossRefGoogle Scholar
  43. [43]
    A. Banfi, G. Marchesini and G. Smye, Away from jet energy flow, JHEP 08 (2002) 006 [hep-ph/0206076] [INSPIRE].ADSCrossRefGoogle Scholar
  44. [44]
    S. Catani, Jet topology and new jet counting algorithms, in the proceedings of the 17th INFN Eloisatron Project Workshop: QCD at 200 TeV, June 11–17, Erice, Italy (1991).Google Scholar

Copyright information

© SISSA, Trieste, Italy 2012

Authors and Affiliations

  • Randall Kelley
    • 1
  • Jonathan R. Walsh
    • 2
  • Saba Zuberi
    • 2
  1. 1.Department of PhysicsHarvard UniversityCambridgeU.S.A.
  2. 2.Theoretical Physics Group, Ernest Orlando Lawrence Berkeley National Laboratory, and Center for Theoretical PhysicsUniversity of CaliforniaBerkeleyU.S.A.

Personalised recommendations