- Physical Review Journals
All JournalsPhysics Magazine

Physical Review D

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Heavy flavor jet substructure at lepton colliders

Prasanna K. Dhani1,*, Oleh Fedkevych2,3,4,†, and Andrea Ghira5,‡

  • *Contact author: dhani@ific.uv.es
  • †Contact author: ofedkevych@gsu.edu
  • ‡Contact author: andrea.ghira@ge.infn.it
PDF

Phys. Rev. D 112, 054004 – Published 4 September, 2025

DOI: https://doi.org/10.1103/516y-k5g2

Abstract

We provide a detailed analysis of event-shape observables, namely the energy correlation function and jet angularity, for heavy-flavor jets produced in electron-positron collisions, focusing on quantum chromodynamics (QCD) interactions. Using modern jet substructure techniques, we investigate the dead-cone effect, where QCD radiation is suppressed around a heavy quark within an angle proportional to its mass. Our analysis achieves next-to-leading logarithmic accuracy, combined with partial fixed-order contributions, to improve the description of the transition near the dead-cone threshold. To ensure a comprehensive perspective, we compare our analytical results with predictions from the pythia, herwig, and sherpa Monte Carlo simulations at past and future lepton colliders.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (118)

  1. D. Britzger, K. Rabbertz, D. Savoiu, G. Sieber, and M. Wobisch, Determination of the strong coupling constant using inclusive jet cross section data from multiple experiments, Eur. Phys. J. C 79, 68 (2019).
  2. S. Chatrchyan et al. (CMS Collaboration), Measurement of the ratio of the inclusive 3-jet cross section to the inclusive 2-jet cross section in pp collisions at s=7  TeV and first determination of the strong coupling constant in the TeV range, Eur. Phys. J. C 73, 2604 (2013).
  3. M. Aaboud et al. (ATLAS Collaboration), Determination of the strong coupling constant αs from transverse energy–energy correlations in multijet events at s=8  TeV using the ATLAS detector, Eur. Phys. J. C 77, 872 (2017).
  4. G. Aad et al. (ATLAS Collaboration), Determination of the parton distribution functions of the proton from ATLAS measurements of differential W± and Z boson production in association with jets, J. High Energy Phys. 07 (2021) 223.
  5. V. Khachatryan et al. (CMS Collaboration), Constraints on parton distribution functions and extraction of the strong coupling constant from the inclusive jet cross section in pp collisions at s=7  TeV, Eur. Phys. J. C 75, 288 (2015).
  6. R. Abdul Khalek et al., Phenomenology of NNLO jet production at the LHC and its impact on parton distributions, Eur. Phys. J. C 80, 797 (2020).
  7. L. A. Harland-Lang, A. D. Martin, and R. S. Thorne, The impact of LHC jet data on the MMHT PDF fit at NNLO, Eur. Phys. J. C 78, 248 (2018).
  8. J. Pumplin, J. Huston, H. L. Lai, P. M. Nadolsky, W.-K. Tung, and C. P. Yuan, Collider inclusive jet data and the gluon distribution, Phys. Rev. D 80, 014019 (2009).
  9. B. J. A. Watt, P. Motylinski, and R. S. Thorne, The effect of LHC jet data on MSTW PDFs, Eur. Phys. J. C 74, 2934 (2014).
  10. A. Tumasyan et al. (CMS Collaboration), Study of quark and gluon jet substructure in Z+jet and dijet events from pp collisions, J. High Energy Phys. 01 (2022) 188.
  11. S. Acharya et al. (ALICE Collaboration), Measurements of the groomed and ungroomed jet angularities in pp collisions at s=5.02  TeV, J. High Energy Phys. 05 (2022) 061.
  12. D. E. Soper and M. Spannowsky, Combining subjet algorithms to enhance ZH detection at the LHC, J. High Energy Phys. 08 (2010) 029.
  13. R. M. Godbole, D. J. Miller, K. A. Mohan, and C. D. White, Jet substructure and probes of CP violation in Vh production, J. High Energy Phys. 04 (2015) 103.
  14. N. Chen, J. Li, Y. Liu, and Z. Liu, LHC searches for the CP-odd Higgs by the jet substructure analysis, Phys. Rev. D 91, 075002 (2015).
  15. D. Adams et al., Towards an understanding of the correlations in jet substructure, Eur. Phys. J. C 75, 409 (2015).
  16. S. Marzani, G. Soyez, and M. Spannowsky, Looking Inside Jets: An Introduction to Jet Substructure and Boosted-Object Phenomenology (Springer, New York, 2019), Vol. 958.
  17. A. J. Larkoski, G. P. Salam, and J. Thaler, Energy correlation functions for jet substructure, J. High Energy Phys. 06 (2013) 108.
  18. I. Moult, L. Necib, and J. Thaler, New angles on energy correlation functions, J. High Energy Phys. 12 (2016) 153.
  19. A. J. Larkoski, J. Thaler, and W. J. Waalewijn, Gaining (mutual) information about quark/gluon discrimination, J. High Energy Phys. 11 (2014) 129.
  20. C. F. Berger, T. Kucs, and G. F. Sterman, Event shape/energy flow correlations, Phys. Rev. D 68, 014012 (2003).
  21. L. G. Almeida, S. J. Lee, G. Perez, G. F. Sterman, I. Sung, and J. Virzi, Substructure of high-pT Jets at the LHC, Phys. Rev. D 79, 074017 (2009).
  22. M. Dasgupta and G. P. Salam, Resummation of nonglobal QCD observables, Phys. Lett. B 512, 323 (2001).
  23. A. J. Larkoski, S. Marzani, G. Soyez, and J. Thaler, Soft drop, J. High Energy Phys. 05 (2014) 146.
  24. C. Frye, A. J. Larkoski, M. D. Schwartz, and K. Yan, Factorization for groomed jet substructure beyond the next-to-leading logarithm, J. High Energy Phys. 07 (2016) 064.
  25. A. Kardos, A. J. Larkoski, and Z. Trócsányi, Groomed jet mass at high precision, Phys. Lett. B 809, 135704 (2020).
  26. L. Cunqueiro and M. Ploskon, Searching for the dead cone effects with iterative declustering of heavy-flavor jets, Phys. Rev. D 99, 074027 (2019).
  27. C. Lee, P. Shrivastava, and V. Vaidya, Predictions for energy correlators probing substructure of groomed heavy quark jets, J. High Energy Phys. 09 (2019) 045.
  28. E. Craft, K. Lee, B. Meçaj, and I. Moult, Beautiful and charming energy correlators, arXiv:2210.09311.
  29. L. Apolinário, Y.-J. Lee, and M. Winn, Heavy quarks and jets as probes of the QGP, Prog. Part. Nucl. Phys. 127, 103990 (2022).
  30. C. Andres, F. Dominguez, J. Holguin, C. Marquet, and I. Moult, Seeing beauty in the quark-gluon plasma with energy correlators, Phys. Rev. D 110, L031503 (2024).
  31. S. Caletti, A. Ghira, and S. Marzani, On heavy-flavour jets with soft drop, Eur. Phys. J. C 84, 212 (2024).
  32. A. Ghira, S. Marzani, and G. Ridolfi, A consistent resummation of mass and soft logarithms in processes with heavy flavours, J. High Energy Phys. 11 (2023) 120.
  33. D. Gaggero, A. Ghira, S. Marzani, and G. Ridolfi, Soft logarithms in processes with heavy quarks, J. High Energy Phys. 09 (2022) 058.
  34. A. Ghira, L. Mai, and S. Marzani, Bridging massive and massless schemes for soft gluon resummation in heavy-flavour production, Eur. Phys. J. C 85, 294 (2025).
  35. S. Wang, W. Dai, E. Wang, X.-N. Wang, and B.-W. Zhang, Heavy-flavour jets in high-energy nuclear collisions, Symmetry 15, 727 (2023).
  36. Q. Zhang, Z.-X. Xu, W. Dai, B.-W. Zhang, and E. Wang, Substructures of heavy flavor jets in pp and PbPb collisions at s=5.02  TeV, arXiv:2303.08620.
  37. P. K. Dhani, O. Fedkevych, A. Ghira, S. Marzani, and G. Soyez, Heavy flavour jet substructure, J. High Energy Phys. 02 (2025) 046.
  38. C.-H. Jiang, H. T. Li, S.-Y. Li, and Z.-G. Si, Mass suppression effect in QCD radiation and hadron angular distribution in jet*, Chin. Phys. C 48, 063101 (2024).
  39. A. Dainese, Unveiling the QCD dead-cone effect at the LHC and its role on energy loss in the quark-gluon plasma, Nucl. Phys. News 34, 17 (2024).
  40. R. von Kuk, J. K. L. Michel, and Z. Sun, Transverse momentum-dependent heavy-quark fragmentation at next-to-leading order, J. High Energy Phys. 07 (2024) 129.
  41. U. G. Aglietti and G. Ferrera, Heavy quark mass effects in the energy-energy correlation in the back-to-back region, Eur. Phys. J. C 85, 272 (2025).
  42. CMS Collaboration, Exploring small-angle emissions in prompt D0 jets in proton-proton collisions at s=5.02  TeV.
  43. S. Acharya et al. (ALICE Collaboration), Measurements of groomed-jet substructure of charm jets tagged by D0 mesons in proton-proton collisions at s=13 TeV, Phys. Rev. Lett. 131, 192301 (2023).
  44. CMS Collaboration, Jet fragmentation function and groomed substructure of bottom quark jets in proton-proton collisions at 5.02 TeV.
  45. A. Banfi, G. P. Salam, and G. Zanderighi, Infrared safe definition of jet flavor, Eur. Phys. J. C 47, 113 (2006).
  46. S. Caletti, A. J. Larkoski, S. Marzani, and D. Reichelt, Practical jet flavour through NNLO, Eur. Phys. J. C 82, 632 (2022).
  47. M. Czakon, A. Mitov, and R. Poncelet, Infrared-safe flavoured anti-kT jets, J. High Energy Phys. 04 (2023) 138.
  48. R. Gauld, A. Huss, and G. Stagnitto, Flavor identification of reconstructed hadronic jets, Phys. Rev. Lett. 130, 161901 (2023); 132, 159901(E) (2024).
  49. F. Caola, R. Grabarczyk, M. L. Hutt, G. P. Salam, L. Scyboz, and J. Thaler, Flavored jets with exact anti-kt kinematics and tests of infrared and collinear safety, Phys. Rev. D 108, 094010 (2023).
  50. ATLAS Collaboration, Optimisation and performance studies of the ATLAS b-tagging algorithms for the 2017-18 LHC run.
  51. ATLAS Collaboration, Topological b-hadron decay reconstruction and identification of b-jets with the JetFitter package in the ATLAS experiment at the LHC.
  52. Y. L. Dokshitzer, V. A. Khoze, and S. I. Troian, On specific QCD properties of heavy quark fragmentation (’dead cone’), J. Phys. G 17, 1602 (1991).
  53. Y. L. Dokshitzer, V. A. Khoze, and S. I. Troian, Specific features of heavy quark production. LPHD approach to heavy particle spectra, Phys. Rev. D 53, 89 (1996).
  54. R. K. Ellis, W. J. Stirling, and B. R. Webber, QCD and Collider Physics (Cambridge University Press, Cambridge, England, 2011), 2, Vol. 8.
  55. S. Acharya et al. (ALICE Collaboration), Direct observation of the dead-cone effect in quantum chromodynamics, Nature (London) 605, 440 (2022);
  56. P. Abreu et al. (DELPHI Collaboration), A Measurement of B meson production and lifetime using D lepton- events in Z0 decays, Z. Phys. C 57, 181 (1993).
  57. R. Akers et al. (OPAL Collaboration), A Measurement of the production of D*+- mesons on the Z0 resonance, Z. Phys. C 67, 27 (1995).
  58. G. Alexander et al. (OPAL Collaboration), A Study of b quark fragmentation into B0 and B+ mesons at LEP, Phys. Lett. B 364, 93 (1995).
  59. K. Abe et al. (SLD Collaboration), Precise measurement of the b quark fragmentation function in Z0 boson decays, Phys. Rev. Lett. 84, 4300 (2000).
  60. P. Abreu et al. (DELPHI Collaboration), Hadronization properties of b quarks compared to light quarks in e+ e−→qq¯ from 183-GeV to 200-GeV, Phys. Lett. B 479, 118 (2000); 492, 398(E) (2000).
  61. A. Heister et al. (ALEPH Collaboration), Study of the fragmentation of b quarks into B mesons at the Z peak, Phys. Lett. B 512, 30 (2001).
  62. G. Aad et al. (ATLAS Collaboration), Measurement of jet shapes in top-quark pair events at s=7  TeV using the ATLAS detector, Eur. Phys. J. C 73, 2676 (2013).
  63. C. W. Bauer, S. Fleming, and M. E. Luke, Summing Sudakov logarithms in B→Xsγin effective field theory., Phys. Rev. D 63, 014006 (2000).
  64. 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, 114020 (2001).
  65. C. W. Bauer, D. Pirjol, and I. W. Stewart, Soft collinear factorization in effective field theory, Phys. Rev. D 65, 054022 (2002).
  66. 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, 014017 (2002).
  67. P. Abreu et al. (DELPHI Collaboration), Determination of alpha(s) in second order QCD from hadronic Z decays, Z. Phys. C 54, 55 (1992).
  68. O. Adrian et al. (L3 Collaboration), Determination of alpha-s from hadronic event shapes measured on the Z0 resonance, Phys. Lett. B 284, 471 (1992).
  69. P. D. Acton et al. (OPAL Collaboration), An Improved measurement of alpha-s (M (Z0)) using energy correlations with the OPAL detector at LEP, Phys. Lett. B 276, 547 (1992).
  70. P. D. Acton et al. (OPAL Collaboration), A determination of alpha-s (M (Z0)) at LEP using resummed QCD calculations, Z. Phys. C 59, 1 (1993).
  71. K. Fujii et al. (LCC Physics Working Group Collaboration), Tests of the standard model at the international linear collider, arXiv:1908.11299.
  72. M. Dong et al. (CEPC Study Group Collaboration), CEPC Conceptual Design Report: Volume 2—Physics & Detector.
  73. A. Abada et al. (FCC Collaboration), FCC-ee: The Lepton Collider: Future Circular Collider Conceptual Design Report Volume 2, Eur. Phys. J. Special Topics 228, 261 (2019).
  74. A. Belloni et al., Report of the topical group on electroweak precision physics and constraining new physics for snowmass 2021, arXiv:2209.08078.
  75. Y. Chen et al., Jet energy spectrum and substructure in e+e− collisions at 91.2 GeV with ALEPH archived data, J. High Energy Phys. 06 (2022) 008.
  76. T. Sjostrand, Multiple parton-parton interactions in hadronic events, in 23rd International Conference on High-Energy Physics (1985), 8.
  77. T. Sjostrand and M. van Zijl, A multiple interaction model for the event structure in hadron collisions, Phys. Rev. D 36, 2019 (1987).
  78. T. Sjostrand and P. Z. Skands, Multiple interactions and the structure of beam remnants, J. High Energy Phys. 03 (2004) 053.
  79. B. Andersson, G. Gustafson, G. Ingelman, and T. Sjostrand, Parton fragmentation and string dynamics, Phys. Rep. 97, 31 (1983).
  80. T. Sjostrand, Jet fragmentation of nearby partons, Nucl. Phys. B248, 469 (1984).
  81. M. Bahr, S. Gieseke, and M. H. Seymour, Simulation of multiple partonic interactions in herwig++, J. High Energy Phys. 07 (2008) 076.
  82. S. Gieseke, F. Loshaj, and P. Kirchgaeßer, Soft and diffractive scattering with the cluster model in herwig, Eur. Phys. J. C 77, 156 (2017).
  83. B. R. Webber, A QCD model for jet fragmentation including soft gluon interference, Nucl. Phys. B238, 492 (1984).
  84. A. Kupco, Cluster hadronization in herwig 5.9, in Workshop on Monte Carlo Generators for HERA Physics (Plenary Starting Meeting) (1998), 4, pp. 292–300, arXiv:hep-ph/9906412.
  85. J.-C. Winter, F. Krauss, and G. Soff, A modified cluster hadronization model, Eur. Phys. J. C 36, 381 (2004).
  86. M. R. Aguilar, Z. Chang, R. K. Elayavalli, R. Fatemi, Y. He, Y. Ji, D. Kalinkin, M. Kelsey, I. Mooney, and V. Verkest, pythia8 underlying event tune for RHIC energies, Phys. Rev. D 105, 016011 (2022).
  87. D. Reichelt, S. Caletti, O. Fedkevych, S. Marzani, S. Schumann, and G. Soyez, Phenomenology of jet angularities at the LHC, J. High Energy Phys. 03 (2022) 131.
  88. S. Catani, S. Dittmaier, M. H. Seymour, and Z. Trocsanyi, The dipole formalism for next-to-leading order QCD calculations with massive partons, Nucl. Phys. B627, 189 (2002).
  89. S. Catani, S. Dittmaier, and Z. Trocsanyi, One loop singular behavior of QCD and SUSY QCD amplitudes with massive partons, Phys. Lett. B 500, 149 (2001).
  90. P. K. Dhani, G. Rodrigo, and G. F. R. Sborlini, Triple-collinear splittings with massive particles, J. High Energy Phys. 12 (2023) 188.
  91. E. Craft, M. Gonzalez, K. Lee, B. Mecaj, and I. Moult, The 1→3 massive splitting functions from QCD factorization and SCET, J. High Energy Phys. 07 (2024) 080.
  92. 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, 432 (1991).
  93. Y. L. Dokshitzer, G. D. Leder, S. Moretti, and B. R. Webber, Better jet clustering algorithms, J. High Energy Phys. 08 (1997) 001.
  94. M. Cacciari, G. P. Salam, and G. Soyez, The anti-kt jet clustering algorithm, J. High Energy Phys. 04 (2008) 063.
  95. M. Cacciari, G. P. Salam, and G. Soyez, FastJet user manual, Eur. Phys. J. C 72, 1896 (2012).
  96. A. Banfi, G. P. Salam, and G. Zanderighi, Principles of general final-state resummation and automated implementation, J. High Energy Phys. 03 (2005) 073.
  97. A. J. Larkoski, D. Neill, and J. Thaler, Jet shapes with the broadening axis, J. High Energy Phys. 04 (2014) 017.
  98. M. Dasgupta, A. Fregoso, S. Marzani, and G. P. Salam, Towards an understanding of jet substructure, J. High Energy Phys. 09 (2013) 029.
  99. S. Catani, B. R. Webber, and G. Marchesini, QCD coherent branching and semiinclusive processes at large x, Nucl. Phys. B349, 635 (1991).
  100. S. Catani, L. Trentadue, G. Turnock, and B. R. Webber, Resummation of large logarithms in e+e− event shape distributions, Nucl. Phys. B407, 3 (1993).
  101. C. Bierlich et al., A comprehensive guide to the physics and usage of pythia 8.3, SciPost Phys. Codebases 2022, 8 (2022).
  102. T. Sjostrand, S. Mrenna, and P. Z. Skands, pythia 6.4 physics and manual, J. High Energy Phys. 05 (2006) 026.
  103. J. Bellm et al., herwig 7.2 release note, Eur. Phys. J. C 80, 452 (2020).
  104. G. Corcella, I. G. Knowles, G. Marchesini, S. Moretti, K. Odagiri, P. Richardson, M. H. Seymour, and B. R. Webber, herwig 6: An Event generator for hadron emission reactions with interfering gluons (including supersymmetric processes), J. High Energy Phys. 01 (2001) 010.
  105. E. Bothmann et al. (Sherpa Collaboration), Event generation with sherpa 2.2, SciPost Phys. 7, 034 (2019).
  106. T. Gleisberg, S. Hoeche, F. Krauss, M. Schonherr, S. Schumann, F. Siegert, and J. Winter, Event generation with sherpa 1.1, J. High Energy Phys. 02 (2009) 007.
  107. J. Alwall, R. Frederix, S. Frixione, V. Hirschi, F. Maltoni, O. Mattelaer, H. S. Shao, T. Stelzer, P. Torrielli, and M. Zaro, The automated computation of tree-level and next-to-leading order differential cross sections, and their matching to parton shower simulations, J. High Energy Phys. 07 (2014) 079.
  108. E. Norrbin and T. Sjostrand, QCD radiation off heavy particles, Nucl. Phys. B603, 297 (2001).
  109. S. Gieseke, P. Stephens, and B. Webber, New formalism for QCD parton showers, J. High Energy Phys. 12 (2003) 045.
  110. A. H. Hoang, S. Plätzer, and D. Samitz, On the cutoff dependence of the quark mass parameter in angular ordered parton showers, J. High Energy Phys. 10 (2018) 200.
  111. K. Cormier, S. Plätzer, C. Reuschle, P. Richardson, and S. Webster, Parton showers and matching uncertainties in top quark pair production with herwig 7, Eur. Phys. J. C 79, 915 (2019).
  112. S. Schumann and F. Krauss, A Parton shower algorithm based on Catani-Seymour dipole factorisation, J. High Energy Phys. 03 (2008) 038.
  113. F. Krauss, D. Napoletano, and S. Schumann, Simulating b-associated production of Z and Higgs bosons with the sherpa event generator, Phys. Rev. D 95, 036012 (2017).
  114. C. Bierlich, G. Gustafson, and L. Lönnblad, Collectivity without plasma in hadronic collisions, Phys. Lett. B 779, 58 (2018).
  115. F. Maltoni, M. Selvaggi, and J. Thaler, Exposing the dead cone effect with jet substructure techniques, Phys. Rev. D 94, 054015 (2016).
  116. A. Buckley, J. Butterworth, D. Grellscheid, H. Hoeth, L. Lonnblad, J. Monk, H. Schulz, and F. Siegert, Rivet user manual, Comput. Phys. Commun. 184, 2803 (2013).
  117. C. Bierlich et al., Robust independent validation of experiment and theory: Rivet version 3, SciPost Phys. 8, 026 (2020).
  118. J. D. Hunter, Matplotlib: A 2D graphics environment, Comput. Sci. Eng. 9, 90 (2007).

Outline

Information

Phys. Rev. D 112, 054004– Published 4 September, 2025
  • Received 25 February 2025
  • Accepted 19 August 2025
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation