Advertisement

Phenomenology with a recoil-free jet axis: TMD fragmentation and the jet shape

  • Duff Neill
  • Andreas Papaefstathiou
  • Wouter J. Waalewijn
  • Lorenzo Zoppi
Open Access
Regular Article - Theoretical Physics
  • 6 Downloads

Abstract

We study the phenomenology of recoil-free jet axes using analytic calculations and Monte Carlo simulations. Our focus is on the average energy as function of the angle with the jet axis (the jet shape), and the energy and transverse momenta of hadrons in a jet (TMD fragmentation). We find that the dependence on the angle (or transverse momentum) is governed by a power law, in contrast to the double-logarithmic dependence for the standard jet axis. The effects of the jet radius, jet algorithm, angular resolution and grooming are investigated. TMD fragmentation is important for constraining the structure of the proton through semi-inclusive deep-inelastic scattering. These observables are also of interest to the LHC, for example to constrain αs from precision jet measurements, or probe the quark-gluon plasma in heavy-ion collisions.

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]
    Y.L. Dokshitzer, G.D. Leder, S. Moretti and B.R. Webber, Better jet clustering algorithms, JHEP 08 (1997) 001 [hep-ph/9707323] [INSPIRE].
  2. [2]
    M. Wobisch and T. Wengler, Hadronization corrections to jet cross-sections in deep inelastic scattering, in proceedings of the Workshop on Monte Carlo Generators for HERA Physics (Plenary Starting Meeting), Hamburg, Germany, 27–30 April 1998, pp. 270–279 [hep-ph/9907280] [INSPIRE].
  3. [3]
    M. Wobisch, Measurement and QCD analysis of jet cross-sections in deep inelastic positron proton collisions at \( \sqrt{s}=300 \) GeV, DESY-THESIS-2000-049 (2000) [INSPIRE].
  4. [4]
    M. Cacciari, G.P. Salam and G. Soyez, The anti-k t jet clustering algorithm, JHEP 04 (2008) 063 [arXiv:0802.1189] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  5. [5]
    M. Dasgupta and G.P. Salam, Resummation of nonglobal QCD observables, Phys. Lett. B 512 (2001) 323 [hep-ph/0104277] [INSPIRE].
  6. [6]
    D. Neill, I. Scimemi and W.J. Waalewijn, Jet axes and universal transverse-momentum-dependent fragmentation, JHEP 04 (2017) 020 [arXiv:1612.04817] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  7. [7]
    Z.-B. Kang, F. Ringer and W.J. Waalewijn, The Energy Distribution of Subjets and the Jet Shape, JHEP 07 (2017) 064 [arXiv:1705.05375] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  8. [8]
    G. Salam, E t Scheme, unpublished.Google Scholar
  9. [9]
    D. Bertolini, T. Chan and J. Thaler, Jet Observables Without Jet Algorithms, JHEP 04 (2014) 013 [arXiv:1310.7584] [INSPIRE].ADSCrossRefGoogle Scholar
  10. [10]
    A.J. Larkoski, D. Neill and J. Thaler, Jet Shapes with the Broadening Axis, JHEP 04 (2014) 017 [arXiv:1401.2158] [INSPIRE].ADSCrossRefGoogle Scholar
  11. [11]
    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].
  12. [12]
    X. Liu, SCET approach to top quark decay, Phys. Lett. B 699 (2011) 87 [arXiv:1011.3872] [INSPIRE].ADSCrossRefGoogle Scholar
  13. [13]
    A. Jain, M. Procura and W.J. Waalewijn, Parton Fragmentation within an Identified Jet at NNLL, JHEP 05 (2011) 035 [arXiv:1101.4953] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  14. [14]
    M. Procura and W.J. Waalewijn, Fragmentation in Jets: Cone and Threshold Effects, Phys. Rev. D 85 (2012) 114041 [arXiv:1111.6605] [INSPIRE].ADSGoogle Scholar
  15. [15]
    A. Jain, M. Procura, B. Shotwell and W.J. Waalewijn, Fragmentation with a Cut on Thrust: Predictions for B-factories, Phys. Rev. D 87 (2013) 074013 [arXiv:1207.4788] [INSPIRE].ADSGoogle Scholar
  16. [16]
    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].ADSCrossRefGoogle Scholar
  17. [17]
    W.J. Waalewijn, Calculating the Charge of a Jet, Phys. Rev. D 86 (2012) 094030 [arXiv:1209.3019] [INSPIRE].ADSGoogle Scholar
  18. [18]
    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].ADSCrossRefGoogle Scholar
  19. [19]
    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
  20. [20]
    F. Arleo, M. Fontannaz, J.-P. Guillet and C.L. Nguyen, Probing fragmentation functions from same-side hadron-jet momentum correlations in p-p collisions, JHEP 04 (2014) 147 [arXiv:1311.7356] [INSPIRE].ADSCrossRefGoogle Scholar
  21. [21]
    C.W. Bauer and E. Mereghetti, Heavy Quark Fragmenting Jet Functions, JHEP 04 (2014) 051 [arXiv:1312.5605] [INSPIRE].ADSCrossRefGoogle Scholar
  22. [22]
    M. Baumgart, A.K. Leibovich, T. Mehen and I.Z. Rothstein, Probing Quarkonium Production Mechanisms with Jet Substructure, JHEP 11 (2014) 003 [arXiv:1406.2295] [INSPIRE].ADSCrossRefGoogle Scholar
  23. [23]
    M. Ritzmann and W.J. Waalewijn, Fragmentation in Jets at NNLO, Phys. Rev. D 90 (2014) 054029 [arXiv:1407.3272] [INSPIRE].ADSGoogle Scholar
  24. [24]
    T. Kaufmann, A. Mukherjee and W. Vogelsang, Hadron Fragmentation Inside Jets in Hadronic Collisions, Phys. Rev. D 92 (2015) 054015 [arXiv:1506.01415] [INSPIRE].ADSGoogle Scholar
  25. [25]
    Y.-T. Chien, Z.-B. Kang, F. Ringer, I. Vitev and H. Xing, Jet fragmentation functions in proton-proton collisions using soft-collinear effective theory, JHEP 05 (2016) 125 [arXiv:1512.06851] [INSPIRE].ADSCrossRefGoogle Scholar
  26. [26]
    R. Bain, L. Dai, A. Hornig, A.K. Leibovich, Y. Makris and T. Mehen, Analytic and Monte Carlo Studies of Jets with Heavy Mesons and Quarkonia, JHEP 06 (2016) 121 [arXiv:1603.06981] [INSPIRE].ADSCrossRefGoogle Scholar
  27. [27]
    L. Dai, C. Kim and A.K. Leibovich, Fragmentation of a Jet with Small Radius, Phys. Rev. D 94 (2016) 114023 [arXiv:1606.07411] [INSPIRE].ADSGoogle Scholar
  28. [28]
    Z.-B. Kang, F. Ringer and I. Vitev, Jet substructure using semi-inclusive jet functions in SCET, JHEP 11 (2016) 155 [arXiv:1606.07063] [INSPIRE].ADSCrossRefGoogle Scholar
  29. [29]
    B.T. Elder, M. Procura, J. Thaler, W.J. Waalewijn and K. Zhou, Generalized Fragmentation Functions for Fractal Jet Observables, JHEP 06 (2017) 085 [arXiv:1704.05456] [INSPIRE].ADSCrossRefGoogle Scholar
  30. [30]
    R. Bain, Y. Makris and T. Mehen, Transverse Momentum Dependent Fragmenting Jet Functions with Applications to Quarkonium Production, JHEP 11 (2016) 144 [arXiv:1610.06508] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  31. [31]
    Z.-B. Kang, X. Liu, F. Ringer and H. Xing, The transverse momentum distribution of hadrons within jets, JHEP 11 (2017) 068 [arXiv:1705.08443] [INSPIRE].ADSCrossRefGoogle Scholar
  32. [32]
    Z.-B. Kang, A. Prokudin, F. Ringer and F. Yuan, Collins azimuthal asymmetries of hadron production inside jets, Phys. Lett. B 774 (2017) 635 [arXiv:1707.00913] [INSPIRE].ADSCrossRefGoogle Scholar
  33. [33]
    S.D. Ellis, Z. Kunszt and D.E. Soper, Jets at hadron colliders at order α s3 : A Look inside, Phys. Rev. Lett. 69 (1992) 3615 [hep-ph/9208249] [INSPIRE].
  34. [34]
    M.H. Seymour, Jet shapes in hadron collisions: Higher orders, resummation and hadronization, Nucl. Phys. B 513 (1998) 269 [hep-ph/9707338] [INSPIRE].
  35. [35]
    H.-n. Li, Z. Li and C.P. Yuan, QCD resummation for jet substructures, Phys. Rev. Lett. 107 (2011) 152001 [arXiv:1107.4535] [INSPIRE].ADSCrossRefGoogle Scholar
  36. [36]
    Y.-T. Chien and I. Vitev, Jet Shape Resummation Using Soft-Collinear Effective Theory, JHEP 12 (2014) 061 [arXiv:1405.4293] [INSPIRE].ADSCrossRefGoogle Scholar
  37. [37]
    T. Sjöstrand et al., An Introduction to PYTHIA 8.2, Comput. Phys. Commun. 191 (2015) 159 [arXiv:1410.3012] [INSPIRE].
  38. [38]
    J. Bellm et al., HERWIG 7.1 Release Note, arXiv:1705.06919 [INSPIRE].
  39. [39]
    R. Meng, F.I. Olness and D.E. Soper, Semiinclusive deeply inelastic scattering at small q T, Phys. Rev. D 54 (1996) 1919 [hep-ph/9511311] [INSPIRE].
  40. [40]
    H. Georgi and H.D. Politzer, Quark Decay Functions and Heavy Hadron Production in QCD, Nucl. Phys. B 136 (1978) 445 [INSPIRE].ADSCrossRefGoogle Scholar
  41. [41]
    R.K. Ellis, H. Georgi, M. Machacek, H.D. Politzer and G.G. Ross, Perturbation Theory and the Parton Model in QCD, Nucl. Phys. B 152 (1979) 285 [INSPIRE].ADSCrossRefGoogle Scholar
  42. [42]
    J.C. Collins and D.E. Soper, Parton Distribution and Decay Functions, Nucl. Phys. B 194 (1982) 445 [INSPIRE].ADSGoogle Scholar
  43. [43]
    Z.-B. Kang, F. Ringer and I. Vitev, The semi-inclusive jet function in SCET and small radius resummation for inclusive jet production, JHEP 10 (2016) 125 [arXiv:1606.06732] [INSPIRE].ADSCrossRefGoogle Scholar
  44. [44]
    V.N. Gribov and L.N. Lipatov, Deep inelastic ep scattering in perturbation theory, Sov. J. Nucl. Phys. 15 (1972) 438 [Yad. Fiz. 15 (1972) 781] [INSPIRE].
  45. [45]
    G. Altarelli and G. Parisi, Asymptotic Freedom in Parton Language, Nucl. Phys. B 126 (1977) 298 [INSPIRE].ADSCrossRefGoogle Scholar
  46. [46]
    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 [Zh. Eksp. Teor. Fiz. 73 (1977) 1216] [INSPIRE].
  47. [47]
    G. Altarelli, R.K. Ellis, G. Martinelli and S.-Y. Pi, Processes Involving Fragmentation Functions Beyond the Leading Order in QCD, Nucl. Phys. B 160 (1979) 301 [INSPIRE].ADSCrossRefGoogle Scholar
  48. [48]
    W. Furmanski and R. Petronzio, Lepton-Hadron Processes Beyond Leading Order in Quantum Chromodynamics, Z. Phys. C 11 (1982) 293 [INSPIRE].ADSGoogle Scholar
  49. [49]
    P. Nason and B.R. Webber, Scaling violation in e + e fragmentation functions: QCD evolution, hadronization and heavy quark mass effects, Nucl. Phys. B 421 (1994) 473 [Erratum ibid. B 480 (1996) 755] [INSPIRE].
  50. [50]
    E.L. Berger, X.-F. Guo and J.-W. Qiu, Inclusive prompt photon production in hadronic final states of e + e annihilation, Phys. Rev. D 53 (1996) 1124 [hep-ph/9507428] [INSPIRE].
  51. [51]
    D. de Florian, R. Sassot, M. Epele, R.J. Hernández-Pinto and M. Stratmann, Parton-to-Pion Fragmentation Reloaded, Phys. Rev. D 91 (2015) 014035 [arXiv:1410.6027] [INSPIRE].ADSGoogle Scholar
  52. [52]
    M. Hirai, S. Kumano, T.H. Nagai and K. Sudoh, Determination of fragmentation functions and their uncertainties, Phys. Rev. D 75 (2007) 094009 [hep-ph/0702250] [INSPIRE].
  53. [53]
    D. Kotlorz and A. Kotlorz, Evolution equations for truncated moments of the parton distributions, Phys. Lett. B 644 (2007) 284 [hep-ph/0610282] [INSPIRE].
  54. [54]
    Z. Ligeti, I.W. Stewart and F.J. Tackmann, Treating the b quark distribution function with reliable uncertainties, Phys. Rev. D 78 (2008) 114014 [arXiv:0807.1926] [INSPIRE].ADSGoogle Scholar
  55. [55]
    R. Abbate, M. Fickinger, A.H. Hoang, V. Mateu and I.W. Stewart, Thrust at N 3 LL with Power Corrections and a Precision Global Fit for α s(m Z), Phys. Rev. D 83 (2011) 074021 [arXiv:1006.3080] [INSPIRE].ADSGoogle Scholar
  56. [56]
    A. Buckley et al., Rivet user manual, Comput. Phys. Commun. 184 (2013) 2803 [arXiv:1003.0694] [INSPIRE].ADSCrossRefGoogle Scholar
  57. [57]
    D. Krohn, J. Thaler and L.-T. Wang, Jet Trimming, JHEP 02 (2010) 084 [arXiv:0912.1342] [INSPIRE].ADSCrossRefGoogle Scholar
  58. [58]
    A.J. Larkoski, S. Marzani, G. Soyez and J. Thaler, Soft Drop, JHEP 05 (2014) 146 [arXiv:1402.2657] [INSPIRE].ADSCrossRefGoogle Scholar
  59. [59]
    J.R. Andersen et al., Les Houches 2015: Physics at TeV Colliders Standard Model Working Group Report, in proceedings of the 9th Les Houches Workshop on Physics at TeV Colliders (PhysTeV 2015), Les Houches, France, 1–19 June 2015, arXiv:1605.04692 [INSPIRE].
  60. [60]
    P. Gras et al., Systematics of quark/gluon tagging, JHEP 07 (2017) 091 [arXiv:1704.03878] [INSPIRE].ADSCrossRefGoogle Scholar

Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Theoretical DivisionLos Alamos National LaboratoryLos AlamosU.S.A.
  2. 2.Institute for Theoretical Physics Amsterdam and Delta Institute for Theoretical PhysicsUniversity of AmsterdamAmsterdamThe Netherlands
  3. 3.Nikhef, Theory GroupAmsterdamThe Netherlands

Personalised recommendations