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How to identify the dead cone in the top-quark jet

Stefan Kluth and Wolfgang Ochs

Redamy Perez-Ramos

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Phys. Rev. D 113, 114048 – Published 26 June, 2026

DOI: https://doi.org/10.1103/ckrs-wt2x

Abstract

The gluon emission from an energetic heavy quark is suppressed in the forward direction below the angle Θ≲mQ/E for a quark of mass mQ and energy E according to perturbative quantum chromodynamics (QCD) (“dead cone”). Another consequence is the suppression of energetic particles in the jet, which has been observed already for c- and b-quark jets. The suppression of the forward particles can be explained by an application of the modified leading logarithmic approximation of perturbative QCD. In this paper, we investigate whether this type of analysis can be carried out also for top-quark jets with a much higher heavy-quark mass allowing for QCD tests in this new kinematic regime. The new aspect of this analysis is the finite lifetime of the top quark. We consider for simplicity the decay t→bℓν, where the b quark radiates gluons as well and partially obscures the dead cone. Guided by the decay amplitude in leading order in αs for e+e−→tt¯, we propose a method to separate the radiation by the tb^ dipole in the decay process, which is superimposed on the primary radiation from the tt¯^ dipole involving the top-quark dead-cone effect. The momentum distributions of partons or hadrons are determined for finite decay angles of the b-quark Θb and extrapolated in the forward direction Θb=0 where the radiation from the decay process is expected to vanish. This method is successfully tested at the parton level, and the results obtained for hadrons are compatible with the modified leading logarithmic approximation relation with an accuracy of around 15%. Our calculations are carried out with the pythia 8.3 Monte Carlo event generator.

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Observation of the dead cone effect in charm and bottom quark jets and its QCD explanation

Stefan Kluth, Wolfgang Ochs, and Redamy Perez Ramos
Phys. Rev. D 107, 094039 (2023)

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References (47)

  1. Y. L. Dokshitzer, V. A. Khoze, and S. I. Troian, Particle spectra in light and heavy quark jets, J. Phys. G 17, 1481 (1991).
  2. 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).
  3. B. A. Schumm, Y. L. Dokshitzer, V. A. Khoze, and D. S. Koetke, MLLA and the average charged multiplicity of events containing heavy quarks in e+e− annihilation, Phys. Rev. Lett. 69, 3025 (1992).
  4. Y. L. Dokshitzer, F. Fabbri, V. A. Khoze, and W. Ochs, Multiplicity difference between heavy and light quark jets revisited, Eur. Phys. J. C 45, 387 (2006).
  5. S. Acharya et al. (ALICE Collaboration), Direct observation of the dead-cone effect in quantum chromodynamics, Nature (London) 605, 440 (2022); 607, E22 (2022).
  6. S. Kluth, W. Ochs, and R. Perez Ramos, Observation of the dead cone effect in charm and bottom quark jets and its QCD explanation, Phys. Rev. D 107, 094039 (2023).
  7. A. Hayrapetyan et al. (CMS Collaboration), Direct evidence of the dead-cone effect in bottom quark initiated jets, Technical Report No. CMS-PAS-SMP-25-008, CERN, Geneva, 2026.
  8. S. Navas et al. (Particle Data Group), Review of particle physics, Phys. Rev. D 110, 030001 (2024).
  9. G. Aad et al. (ATLAS Collaboration), Measurement of the top quark mass with the template method in the tt¯→ lepton+jets channel using ATLAS data, Eur. Phys. J. C 72, 2046 (2012).
  10. A. Tumasyan et al. (CMS Collaboration), Measurement of the top quark mass using a profile likelihood approach with the lepton+jets final states in proton–proton collisions at s=13  TeV, Eur. Phys. J. C 83, 963 (2023).
  11. G. Aad et al. (ATLAS Collaboration), Measurement of the top quark mass with the ATLAS detector using tt¯ events with a high transverse momentum top quark, Phys. Lett. B 867, 139608 (2025).
  12. G. V. Jikia, Measuring the heavy top quark width by soft gluon radiation in e+e−→tt¯, Phys. Lett. B 257, 196 (1991).
  13. V. A. Khoze, W. J. Stirling, and L. H. Orr, Soft gluon radiation in e+e−→tt¯, Nucl. Phys. B378, 413 (1992).
  14. F. Maltoni, M. Selvaggi, and J. Thaler, Exposing the dead cone effect with jet substructure techniques, Phys. Rev. D 94, 054015 (2016).
  15. C. Bierlich, S. Chakraborty, N. Desai, L. Gellersen, I. Helenius, P. Ilten, L. Lönnblad, S. Mrenna, S. Prestel, C. T. Preuss, T. Sjöstrand, P. Skands, M. Utheim, and R. Verheyen, A comprehensive guide to the physics and usage of pythia 8.3, SciPost Phys. Codebases 2022, 8 (2022).
  16. T. Sjostrand, S. Ask, J. R. Christiansen, R. Corke, N. Desai, P. Ilten, S. Mrenna, S. Prestel, C. O. Rasmussen, and P. Z. Skands, An introduction to pythia 8.2, Comput. Phys. Commun. 191, 159 (2015).
  17. 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.
  18. B. Andersson, G. Gustafson, G. Ingelman, and T. Sjöstrand, Parton fragmentation and string dynamics, Phys. Rep. 97, 31 (1983).
  19. Y. L. Dokshitzer, V. A. Khoze, A. H. Mueller, and S. I. Troyan, Basics of Perturbative QCD (Editions Frontières, Gif-sur-Yvette, France, 1991).
  20. B. I. Ermolaev and V. S. Fadin, Log–log asymptotic form of exclusive cross-sections in quantum chromodynamics, JETP Lett. 33, 269 (1981), http://jetpletters.ru/ps/1505/article_23008.shtml.
  21. A. H. Mueller, On the multiplicity of hadrons in QCD jets, Phys. Lett. 104B, 161 (1981).
  22. V. A. Khoze and T. Sjöstrand, Colour correlations and multiplicities in top events, Phys. Lett. B 328, 466 (1994).
  23. R. K. Ellis, W. J. Stirling, and B. R. Webber, QCD and Collider Physics (Cambridge University Press, Cambridge, England, 2011), 10.1017/CBO9780511628788.
  24. M. Cacciari, G. P. Salam, and G. Soyez, fastjet user manual, Eur. Phys. J. C 72, 1896 (2012).
  25. M. Cacciari and G. P. Salam, Dispelling the N3 myth for the kt jet-finder, Phys. Lett. B 641, 57 (2006).
  26. G. Aad et al. (ATLAS Collaboration), Performance of b-jet identification in the ATLAS experiment, J. Instrum. 11, P04008 (2016).
  27. G. Aad et al. (ATLAS Collaboration), Performance of jet substructure techniques for large-R jets in proton–proton collisions at s=7  TeV using the ATLAS detector, J. High Energy Phys. 09 (2013) 076.
  28. S. Chatrchyan et al. (CMS Collaboration), Identification of b-quark jets with the CMS experiment, J. Instrum. 8, P04013 (2013).
  29. P. Martín-Ramiro and J. M. Moreno, Improving tt¯ reconstruction in the dilepton channel at future lepton colliders, arXiv:2003.12320.
  30. T. Behnke et al., The international linear collider technical design report—volume 4: Detectors, arXiv:1306.6329.
  31. S. Kluth, W. Ochs, and R. Perez-Ramos, Dead cone effect in charm and bottom quark jets, Nucl. Part. Phys. Proc. 343, 75 (2024).
  32. D. Acosta et al. (CDF Collaboration), Momentum distribution of charged particles in jets in dijet events in pp¯ collisions at s=1.8  TeV and comparisons to perturbative QCD predictions, Phys. Rev. D 68, 012003 (2003).
  33. C. P. Fong and B. R. Webber, One and two particle distributions at small x in QCD jets, Nucl. Phys. B355, 54 (1991).
  34. Y. L. Dokshitzer, V. A. Khoze, and S. I. Troian, Phenomenology of the particle spectra in QCD jets in a modified leading logarithmic approximation, Z. Phys. C 55, 107 (1992).
  35. Y. I. Azimov, Y. L. Dokshitzer, V. A. Khoze, and S. I. Troyan, Similarity of parton and hadron spectra in QCD jets, Z. Phys. C 27, 65 (1985).
  36. Y. I. Azimov, Y. L. Dokshitzer, V. A. Khoze, and S. I. Troyan, Humpbacked QCD plateau in hadron spectra, Z. Phys. C 31, 213 (1986).
  37. H. Brooks, P. Skands, and R. Verheyen, Interleaved resonance decays and electroweak radiation in the Vincia parton shower, SciPost Phys. 12, 101 (2022).
  38. H. Brooks and P. Skands, Coherent showers in decays of colored resonances, Phys. Rev. D 100, 076006 (2019).
  39. P. Skands (private communication).
  40. S. Dittmaier and M. Reyer, Electroweak splitting functions in the standard model and beyond, J. High Energy Phys. 01 (2026) 119.
  41. M. Aaboud et al. (ATLAS Collaboration), Measurements of top-quark pair differential cross-sections in the lepton+jets channel in pp collisions at s=13  TeV using the ATLAS detector, J. High Energy Phys. 11 (2017) 191.
  42. V. Khachatryan et al. (CMS Collaboration), Measurement of differential cross sections for top quark pair production using the lepton+jets final state in proton–proton collisions at s=13  TeV, Phys. Rev. D 95, 092001 (2017).
  43. A. M. Sirunyan et al. (CMS Collaboration), Measurement of the tt¯ production cross section, the top quark mass, and the strong coupling constant using dilepton events in pp collisions at s=13  TeV, Eur. Phys. J. C 79, 368 (2019).
  44. G. Aad et al. (ATLAS Collaboration), Measurements of top-quark pair single- and double-differential cross-sections in the all-hadronic channel in pp collisions at s=13  TeV using the ATLAS detector, J. High Energy Phys. 01 (2021) 033.
  45. A. Tumasyan et al. (CMS Collaboration), Measurement of the differential tt¯ production cross section as a function of the jet mass and extraction of the top quark mass in hadronic decays of boosted top quarks, Eur. Phys. J. C 83, 560 (2023).
  46. Y. L. Dokshitzer, G. D. Leder, S. Moretti, and B. R. Webber, Better jet clustering algorithms, J. High Energy Phys. 08 (1997) 001.
  47. A. J. Larkoski, S. Marzani, G. Soyez, and J. Thaler, Soft drop, J. High Energy Phys. 05 (2014) 146.

Outline

Information

Phys. Rev. D 113, 114048– Published 26 June, 2026
  • Received 29 December 2025
  • Accepted 5 June 2026
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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.

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