Download PDF

How much information is in a jet?

Open Access
Regular Article - Theoretical Physics
First Online:
Received:
Accepted:

Abstract

Machine learning techniques are increasingly being applied toward data analyses at the Large Hadron Collider, especially with applications for discrimination of jets with different originating particles. Previous studies of the power of machine learning to jet physics have typically employed image recognition, natural language processing, or other algorithms that have been extensively developed in computer science. While these studies have demonstrated impressive discrimination power, often exceeding that of widely-used observables, they have been formulated in a non-constructive manner and it is not clear what additional information the machines are learning. In this paper, we study machine learning for jet physics constructively, expressing all of the information in a jet onto sets of observables that completely and minimally span N-body phase space. For concreteness, we study the application of machine learning for discrimination of boosted, hadronic decays of Z bosons from jets initiated by QCD processes. Our results demonstrate that the information in a jet that is useful for discrimination power of QCD jets from Z bosons is saturated by only considering observables that are sensitive to 4-body (8 dimensional) phase space.

Keywords

Jets QCD Phenomenology 
Download to read the full article text

References

  1. [1]
    D. Adams et al., Towards an Understanding of the Correlations in Jet Substructure, Eur. Phys. J. C 75 (2015) 409 [arXiv:1504.00679] [INSPIRE].ADSCrossRefGoogle Scholar
  2. [2]
    A. Altheimer 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].
  3. [3]
    A. Altheimer 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
  4. [4]
    A. Abdesselam 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
  5. [5]
    F.V. Tkachov, Measuring multijet structure of hadronic energy flow or What is a jet?, Int. J. Mod. Phys. A 12 (1997) 5411 [hep-ph/9601308] [INSPIRE].
  6. [6]
    N.A. Sveshnikov and F.V. Tkachov, Jets and quantum field theory, Phys. Lett. B 382 (1996) 403 [hep-ph/9512370] [INSPIRE].
  7. [7]
    P.S. Cherzor and N.A. Sveshnikov, Jet observables and energy momentum tensor, in Quantum field theory and high-energy physics. Proceedings, Workshop, QFTHEP’97, Samara, Russia, September 4–10, 1997, pp. 402–407, (1997), hep-ph/9710349 [INSPIRE].
  8. [8]
    F.V. Tkachov, A theory of jet definition, Int. J. Mod. Phys. A 17 (2002) 2783 [hep-ph/9901444] [INSPIRE].
  9. [9]
    J. Cogan, M. Kagan, E. Strauss and A. Schwarztman, Jet-Images: Computer Vision Inspired Techniques for Jet Tagging, JHEP 02 (2015) 118 [arXiv:1407.5675] [INSPIRE].ADSCrossRefGoogle Scholar
  10. [10]
    L.G. Almeida, M. Backovic, M. Cliche, S.J. Lee and M. Perelstein, Playing Tag with ANN: Boosted Top Identification with Pattern Recognition, JHEP 07 (2015) 086 [arXiv:1501.05968] [INSPIRE].ADSCrossRefGoogle Scholar
  11. [11]
    L. de Oliveira, M. Kagan, L. Mackey, B. Nachman and A. Schwartzman, Jet-images — deep learning edition, JHEP 07 (2016) 069 [arXiv:1511.05190] [INSPIRE].CrossRefGoogle Scholar
  12. [12]
    P. Baldi, K. Bauer, C. Eng, P. Sadowski and D. Whiteson, Jet Substructure Classification in High-Energy Physics with Deep Neural Networks, Phys. Rev. D 93 (2016) 094034 [arXiv:1603.09349] [INSPIRE].ADSGoogle Scholar
  13. [13]
    D. Guest, J. Collado, P. Baldi, S.-C. Hsu, G. Urban and D. Whiteson, Jet Flavor Classification in High-Energy Physics with Deep Neural Networks, Phys. Rev. D 94 (2016) 112002 [arXiv:1607.08633] [INSPIRE].ADSGoogle Scholar
  14. [14]
    J.S. Conway, R. Bhaskar, R.D. Erbacher and J. Pilot, Identification of High-Momentum Top Quarks, Higgs Bosons and W and Z Bosons Using Boosted Event Shapes, Phys. Rev. D 94 (2016) 094027 [arXiv:1606.06859] [INSPIRE].ADSGoogle Scholar
  15. [15]
    J. Barnard, E.N. Dawe, M.J. Dolan and N. Rajcic, Parton Shower Uncertainties in Jet Substructure Analyses with Deep Neural Networks, Phys. Rev. D 95 (2017) 014018 [arXiv:1609.00607] [INSPIRE].ADSGoogle Scholar
  16. [16]
    P.T. Komiske, E.M. Metodiev and M.D. Schwartz, Deep learning in color: towards automated quark/gluon jet discrimination, JHEP 01 (2017) 110 [arXiv:1612.01551] [INSPIRE].ADSCrossRefGoogle Scholar
  17. [17]
    L. de Oliveira, M. Paganini and B. Nachman, Learning Particle Physics by Example: Location-Aware Generative Adversarial Networks for Physics Synthesis, arXiv:1701.05927 [INSPIRE].
  18. [18]
    G. Kasieczka, T. Plehn, M. Russell and T. Schell, Deep-learning Top Taggers or The End of QCD?, JHEP 05 (2017) 006 [arXiv:1701.08784] [INSPIRE].ADSCrossRefGoogle Scholar
  19. [19]
    G. Louppe, K. Cho, C. Becot and K. Cranmer, QCD-Aware Recursive Neural Networks for Jet Physics, arXiv:1702.00748 [INSPIRE].
  20. [20]
    L.M. Dery, B. Nachman, F. Rubbo and A. Schwartzman, Weakly Supervised Classification in High Energy Physics, JHEP 05 (2017) 145 [arXiv:1702.00414] [INSPIRE].ADSCrossRefGoogle Scholar
  21. [21]
    J. Pearkes, W. Fedorko, A. Lister and C. Gay, Jet Constituents for Deep Neural Network Based Top Quark Tagging, arXiv:1704.02124 [INSPIRE].
  22. [22]
    A.J. Larkoski and J. Thaler, Unsafe but Calculable: Ratios of Angularities in Perturbative QCD, JHEP 09 (2013) 137 [arXiv:1307.1699] [INSPIRE].ADSCrossRefGoogle Scholar
  23. [23]
    A.J. Larkoski, S. Marzani and J. Thaler, Sudakov Safety in Perturbative QCD, Phys. Rev. D 91 (2015) 111501 [arXiv:1502.01719] [INSPIRE].ADSGoogle Scholar
  24. [24]
    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
  25. [25]
    J. Thaler and K. Van Tilburg, Identifying Boosted Objects with N-subjettiness, JHEP 03 (2011) 015 [arXiv:1011.2268] [INSPIRE].ADSCrossRefGoogle Scholar
  26. [26]
    J. Thaler and K. Van Tilburg, Maximizing Boosted Top Identification by Minimizing N-subjettiness, JHEP 02 (2012) 093 [arXiv:1108.2701] [INSPIRE].ADSCrossRefGoogle Scholar
  27. [27]
    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
  28. [28]
    I. Moult, L. Necib and J. Thaler, New Angles on Energy Correlation Functions, JHEP 12 (2016) 153 [arXiv:1609.07483] [INSPIRE].ADSCrossRefGoogle Scholar
  29. [29]
    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
  30. [30]
    S.D. Ellis and D.E. Soper, Successive combination jet algorithm for hadron collisions, Phys. Rev. D 48 (1993) 3160 [hep-ph/9305266] [INSPIRE].
  31. [31]
    G.C. Blazey et al., Run II jet physics, in QCD and weak boson physics in Run II. Proceedings, Batavia, U.S.A., March 4-6, June 3-4, November 4-6, 1999, pp. 47–77, (2000), hep-ex/0005012 [INSPIRE].
  32. [32]
    D. Bertolini, T. Chan and J. Thaler, Jet Observables Without Jet Algorithms, JHEP 04 (2014) 013 [arXiv:1310.7584] [INSPIRE].ADSCrossRefGoogle Scholar
  33. [33]
    A.J. Larkoski, D. Neill and J. Thaler, Jet Shapes with the Broadening Axis, JHEP 04 (2014) 017 [arXiv:1401.2158] [INSPIRE].ADSCrossRefGoogle Scholar
  34. [34]
    A.J. Larkoski and J. Thaler, Aspects of jets at 100 TeV, Phys. Rev. D 90 (2014) 034010 [arXiv:1406.7011] [INSPIRE].ADSGoogle Scholar
  35. [35]
    J. Alwall et al., The automated computation of tree-level and next-to-leading order differential cross sections and their matching to parton shower simulations, JHEP 07 (2014) 079 [arXiv:1405.0301] [INSPIRE].ADSCrossRefGoogle Scholar
  36. [36]
    T. Sjöstrand, S. Mrenna and P.Z. Skands, PYTHIA 6.4 Physics and Manual, JHEP 05 (2006) 026 [hep-ph/0603175] [INSPIRE].
  37. [37]
    T. Sjötrand et al., An introduction to PYTHIA 8.2, Comput. Phys. Commun. 191 (2015) 159 [arXiv:1410.3012] [INSPIRE].
  38. [38]
    M. Bahr et al., HERWIG++ Physics and Manual, Eur. Phys. J. C 58 (2008) 639 [arXiv:0803.0883] [INSPIRE].ADSCrossRefGoogle Scholar
  39. [39]
    J. Bellm et al., HERWIG 7.0/HERWIG++ 3.0 release note, Eur. Phys. J. C 76 (2016) 196 [arXiv:1512.01178] [INSPIRE].
  40. [40]
    M. Cacciari, G.P. Salam and G. Soyez, FastJet User Manual, Eur. Phys. J. C 72 (2012) 1896 [arXiv:1111.6097] [INSPIRE].ADSCrossRefGoogle Scholar
  41. [41]
    M. Cacciari and G.P. Salam, Dispelling the N 3 myth for the k t jet-finder, Phys. Lett. B 641 (2006) 57 [hep-ph/0512210] [INSPIRE].
  42. [42]
    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
  43. [43]
    A.J. Larkoski, I. Moult and D. Neill, Power Counting to Better Jet Observables, JHEP 12 (2014) 009 [arXiv:1409.6298] [INSPIRE].ADSCrossRefGoogle Scholar
  44. [44]
    The HDF Group, Hierarchical Data Format, version 5, 1997-NNNN, http://www.hdfgroup.org/HDF5/.
  45. [45]
    F. Chollet, Keras, https://github.com/fchollet/keras, (2015).
  46. [46]
    F. Pedregosa et al., Scikit-learn: Machine Learning in Python, J. Mach. Learn. Res. 12 (2011) 2825.MathSciNetMATHGoogle Scholar
  47. [47]
    N. Srivastava, G. Hinton, A. Krizhevsky, I. Sutskever and R. Salakhutdinov, Dropout: A simple way to prevent neural networks from overfitting, J. Mach. Learn. Res. 15 (2014) 1929.MathSciNetMATHGoogle Scholar
  48. [48]
    V. Nair and G.E. Hinton, Rectified linear units improve restricted boltzmann machines., in ICML, J. Fürnkranz and T. Joachims eds., Omnipress, (2010), pp. 807–814.Google Scholar
  49. [49]
    D.P. Kingma and J. Ba, Adam: A method for stochastic optimization, arXiv:1412.6980.
  50. [50]
    A.J. Larkoski, I. Moult and D. Neill, Non-Global Logarithms, Factorization and the Soft Substructure of Jets, JHEP 09 (2015) 143 [arXiv:1501.04596] [INSPIRE].ADSCrossRefGoogle Scholar
  51. [51]
    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].ADSCrossRefGoogle Scholar
  52. [52]
    M. Procura, W.J. Waalewijn and L. Zeune, Resummation of Double-Differential Cross sections and Fully-Unintegrated Parton Distribution Functions, JHEP 02 (2015) 117 [arXiv:1410.6483] [INSPIRE].ADSCrossRefGoogle Scholar
  53. [53]
    A.J. Larkoski and I. Moult, The Singular Behavior of Jet Substructure Observables, Phys. Rev. D 93 (2016) 014017 [arXiv:1510.08459] [INSPIRE].ADSGoogle Scholar
  54. [54]
    G.P. Salam, L. Schunk and G. Soyez, Dichroic subjettiness ratios to distinguish colour flows in boosted boson tagging, JHEP 03 (2017) 022 [arXiv:1612.03917] [INSPIRE].ADSCrossRefGoogle Scholar
  55. [55]
    J. Gallicchio and M.D. Schwartz, Quark and Gluon Jet Substructure, JHEP 04 (2013) 090 [arXiv:1211.7038] [INSPIRE].ADSCrossRefGoogle Scholar
  56. [56]
    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].
  57. [57]
    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
  58. [58]
    E. Izaguirre, B. Shuve and I. Yavin, Improving Identification of Dijet Resonances at Hadron Colliders, Phys. Rev. Lett. 114 (2015) 041802 [arXiv:1407.7037] [INSPIRE].ADSCrossRefGoogle Scholar
  59. [59]
    A.J. Larkoski, I. Moult and D. Neill, Analytic Boosted Boson Discrimination, JHEP 05 (2016) 117 [arXiv:1507.03018] [INSPIRE].ADSCrossRefGoogle Scholar
  60. [60]
    J.R. Andersen et al., Les Houches 2015: Physics at TeV Colliders Standard Model Working Group Report, in 9th Les Houches Workshop on Physics at TeV Colliders (PhysTeV 2015) Les Houches, France, June 1-19, 2015, (2016), arXiv:1605.04692 [INSPIRE].
  61. [61]
    ATLAS collaboration, Measurement of the charged-particle multiplicity inside jets from \( \sqrt{s}=8 \) TeV pp collisions with the ATLAS detector, Eur. Phys. J. C 76 (2016) 322 [arXiv:1602.00988] [INSPIRE].
  62. [62]
    P. Gras et al., Systematics of quark/gluon tagging, arXiv:1704.03878 [INSPIRE].
  63. [63]
    A. Hocker et al., TMVA - Toolkit for Multivariate Data Analysis, PoS(ACAT)040 [physics/0703039] [INSPIRE].
  64. [64]
    P. Speckmayer, A. Hocker, J. Stelzer and H. Voss, The toolkit for multivariate data analysis, TMVA 4, J. Phys. Conf. Ser. 219 (2010) 032057 [INSPIRE].CrossRefGoogle Scholar

Copyright information

© The Author(s) 2017

Authors and Affiliations

  1. 1.Physics DepartmentReed CollegePortlandU.S.A.

Personalised recommendations