Skip to main content

The Lund jet plane

A preprint version of the article is available at arXiv.


Lund diagrams, a theoretical representation of the phase space within jets, have long been used in discussing parton showers and resummations. We point out that they can be created for individual jets through repeated Cambridge/Aachen declustering, providing a powerful visual representation of the radiation within any given jet. Concentrating here on the primary Lund plane, we outline some of its analytical properties, highlight its scope for constraining Monte Carlo simulations and comment on its relation with existing observables such as the zg variable and the iterated soft-drop multiplicity. We then examine its use for boosted electroweak boson tagging at high momenta. It provides good performance when used as an input to machine learning. Much of this performance can be reproduced also within a transparent log-likelihood method, whose underlying assumption is that different regions of the primary Lund plane are largely decorrelated. This suggests a potential for unique insight and experimental validation of the features being used by machine-learning approaches.


  1. [1]

    A.J. Larkoski, I. Moult and B. Nachman, Jet Substructure at the Large Hadron Collider: A Review of Recent Advances in Theory and Machine Learning, arXiv:1709.04464 [INSPIRE].

  2. [2]

    L. Asquith et al., Jet Substructure at the Large Hadron Collider: Experimental Review, arXiv:1803.06991 [INSPIRE].

  3. [3]

    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].

    ADS  Article  Google Scholar 

  4. [4]

    J. Thaler and L.-T. Wang, Strategies to Identify Boosted Tops, JHEP 07 (2008) 092 [arXiv:0806.0023] [INSPIRE].

    ADS  Article  Google Scholar 

  5. [5]

    D.E. Kaplan, K. Rehermann, M.D. Schwartz and B. Tweedie, Top Tagging: A Method for Identifying Boosted Hadronically Decaying Top Quarks, Phys. Rev. Lett. 101 (2008) 142001 [arXiv:0806.0848] [INSPIRE].

    ADS  Article  Google Scholar 

  6. [6]

    S.D. Ellis, C.K. Vermilion and J.R. Walsh, Techniques for improved heavy particle searches with jet substructure, Phys. Rev. D 80 (2009) 051501 [arXiv:0903.5081] [INSPIRE].

  7. [7]

    S.D. Ellis, C.K. Vermilion and J.R. Walsh, Recombination Algorithms and Jet Substructure: Pruning as a Tool for Heavy Particle Searches, Phys. Rev. D 81 (2010) 094023 [arXiv:0912.0033] [INSPIRE].

  8. [8]

    T. Plehn, G.P. Salam and M. Spannowsky, Fat Jets for a Light Higgs, Phys. Rev. Lett. 104 (2010) 111801 [arXiv:0910.5472] [INSPIRE].

  9. [9]

    J. Thaler and K. Van Tilburg, Identifying Boosted Objects with N-subjettiness, JHEP 03 (2011) 015 [arXiv:1011.2268] [INSPIRE].

  10. [10]

    J. Thaler and K. Van Tilburg, Maximizing Boosted Top Identification by Minimizing N-subjettiness, JHEP 02 (2012) 093 [arXiv:1108.2701] [INSPIRE].

    ADS  Article  Google Scholar 

  11. [11]

    A.J. Larkoski, G.P. Salam and J. Thaler, Energy Correlation Functions for Jet Substructure, JHEP 06 (2013) 108 [arXiv:1305.0007] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  12. [12]

    Y.-T. Chien, Telescoping jets: Probing hadronic event structure with multiple R’s, Phys. Rev. D 90 (2014) 054008 [arXiv:1304.5240] [INSPIRE].

  13. [13]

    A.J. Larkoski, I. Moult and D. Neill, Power Counting to Better Jet Observables, JHEP 12 (2014) 009 [arXiv:1409.6298] [INSPIRE].

  14. [14]

    A.J. Larkoski, J. Thaler and W.J. Waalewijn, Gaining (Mutual) Information about Quark/Gluon Discrimination, JHEP 11 (2014) 129 [arXiv:1408.3122] [INSPIRE].

    ADS  Article  Google Scholar 

  15. [15]

    I. Moult, L. Necib and J. Thaler, New Angles on Energy Correlation Functions, JHEP 12 (2016) 153 [arXiv:1609.07483] [INSPIRE].

  16. [16]

    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].

    ADS  Article  Google Scholar 

  17. [17]

    M.H. Seymour, Jet shapes in hadron collisions: Higher orders, resummation and hadronization, Nucl. Phys. B 513 (1998) 269 [hep-ph/9707338] [INSPIRE].

  18. [18]

    I. Feige, M.D. Schwartz, I.W. Stewart and J. Thaler, Precision Jet Substructure from Boosted Event Shapes, Phys. Rev. Lett. 109 (2012) 092001 [arXiv:1204.3898] [INSPIRE].

  19. [19]

    M. Dasgupta, A. Fregoso, S. Marzani and G.P. Salam, Towards an understanding of jet substructure, JHEP 09 (2013) 029 [arXiv:1307.0007] [INSPIRE].

    ADS  Article  Google Scholar 

  20. [20]

    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].

  21. [21]

    Y.-T. Chien and I. Vitev, Jet Shape Resummation Using Soft-Collinear Effective Theory, JHEP 12 (2014) 061 [arXiv:1405.4293] [INSPIRE].

    ADS  Article  Google Scholar 

  22. [22]

    D. Bertolini, J. Thaler and J.R. Walsh, The First Calculation of Fractional Jets, JHEP 05 (2015) 008 [arXiv:1501.01965] [INSPIRE].

  23. [23]

    M. Dasgupta, L. Schunk and G. Soyez, Jet shapes for boosted jet two-prong decays from first-principles, JHEP 04 (2016) 166 [arXiv:1512.00516] [INSPIRE].

    ADS  Google Scholar 

  24. [24]

    C. Frye, A.J. Larkoski, M.D. Schwartz and K. Yan, Precision physics with pile-up insensitive observables, arXiv:1603.06375 [INSPIRE].

  25. [25]

    C. Frye, A.J. Larkoski, M.D. Schwartz and K. Yan, Factorization for groomed jet substructure beyond the next-to-leading logarithm, JHEP 07 (2016) 064 [arXiv:1603.09338] [INSPIRE].

    ADS  Article  Google Scholar 

  26. [26]

    M. Dasgupta, A. Powling, L. Schunk and G. Soyez, Improved jet substructure methods: Y-splitter and variants with grooming, JHEP 12 (2016) 079 [arXiv:1609.07149] [INSPIRE].

    ADS  Article  Google Scholar 

  27. [27]

    S. Marzani, L. Schunk and G. Soyez, The jet mass distribution after Soft Drop, Eur. Phys. J. C 78 (2018) 96 [arXiv:1712.05105] [INSPIRE].

  28. [28]

    S. Marzani, L. Schunk and G. Soyez, A study of jet mass distributions with grooming, JHEP 07 (2017) 132 [arXiv:1704.02210] [INSPIRE].

    ADS  Article  Google Scholar 

  29. [29]

    A.J. Larkoski, I. Moult and D. Neill, Factorization and Resummation for Groomed Multi-Prong Jet Shapes, JHEP 02 (2018) 144 [arXiv:1710.00014] [INSPIRE].

    ADS  Article  Google Scholar 

  30. [30]

    I. Moult, B. Nachman and D. Neill, Convolved Substructure: Analytically Decorrelating Jet Substructure Observables, JHEP 05 (2018) 002 [arXiv:1710.06859] [INSPIRE].

    ADS  Article  Google Scholar 

  31. [31]

    CMS collaboration, Identification techniques for highly boosted W bosons that decay into hadrons, JHEP 12 (2014) 017 [arXiv:1410.4227] [INSPIRE].

  32. [32]

    ATLAS collaboration, Identification of boosted, hadronically decaying W bosons and comparisons with ATLAS data taken at \( \sqrt{s}=8 \) TeV, Eur. Phys. J. C 76 (2016) 154 [arXiv:1510.05821] [INSPIRE].

  33. [33]

    ATLAS collaboration, Search for high-mass diboson resonances with boson-tagged jets in proton-proton collisions at \( \sqrt{s}=8 \) TeV with the ATLAS detector, JHEP 12 (2015) 055 [arXiv:1506.00962] [INSPIRE].

  34. [34]

    ATLAS collaboration, Measurement of the Soft-Drop Jet Mass in pp Collisions at \( \sqrt{s}=13 \) TeV with the ATLAS Detector, Phys. Rev. Lett. 121(2018) 092001 [arXiv:1711.08341] [INSPIRE].

  35. [35]

    CMS collaboration, Measurement of jet substructure observables in tt events from pp collisions at \( \sqrt{s}=13 \) TeV, CMS-PAS-TOP-17-013 (2017).

  36. [36]

    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].

    ADS  Article  Google Scholar 

  37. [37]

    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].

    Article  Google Scholar 

  38. [38]

    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].

    ADS  Article  MATH  Google Scholar 

  39. [39]

    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].

    ADS  Article  Google Scholar 

  40. [40]

    G. Louppe, K. Cho, C. Becot and K. Cranmer, QCD-Aware Recursive Neural Networks for Jet Physics, arXiv:1702.00748 [INSPIRE].

  41. [41]

    S. Egan, W. Fedorko, A. Lister, J. Pearkes and C. Gay, Long Short-Term Memory (LSTM) networks with jet constituents for boosted top tagging at the LHC, arXiv:1711.09059 [INSPIRE].

  42. [42]

    A. Andreassen, I. Feige, C. Frye and M.D. Schwartz, JUNIPR: a Framework for Unsupervised Machine Learning in Particle Physics, arXiv:1804.09720 [INSPIRE].

  43. [43]

    K. Datta and A. Larkoski, How Much Information is in a Jet?, JHEP 06 (2017) 073 [arXiv:1704.08249] [INSPIRE].

    ADS  Article  Google Scholar 

  44. [44]

    K. Datta and A.J. Larkoski, Novel Jet Observables from Machine Learning, JHEP 03 (2018) 086 [arXiv:1710.01305] [INSPIRE].

  45. [45]

    P.T. Komiske, E.M. Metodiev and J. Thaler, Energy flow polynomials: A complete linear basis for jet substructure, JHEP 04 (2018) 013 [arXiv:1712.07124] [INSPIRE].

    Article  Google Scholar 

  46. [46]

    E.M. Metodiev, B. Nachman and J. Thaler, Classification without labels: Learning from mixed samples in high energy physics, JHEP 10 (2017) 174 [arXiv:1708.02949] [INSPIRE].

    ADS  Article  Google Scholar 

  47. [47]

    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].

    ADS  Article  MATH  Google Scholar 

  48. [48]

    B. Andersson, G. Gustafson, L. Lönnblad and U. Pettersson, Coherence Effects in Deep Inelastic Scattering, Z. Phys. C 43 (1989) 625 [INSPIRE].

  49. [49]

    Y.L. Dokshitzer, G.D. Leder, S. Moretti and B.R. Webber, Better jet clustering algorithms, JHEP 08 (1997) 001 [hep-ph/9707323] [INSPIRE].

  50. [50]

    M. Wobisch and T. Wengler, Hadronization corrections to jet cross-sections in deep inelastic scattering, in Monte Carlo generators for HERA physics. Proceedings, Workshop, Hamburg, Germany, 1998-1999, pp. 270-279, hep-ph/9907280 [INSPIRE].

  51. [51]

    M. Cacciari, G.P. Salam and G. Soyez, The anti-k t jet clustering algorithm, JHEP 04 (2008) 063 [arXiv:0802.1189] [INSPIRE].

    ADS  Article  MATH  Google Scholar 

  52. [52]

    T. Sjöstrand et al., An Introduction to PYTHIA 8.2, Comput. Phys. Commun. 191 (2015) 159 [arXiv:1410.3012] [INSPIRE].

  53. [53]

    P. Skands, S. Carrazza and J. Rojo, Tuning PYTHIA 8.1: the Monash 2013 Tune, Eur. Phys. J. C 74 (2014) 3024 [arXiv:1404.5630] [INSPIRE].

  54. [54]

    M. Dasgupta, F. Dreyer, G.P. Salam and G. Soyez, Small-radius jets to all orders in QCD, JHEP 04 (2015) 039 [arXiv:1411.5182] [INSPIRE].

    ADS  Article  Google Scholar 

  55. [55]

    M. Dasgupta, F.A. Dreyer, G.P. Salam and G. Soyez, Inclusive jet spectrum for small-radius jets, JHEP 06 (2016) 057 [arXiv:1602.01110] [INSPIRE].

    ADS  Article  Google Scholar 

  56. [56]

    M. Dasgupta and G.P. Salam, Resummation of nonglobal QCD observables, Phys. Lett. B 512 (2001) 323 [hep-ph/0104277] [INSPIRE].

  57. [57]

    R.B. Appleby and M.H. Seymour, Nonglobal logarithms in interjet energy flow with kt clustering requirement, JHEP 12 (2002) 063 [hep-ph/0211426] [INSPIRE].

  58. [58]

    Y. Delenda, R. Appleby, M. Dasgupta and A. Banfi, On QCD resummation with k(t) clustering, JHEP 12 (2006) 044 [hep-ph/0610242] [INSPIRE].

  59. [59]

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

  60. [60]

    J. Bellm et al., HERWIG 7.1 Release Note, arXiv:1705.06919 [INSPIRE].

  61. [61]

    Y.L. Dokshitzer and B.R. Webber, Calculation of power corrections to hadronic event shapes, Phys. Lett. B 352 (1995) 451 [hep-ph/9504219] [INSPIRE].

  62. [62]

    Y.L. Dokshitzer, G. Marchesini and B.R. Webber, Dispersive approach to power behaved contributions in QCD hard processes, Nucl. Phys. B 469 (1996) 93 [hep-ph/9512336] [INSPIRE].

  63. [63]

    J.R. Forshaw, A. Kyrieleis and M.H. Seymour, Super-leading logarithms in non-global observables in QCD, JHEP 08 (2006) 059 [hep-ph/0604094] [INSPIRE].

  64. [64]

    S. Catani, D. de Florian and G. Rodrigo, Space-like (versus time-like) collinear limits in QCD: Is factorization violated?, JHEP 07 (2012) 026 [arXiv:1112.4405] [INSPIRE].

    ADS  Article  Google Scholar 

  65. [65]

    S. Catani and M.H. 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].

  66. [66]

    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].

  67. [67]

    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].

  68. [68]

    M. Cacciari, G.P. Salam and G. Soyez, FastJet User Manual, Eur. Phys. J. C 72 (2012) 1896 [arXiv:1111.6097] [INSPIRE].

  69. [69]

    C. Frye, A.J. Larkoski, J. Thaler and K. Zhou, Casimir Meets Poisson: Improved Quark/Gluon Discrimination with Counting Observables, JHEP 09 (2017) 083 [arXiv:1704.06266] [INSPIRE].

    ADS  Article  Google Scholar 

  70. [70]

    A.J. Larkoski, S. Marzani, G. Soyez and J. Thaler, Soft Drop, JHEP 05 (2014) 146 [arXiv:1402.2657] [INSPIRE].

    ADS  Article  Google Scholar 

  71. [71]

    A. Larkoski, S. Marzani, J. Thaler, A. Tripathee and W. Xue, Exposing the QCD Splitting Function with CMS Open Data, Phys. Rev. Lett. 119 (2017) 132003 [arXiv:1704.05066] [INSPIRE].

    ADS  Article  Google Scholar 

  72. [72]

    D.E. Soper and M. Spannowsky, Finding physics signals with shower deconstruction, Phys. Rev. D 84 (2011) 074002 [arXiv:1102.3480] [INSPIRE].

  73. [73]

    S. Hochreiter and J. Schmidhuber, Long short-term memory, Neural Comput. 9 (1997) 1735.

    Article  Google Scholar 

  74. [74]

    K. Cho, B. van Merrienboer, Ç. Gülçehre, F. Bougares, H. Schwenkand Y. Bengio, Learning phrase representations using RNN encoder-decoder for statistical machine translation, arXiv:1406.1078.

  75. [75]

    F. Chollet, Keras,, (2015).

  76. [76]

    M. Abadi et al., TensorFlow: Large-scale machine learning on heterogeneous systems, (2015), software available from

  77. [77]

    K. He, X. Zhang, S. Ren and J. Sun, Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification, arXiv:1502.01852 [INSPIRE].

  78. [78]

    D.P. Kingma and J. Ba, Adam: A Method for Stochastic Optimization, arXiv:1412.6980 [INSPIRE].

  79. [79]

    A. Hocker et al., TMVA — Toolkit for Multivariate Data Analysis, PoS(ACAT)040 [physics/0703039] [INSPIRE].

  80. [80]

    J.R. Andersen et al., Les Houches 2017: Physics at TeV Colliders Standard Model Working Group Report, arXiv:1803.07977 [INSPIRE].

  81. [81]

    DELPHES 3 collaboration, J. de Favereau et al., DELPHES 3, A modular framework for fast simulation of a generic collider experiment, JHEP 02 (2014) 057 [arXiv:1307.6346] [INSPIRE].

  82. [82]

    A. Katz, M. Son and B. Tweedie, Jet Substructure and the Search for Neutral Spin-One Resonances in Electroweak Boson Channels, JHEP 03 (2011) 011 [arXiv:1010.5253] [INSPIRE].

    ADS  Article  Google Scholar 

  83. [83]

    M. Son, C. Spethmann and B. Tweedie, Diboson-Jets and the Search for Resonant Zh Production, JHEP 08 (2012) 160 [arXiv:1204.0525] [INSPIRE].

    ADS  Article  Google Scholar 

  84. [84]

    S. Schaetzel and M. Spannowsky, Tagging highly boosted top quarks, Phys. Rev. D 89 (2014) 014007 [arXiv:1308.0540] [INSPIRE].

  85. [85]

    A.J. Larkoski, F. Maltoni and M. Selvaggi, Tracking down hyper-boosted top quarks, JHEP 06 (2015) 032 [arXiv:1503.03347] [INSPIRE].

    ADS  Article  Google Scholar 

  86. [86]

    S. Bressler, T. Flacke, Y. Kats, S.J. Lee and G. Perez, Hadronic Calorimeter Shower Size: Challenges and Opportunities for Jet Substructure in the Superboosted Regime, Phys. Lett. B 756 (2016) 137 [arXiv:1506.02656] [INSPIRE].

  87. [87]

    Z. Han, M. Son and B. Tweedie, Top-Tagging at the Energy Frontier, Phys. Rev. D 97 (2018) 036023 [arXiv:1707.06741] [INSPIRE].

  88. [88]

    CMS collaboration, V Tagging Observables and Correlations, CMS-PAS-JME-14-002.

  89. [89]

    ATLAS Collaboration, Jet mass reconstruction with the ATLAS Detector in early Run 2 data, ATLAS-CONF-2016-035.

  90. [90]

    M. Cacciari, G.P. Salam and G. Soyez, SoftKiller, a particle-level pileup removal method, Eur. Phys. J. C 75 (2015) 59 [arXiv:1407.0408] [INSPIRE].

  91. [91]

    D. Bertolini, P. Harris, M. Low and N. Tran, Pileup Per Particle Identification, JHEP 10 (2014) 059 [arXiv:1407.6013] [INSPIRE].

  92. [92]

    P. Berta, M. Spousta, D.W. Miller and R. Leitner, Particle-level pileup subtraction for jets and jet shapes, JHEP 06 (2014) 092 [arXiv:1403.3108] [INSPIRE].

    ADS  Article  Google Scholar 

  93. [93]

    P.T. Komiske, E.M. Metodiev, B. Nachman and M.D. Schwartz, Pileup Mitigation with Machine Learning (PUMML), JHEP 12 (2017) 051 [arXiv:1707.08600] [INSPIRE].

    ADS  Article  Google Scholar 

  94. [94]

    M. Cacciari and G.P. Salam, Pileup subtraction using jet areas, Phys. Lett. B 659 (2008) 119 [arXiv:0707.1378] [INSPIRE].

  95. [95]

    M. Cacciari, G.P. Salam and G. Soyez, The Catchment Area of Jets, JHEP 04 (2008) 005 [arXiv:0802.1188] [INSPIRE].

    ADS  Article  Google Scholar 

  96. [96]

    D. Krohn, J. Thaler and L.-T. Wang, Jet Trimming, JHEP 02 (2010) 084 [arXiv:0912.1342] [INSPIRE].

  97. [97]

    F.A. Dreyer, L. Necib, G. Soyez and J. Thaler, Recursive Soft Drop, JHEP 06 (2018) 093 [arXiv:1804.03657] [INSPIRE].

    ADS  Article  Google Scholar 

  98. [98]

    I.J. Goodfellow et al., Generative Adversarial Networks, Adv. Neural Inf. Process. Syst. 27 (2014) 2672 [arXiv:1406.2661] [INSPIRE].

  99. [99]

    G. Louppe, M. Kagan and K. Cranmer, Learning to Pivot with Adversarial Networks, arXiv:1611.01046 [INSPIRE].

  100. [100]

    C. Shimmin et al., Decorrelated Jet Substructure Tagging using Adversarial Neural Networks, Phys. Rev. D 96 (2017) 074034 [arXiv:1703.03507] [INSPIRE].

  101. [101]

    H.A. Andrews et al., Novel tools and observables for jet physics in heavy-ion collisions, arXiv:1808.03689 [INSPIRE].

  102. [102]

    Y.-T. Chien and R. Kunnawalkam Elayavalli, Probing heavy ion collisions using quark and gluon jet substructure, arXiv:1803.03589 [INSPIRE].

  103. [103]

    ALICE collaboration, H. Andrews, Exploring phase space of jet splittings at alice using grooming and recursive techniques, (2018). Talk at Quark Matter 2018, Venice, Italy,

  104. [104]

    J. Dolen, P. Harris, S. Marzani, S. Rappoccio and N. Tran, Thinking outside the ROCs: Designing Decorrelated Taggers (DDT) for jet substructure, JHEP 05 (2016) 156 [arXiv:1603.00027] [INSPIRE].

    ADS  Article  Google Scholar 

  105. [105]

    Z. Hall and J. Thaler, Photon isolation and jet substructure, JHEP 09 (2018) 164 [arXiv:1805.11622] [INSPIRE].

    ADS  Article  Google Scholar 

  106. [106]

    K.S. Tai, R. Socher and C.D. Manning, Improved semantic representations from tree-structured long short-term memory networks, [arXiv:1503.00075].

  107. [107]

    M. Dasgupta, F.A. Dreyer, K. Hamilton, P.F. Monni and G.P. Salam, Logarithmic accuracy of parton showers: a fixed-order study, JHEP 09 (2018) 033 [arXiv:1805.09327] [INSPIRE].

    ADS  Article  Google Scholar 

  108. [108]

    B.T. Elder and J. Thaler, Aspects of Track-Assisted Mass, arXiv:1805.11109 [INSPIRE].

Download references

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.

Author information



Corresponding author

Correspondence to Grégory Soyez.

Additional information

ArXiv ePrint: 1807.04758

On leave from CNRS, UMR 7589, LPTHE, F-75005, Paris, France. (Gavin P. Salam)

Rights and permissions

Open Access  This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.

The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

To view a copy of this licence, visit

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Dreyer, F.A., Salam, G.P. & Soyez, G. The Lund jet plane. J. High Energ. Phys. 2018, 64 (2018).

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI:


  • Jets
  • QCD Phenomenology