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Journal of High Energy Physics

, 2014:129 | Cite as

Gaining (mutual) information about quark/gluon discrimination

  • Andrew J. Larkoski
  • Jesse ThalerEmail author
  • Wouter J. Waalewijn
Open Access
Regular Article - Theoretical Physics

Abstract

Discriminating quark jets from gluon jets is an important but challenging problem in jet substructure. In this paper, we use the concept of mutual information to illuminate the physics of quark/gluon tagging. Ideal quark/gluon separation requires only one bit of truth information, so even if two discriminant variables are largely uncorrelated, they can still share the same “truth overlap”. Mutual information can be used to diagnose such situations, and thus determine which discriminant variables are redundant and which can be combined to improve performance. Using both parton showers and analytic resummation, we study a two-parameter family of generalized angularities, which includes familiar infrared and collinear (IRC) safe observables like thrust and broadening, as well as IRC unsafe variants like p T D and hadron multiplicity. At leading-logarithmic (LL) order, the bulk of these variables exhibit Casimir scaling, such that their truth overlap is a universal function of the color factor ratio C A /C F . Only at next-to-leading-logarithmic (NLL) order can one see a difference in quark/gluon performance. For the IRC safe angularities, we show that the quark/gluon performance can be improved by combining angularities with complementary angular exponents. Interestingly, LL order, NLL order, Pythia 8, and Herwig++ all exhibit similar correlations between observables, but there are significant differences in the predicted quark/gluon discrimination power. For the IRC unsafe angularities, we show that the mutual information can be calculated analytically with the help of a nonperturbative “weighted-energy function”, providing evidence for the complementarity of safe and unsafe observables for quark/gluon discrimination.

Keywords

Jets QCD Phenomenology 

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]
    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].CrossRefADSGoogle Scholar
  2. [2]
    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].CrossRefADSGoogle Scholar
  3. [3]
    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].CrossRefADSGoogle Scholar
  4. [4]
    J. Gallicchio and M.D. Schwartz, Quark and Gluon Tagging at the LHC, Phys. Rev. Lett. 107 (2011) 172001 [arXiv:1106.3076] [INSPIRE].CrossRefADSGoogle Scholar
  5. [5]
    J. Gallicchio and M.D. Schwartz, Quark and Gluon Jet Substructure, JHEP 04 (2013) 090 [arXiv:1211.7038] [INSPIRE].CrossRefADSGoogle Scholar
  6. [6]
    D. Krohn, M.D. Schwartz, T. Lin and W.J. Waalewijn, Jet Charge at the LHC, Phys. Rev. Lett. 110 (2013) 212001 [arXiv:1209.2421] [INSPIRE].CrossRefADSGoogle Scholar
  7. [7]
    CMS collaboration, Search for a Higgs boson in the decay channel H to ZZ(*) to q qbar ℓ l+ in pp collisions at \( \sqrt{s}=7 \) TeV, JHEP 04 (2012) 036 [arXiv:1202.1416] [INSPIRE].ADSGoogle Scholar
  8. [8]
    F. Pandolfi and D. Del Re, Search for the Standard Model Higgs Boson in the HZZllqq Decay Channel at CMS, PhD thesis, Zurich, ETH, 2012.Google Scholar
  9. [9]
    A.J. Larkoski, G.P. Salam and J. Thaler, Energy Correlation Functions for Jet Substructure, JHEP 06 (2013) 108 [arXiv:1305.0007] [INSPIRE].CrossRefMathSciNetADSGoogle Scholar
  10. [10]
    CMS Collaboration, Performance of quark/gluon discrimination in 8 TeV pp data, CMS-PAS-JME-13-002.
  11. [11]
    CMS Collaboration, Pileup Jet Identification, CMS-PAS-JME-13-005.
  12. [12]
    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
  13. [13]
    ATLAS collaboration, Performance and Validation of Q-Jets at the ATLAS Detector in pp Collisions at \( \sqrt{s}=8 \) TeV in 2012, ATLAS-CONF-2013-087.
  14. [14]
    CMS Collaboration, Identifying Hadronically Decaying Vector Bosons Merged into a Single Jet, CMS-PAS-JME-13-006.
  15. [15]
    P. Carruthers and C.C. Shih, Mutual Information and Forward Backward Correlations in MultiHadron Production, Phys. Rev. Lett. 62 (1989) 2073 [INSPIRE].CrossRefADSGoogle Scholar
  16. [16]
    I. Narsky and F.C. Porter, Statistical analysis techniques in particle physics, Wiley-VCH, Berlin, 2014.Google Scholar
  17. [17]
    H. Casini and M. Huerta, A Finite entanglement entropy and the c-theorem, Phys. Lett. B 600 (2004) 142 [hep-th/0405111] [INSPIRE].CrossRefMathSciNetADSGoogle Scholar
  18. [18]
    Physical Review Letters 100 (2008) 070502 [arXiv:0704.3906].
  19. [19]
    P. Calabrese and J. Cardy, Entanglement entropy and conformal field theory, J. Phys. A 42 (2009) 504005 [arXiv:0905.4013] [INSPIRE].
  20. [20]
    M. Headrick, Entanglement Renyi entropies in holographic theories, Phys. Rev. D 82 (2010) 126010 [arXiv:1006.0047] [INSPIRE].ADSGoogle Scholar
  21. [21]
    D. Bertolini, T. Chan and J. Thaler, Jet Observables Without Jet Algorithms, JHEP 04 (2014) 013 [arXiv:1310.7584] [INSPIRE].CrossRefADSGoogle Scholar
  22. [22]
    A.J. Larkoski, D. Neill and J. Thaler, Jet Shapes with the Broadening Axis, JHEP 04 (2014) 017 [arXiv:1401.2158] [INSPIRE].CrossRefADSGoogle Scholar
  23. [23]
    G. Salam, Notes on the Winner-Take-All Axis, unpublished.Google Scholar
  24. [24]
    S. Catani, G. Turnock and B.R. Webber, Jet broadening measures in e + e annihilation, Phys. Lett. B 295 (1992) 269 [INSPIRE].CrossRefADSGoogle Scholar
  25. [25]
    Y.L. Dokshitzer, A. Lucenti, G. Marchesini and G.P. Salam, On the QCD analysis of jet broadening, JHEP 01 (1998) 011 [hep-ph/9801324] [INSPIRE].CrossRefADSGoogle Scholar
  26. [26]
    A. Banfi, G.P. Salam and G. Zanderighi, Principles of general final-state resummation and automated implementation, JHEP 03 (2005) 073 [hep-ph/0407286] [INSPIRE].CrossRefADSGoogle Scholar
  27. [27]
    A.J. Larkoski and J. Thaler, Aspects of Jets at 100 TeV, Phys. Rev. D 90 (2014) 034010 [arXiv:1406.7011] [INSPIRE].ADSGoogle Scholar
  28. [28]
    C.F. Berger, T. Kucs and G.F. Sterman, Event shape/energy flow correlations, Phys. Rev. D 68 (2003) 014012 [hep-ph/0303051] [INSPIRE].ADSGoogle Scholar
  29. [29]
    L.G. Almeida, S.J. Lee, G. Perez, G.F. Sterman, I. Sung et al., Substructure of high-p T Jets at the LHC, Phys. Rev. D 79 (2009) 074017 [arXiv:0807.0234] [INSPIRE].ADSGoogle Scholar
  30. [30]
    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].CrossRefADSGoogle Scholar
  31. [31]
    P.E.L. Rakow and B.R. Webber, Transverse Momentum Moments of Hadron Distributions in QCD Jets, Nucl. Phys. B 191 (1981) 63 [INSPIRE].CrossRefADSGoogle Scholar
  32. [32]
    R.K. Ellis and B. Webber, QCD Jet Broadening in Hadron Hadron Collisions, Conf. Proc. C860623 (1986) 74.Google Scholar
  33. [33]
    E. Farhi, A QCD Test for Jets, Phys. Rev. Lett. 39 (1977) 1587 [INSPIRE].CrossRefADSGoogle Scholar
  34. [34]
    M. Dasgupta, A. Fregoso, S. Marzani and G.P. Salam, Towards an understanding of jet substructure, JHEP 09 (2013) 029 [arXiv:1307.0007] [INSPIRE].CrossRefADSGoogle Scholar
  35. [35]
    M. Dasgupta, A. Fregoso, S. Marzani and A. Powling, Jet substructure with analytical methods, Eur. Phys. J. C 73 (2013) 2623 [arXiv:1307.0013] [INSPIRE].CrossRefADSGoogle Scholar
  36. [36]
    A.J. Larkoski, S. Marzani, G. Soyez and J. Thaler, Soft Drop, JHEP 05 (2014) 146 [arXiv:1402.2657] [INSPIRE].CrossRefADSGoogle Scholar
  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].CrossRefADSGoogle Scholar
  38. [38]
    W.J. Waalewijn, Calculating the Charge of a Jet, Phys. Rev. D 86 (2012) 094030 [arXiv:1209.3019] [INSPIRE].ADSGoogle Scholar
  39. [39]
    H.-M. Chang, M. Procura, J. Thaler and W.J. Waalewijn, Calculating Track-Based Observables for the LHC, Phys. Rev. Lett. 111 (2013) 102002 [arXiv:1303.6637] [INSPIRE].CrossRefADSGoogle Scholar
  40. [40]
    H.-M. Chang, M. Procura, J. Thaler and W.J. Waalewijn, Calculating Track Thrust with Track Functions, Phys. Rev. D 88 (2013) 034030 [arXiv:1306.6630] [INSPIRE].ADSGoogle Scholar
  41. [41]
    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].CrossRefADSGoogle Scholar
  42. [42]
    I.W. Stewart, F.J. Tackmann and W.J. Waalewijn, Dissecting Soft Radiation with Factorization, arXiv:1405.6722 [INSPIRE].
  43. [43]
    J. Gallicchio and M.D. Schwartz, Pure Samples of Quark and Gluon Jets at the LHC, JHEP 10 (2011) 103 [arXiv:1104.1175] [INSPIRE].CrossRefADSGoogle Scholar
  44. [44]
    M.A. Nielsen and I.L. Chuang, Quantum Computation and Quantum Information, Cambridge University Press, 2000.Google Scholar
  45. [45]
    T. Sjöstrand, S. Mrenna and P.Z. Skands, PYTHIA 6.4 Physics and Manual, JHEP 05 (2006) 026 [hep-ph/0603175] [INSPIRE].CrossRefADSGoogle Scholar
  46. [46]
    T. Sjöstrand, S. Mrenna and P.Z. Skands, A Brief Introduction to PYTHIA 8.1, Comput. Phys. Commun. 178 (2008) 852 [arXiv:0710.3820] [INSPIRE].CrossRefzbMATHADSGoogle Scholar
  47. [47]
    M. Bahr, S. Gieseke, M.A. Gigg, D. Grellscheid, K. Hamilton et al., HERWIG++ Physics and Manual, Eur. Phys. J. C 58 (2008) 639 [arXiv:0803.0883] [INSPIRE].CrossRefADSGoogle Scholar
  48. [48]
    S. Gieseke, D. Grellscheid, K. Hamilton, A. Papaefstathiou, S. Platzer et al., HERWIG++ 2.5 Release Note, arXiv:1102.1672 [INSPIRE].
  49. [49]
    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].CrossRefADSGoogle Scholar
  50. [50]
    J. Thaler and K. Van Tilburg, Identifying Boosted Objects with N-subjettiness, JHEP 03 (2011) 015 [arXiv:1011.2268] [INSPIRE].CrossRefADSGoogle Scholar
  51. [51]
    J. Thaler and K. Van Tilburg, Maximizing Boosted Top Identification by Minimizing N-subjettiness, JHEP 02 (2012) 093 [arXiv:1108.2701] [INSPIRE].CrossRefADSGoogle Scholar
  52. [52]
    M. Cacciari, G.P. Salam and G. Soyez, FastJet User Manual, Eur. Phys. J. C 72 (2012) 1896 [arXiv:1111.6097] [INSPIRE].CrossRefADSGoogle Scholar
  53. [53]
    A.J. Larkoski and J. Thaler, Unsafe but Calculable: Ratios of Angularities in Perturbative QCD, JHEP 09 (2013) 137 [arXiv:1307.1699] [INSPIRE].CrossRefADSGoogle Scholar
  54. [54]
    A.J. Larkoski, I. Moult and D. Neill, Toward Multi-Differential Cross Sections: Measuring Two Angularities on a Single Jet, JHEP 09 (2014) 046 [arXiv:1401.4458] [INSPIRE].CrossRefADSGoogle Scholar
  55. [55]
    M. Procura, W.J. Waalewijn and L. Zeune, Resummation of Double-Differential Cross Sections and Fully-Unintegrated Parton Distribution Functions, arXiv:1410.6483 [INSPIRE].
  56. [56]
    C.W. Bauer, S. Fleming and M.E. Luke, Summing Sudakov logarithms in BX s γ in effective field theory, Phys. Rev. D 63 (2000) 014006 [hep-ph/0005275] [INSPIRE].ADSGoogle Scholar
  57. [57]
    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
  58. [58]
    C.W. Bauer and I.W. Stewart, Invariant operators in collinear effective theory, Phys. Lett. B 516 (2001) 134 [hep-ph/0107001] [INSPIRE].CrossRefADSGoogle Scholar
  59. [59]
    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
  60. [60]
    D.E. Soper and M. Spannowsky, Finding physics signals with shower deconstruction, Phys. Rev. D 84 (2011) 074002 [arXiv:1102.3480] [INSPIRE].ADSGoogle Scholar
  61. [61]
    A. Capella, I.M. Dremin, J.W. Gary, V.A. Nechitailo and J. Tran Thanh Van, Evolution of average multiplicities of quark and gluon jets, Phys. Rev. D 61 (2000) 074009 [hep-ph/9910226] [INSPIRE].ADSGoogle Scholar
  62. [62]
    P. Bolzoni, B.A. Kniehl and A.V. Kotikov, Gluon and quark jet multiplicities at N 3 LO+NNLL, Phys. Rev. Lett. 109 (2012) 242002 [arXiv:1209.5914] [INSPIRE].CrossRefADSGoogle Scholar
  63. [63]
    M. Procura and I.W. Stewart, Quark Fragmentation within an Identified Jet, Phys. Rev. D 81 (2010) 074009 [Erratum ibid. D 83 (2011) 039902] [arXiv:0911.4980] [INSPIRE].
  64. [64]
    A. Jain, M. Procura and W.J. Waalewijn, Parton Fragmentation within an Identified Jet at NNLL, JHEP 05 (2011) 035 [arXiv:1101.4953] [INSPIRE].CrossRefADSGoogle Scholar
  65. [65]
    V.N. Gribov and L.N. Lipatov, Deep inelastic e p scattering in perturbation theory, Sov. J. Nucl. Phys. 15 (1972) 438 [INSPIRE].Google Scholar
  66. [66]
    H. Georgi and H.D. Politzer, Electroproduction scaling in an asymptotically free theory of strong interactions, Phys. Rev. D 9 (1974) 416 [INSPIRE].ADSGoogle Scholar
  67. [67]
    D.J. Gross and F. Wilczek, asymptotically free gauge theories. 2., Phys. Rev. D 9 (1974) 980 [INSPIRE].
  68. [68]
    G. Altarelli and G. Parisi, Asymptotic Freedom in Parton Language, Nucl. Phys. B 126 (1977) 298 [INSPIRE].CrossRefADSGoogle Scholar
  69. [69]
    Y.L. Dokshitzer, Calculation of the Structure Functions for Deep Inelastic Scattering and e + e Annihilation by Perturbation Theory in Quantum Chromodynamics., Sov. Phys. JETP 46 (1977) 641 [INSPIRE].ADSGoogle Scholar
  70. [70]
    M. Dasgupta and G.P. Salam, Resummation of nonglobal QCD observables, Phys. Lett. B 512 (2001) 323 [hep-ph/0104277] [INSPIRE].ADSGoogle Scholar
  71. [71]
    S. Catani, B.R. Webber and G. Marchesini, QCD coherent branching and semiinclusive processes at large x, Nucl. Phys. B 349 (1991) 635 [INSPIRE].CrossRefADSGoogle Scholar
  72. [72]
    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].CrossRefADSGoogle Scholar
  73. [73]
    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].CrossRefADSGoogle Scholar
  74. [74]
    L.G. Almeida, S.D. Ellis, C. Lee, G. Sterman, I. Sung et al., Comparing and counting logs in direct and effective methods of QCD resummation, JHEP 04 (2014) 174 [arXiv:1401.4460] [INSPIRE].CrossRefADSGoogle Scholar

Copyright information

© The Author(s) 2014

Authors and Affiliations

  • Andrew J. Larkoski
    • 1
  • Jesse Thaler
    • 1
    Email author
  • Wouter J. Waalewijn
    • 2
    • 3
  1. 1.Center for Theoretical PhysicsMassachusetts Institute of TechnologyCambridgeU.S.A.
  2. 2.Nikhef, Theory GroupAmsterdamThe Netherlands
  3. 3.ITFAUniversity of AmsterdamAmsterdamThe Netherlands

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