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.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Y.L. Dokshitzer, G.D. Leder, S. Moretti and B.R. Webber, Better jet clustering algorithms, JHEP 08 (1997) 001 [hep-ph/9707323] [INSPIRE].
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].
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].
M. Cacciari, G.P. Salam and G. Soyez, The anti-k t jet clustering algorithm, JHEP 04 (2008) 063 [arXiv:0802.1189] [INSPIRE].
M. Dasgupta and G.P. Salam, Resummation of nonglobal QCD observables, Phys. Lett. B 512 (2001) 323 [hep-ph/0104277] [INSPIRE].
D. Neill, I. Scimemi and W.J. Waalewijn, Jet axes and universal transverse-momentum-dependent fragmentation, JHEP 04 (2017) 020 [arXiv:1612.04817] [INSPIRE].
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].
G. Salam, E ∞ t Scheme, unpublished.
D. Bertolini, T. Chan and J. Thaler, Jet Observables Without Jet Algorithms, JHEP 04 (2014) 013 [arXiv:1310.7584] [INSPIRE].
A.J. Larkoski, D. Neill and J. Thaler, Jet Shapes with the Broadening Axis, JHEP 04 (2014) 017 [arXiv:1401.2158] [INSPIRE].
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].
X. Liu, SCET approach to top quark decay, Phys. Lett. B 699 (2011) 87 [arXiv:1011.3872] [INSPIRE].
A. Jain, M. Procura and W.J. Waalewijn, Parton Fragmentation within an Identified Jet at NNLL, JHEP 05 (2011) 035 [arXiv:1101.4953] [INSPIRE].
M. Procura and W.J. Waalewijn, Fragmentation in Jets: Cone and Threshold Effects, Phys. Rev. D 85 (2012) 114041 [arXiv:1111.6605] [INSPIRE].
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].
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].
W.J. Waalewijn, Calculating the Charge of a Jet, Phys. Rev. D 86 (2012) 094030 [arXiv:1209.3019] [INSPIRE].
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].
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].
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].
C.W. Bauer and E. Mereghetti, Heavy Quark Fragmenting Jet Functions, JHEP 04 (2014) 051 [arXiv:1312.5605] [INSPIRE].
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].
M. Ritzmann and W.J. Waalewijn, Fragmentation in Jets at NNLO, Phys. Rev. D 90 (2014) 054029 [arXiv:1407.3272] [INSPIRE].
T. Kaufmann, A. Mukherjee and W. Vogelsang, Hadron Fragmentation Inside Jets in Hadronic Collisions, Phys. Rev. D 92 (2015) 054015 [arXiv:1506.01415] [INSPIRE].
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].
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].
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].
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].
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].
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].
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].
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].
S.D. Ellis, Z. Kunszt and D.E. Soper, Jets at hadron colliders at order α 3 s : A Look inside, Phys. Rev. Lett. 69 (1992) 3615 [hep-ph/9208249] [INSPIRE].
M.H. Seymour, Jet shapes in hadron collisions: Higher orders, resummation and hadronization, Nucl. Phys. B 513 (1998) 269 [hep-ph/9707338] [INSPIRE].
H.-n. Li, Z. Li and C.P. Yuan, QCD resummation for jet substructures, Phys. Rev. Lett. 107 (2011) 152001 [arXiv:1107.4535] [INSPIRE].
Y.-T. Chien and I. Vitev, Jet Shape Resummation Using Soft-Collinear Effective Theory, JHEP 12 (2014) 061 [arXiv:1405.4293] [INSPIRE].
T. Sjöstrand et al., An Introduction to PYTHIA 8.2, Comput. Phys. Commun. 191 (2015) 159 [arXiv:1410.3012] [INSPIRE].
J. Bellm et al., HERWIG 7.1 Release Note, arXiv:1705.06919 [INSPIRE].
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].
H. Georgi and H.D. Politzer, Quark Decay Functions and Heavy Hadron Production in QCD, Nucl. Phys. B 136 (1978) 445 [INSPIRE].
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].
J.C. Collins and D.E. Soper, Parton Distribution and Decay Functions, Nucl. Phys. B 194 (1982) 445 [INSPIRE].
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].
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].
G. Altarelli and G. Parisi, Asymptotic Freedom in Parton Language, Nucl. Phys. B 126 (1977) 298 [INSPIRE].
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].
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].
W. Furmanski and R. Petronzio, Lepton-Hadron Processes Beyond Leading Order in Quantum Chromodynamics, Z. Phys. C 11 (1982) 293 [INSPIRE].
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].
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].
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].
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].
D. Kotlorz and A. Kotlorz, Evolution equations for truncated moments of the parton distributions, Phys. Lett. B 644 (2007) 284 [hep-ph/0610282] [INSPIRE].
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].
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].
A. Buckley et al., Rivet user manual, Comput. Phys. Commun. 184 (2013) 2803 [arXiv:1003.0694] [INSPIRE].
D. Krohn, J. Thaler and L.-T. Wang, Jet Trimming, JHEP 02 (2010) 084 [arXiv:0912.1342] [INSPIRE].
A.J. Larkoski, S. Marzani, G. Soyez and J. Thaler, Soft Drop, JHEP 05 (2014) 146 [arXiv:1402.2657] [INSPIRE].
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].
P. Gras et al., Systematics of quark/gluon tagging, JHEP 07 (2017) 091 [arXiv:1704.03878] [INSPIRE].
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
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1810.12915
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 https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Neill, D., Papaefstathiou, A., Waalewijn, W.J. et al. Phenomenology with a recoil-free jet axis: TMD fragmentation and the jet shape. J. High Energ. Phys. 2019, 67 (2019). https://doi.org/10.1007/JHEP01(2019)067
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP01(2019)067