Abstract
We study jets with identified hadrons in which a family of jet-shape variables called angularities are measured, extending the concept of fragmenting jet functions (FJFs) to these observables. FJFs determine the fraction of energy, z, carried by an identified hadron in a jet with angularity, τ a . The FJFs are convolutions of fragmentation functions (FFs), evolved to the jet energy scale, with perturbatively calculable matching coefficients. Renormalization group equations are used to provide resummed calculations with next-to-leading logarithm prime (NLL’) accuracy. We apply this formalism to two-jet events in e + e − collisions with B mesons in the jets, and three-jet events in which a J/ψ is produced in the gluon jet. In the case of B mesons, we use a phenomenological FF extracted from e + e − collisions at the Z 0 pole evaluated at the scale μ = m b . For events with J/ψ, the FF can be evaluated in terms of Non-Relativistic QCD (NRQCD) matrix elements at the scale μ = 2m c . The z and τ a distributions from our NLL’ calculations are compared with predictions from monte carlo event generators. While we find consistency between the predictions for B mesons and the J/ψ distributions in τ a , we find the z distributions for J/ψ differ significantly. We describe an attempt to merge PYTHIA showers with NRQCD FFs that gives good agreement with NLL’ calculations of the z distributions.
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References
L.G. Almeida, S.D. Ellis, C. Lee, G. Sterman, I. Sung and J.R. Walsh, Comparing and counting logs in direct and effective methods of QCD resummation, JHEP 04 (2014) 174 [arXiv:1401.4460] [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].
A. Jain, M. Procura and W.J. Waalewijn, Fully-Unintegrated Parton Distribution and Fragmentation Functions at Perturbative k T , JHEP 04 (2012) 132 [arXiv:1110.0839] [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].
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].
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].
G.T. Bodwin, E. Braaten and G.P. Lepage, Rigorous QCD analysis of inclusive annihilation and production of heavy quarkonium, Phys. Rev. D 51 (1995) 1125 [Erratum ibid. D 55 (1997) 5853] [hep-ph/9407339] [INSPIRE].
C.F. Berger, T. Kucs and G.F. Sterman, Event shape/energy flow correlations, Phys. Rev. D 68 (2003) 014012 [hep-ph/0303051] [INSPIRE].
J. Alwall et al., The automated computation of tree-level and next-to-leading order differential cross sections and their matching to parton shower simulations, JHEP 07 (2014) 079 [arXiv:1405.0301] [INSPIRE].
T. Sjöstrand, S. Mrenna and P.Z. Skands, PYTHIA 6.4 Physics and Manual, JHEP 05 (2006) 026 [hep-ph/0603175] [INSPIRE].
T. Sjöstrand et al., An Introduction to PYTHIA 8.2, Comput. Phys. Commun. 191 (2015) 159 [arXiv:1410.3012] [INSPIRE].
M. Bahr et al., HERWIG++ Physics and Manual, Eur. Phys. J. C 58 (2008) 639 [arXiv:0803.0883] [INSPIRE].
S.D. Ellis, C.K. Vermilion, J.R. Walsh, A. Hornig and C. Lee, Jet Shapes and Jet Algorithms in SCET, JHEP 11 (2010) 101 [arXiv:1001.0014] [INSPIRE].
Y.-T. Chien, A. Hornig and C. Lee, Soft-collinear mode for jet cross sections in soft collinear effective theory, Phys. Rev. D 93 (2016) 014033 [arXiv:1509.04287] [INSPIRE].
V.G. Kartvelishvili and A.K. Likhoded, Heavy Quark Fragmentation Into Mesons and Baryons, Sov. J. Nucl. Phys. 29 (1979) 390 [INSPIRE].
B.A. Kniehl, G. Kramer, I. Schienbein and H. Spiesberger, Finite-mass effects on inclusive B meson hadroproduction, Phys. Rev. D 77 (2008) 014011 [arXiv:0705.4392] [INSPIRE].
M. Cacciari, G.P. Salam and G. Soyez, FastJet User Manual, Eur. Phys. J. C 72 (2012) 1896 [arXiv:1111.6097] [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. Hornig, Y. Makris and T. Mehen, Jet Shapes in Dijet Events at the LHC in SCET, JHEP 04 (2016) 097 [arXiv:1601.01319] [INSPIRE].
E. Braaten, K.-m. Cheung and T.C. Yuan, Z 0 decay into charmonium via charm quark fragmentation, Phys. Rev. D 48 (1993) 4230 [hep-ph/9302307] [INSPIRE].
E. Braaten and T.C. Yuan, Gluon fragmentation into heavy quarkonium, Phys. Rev. Lett. 71 (1993) 1673 [hep-ph/9303205] [INSPIRE].
E. Braaten and S. Fleming, Color octet fragmentation and the psi-prime surplus at the Tevatron, Phys. Rev. Lett. 74 (1995) 3327 [hep-ph/9411365] [INSPIRE].
E. Braaten and Y.-Q. Chen, Helicity decomposition for inclusive J/ψ production, Phys. Rev. D 54 (1996) 3216 [hep-ph/9604237] [INSPIRE].
M. Butenschoen and B.A. Kniehl, World data of J/ψ production consolidate NRQCD factorization at NLO, Phys. Rev. D 84 (2011) 051501 [arXiv:1105.0820] [INSPIRE].
M. Butenschoen and B.A. Kniehl, Next-to-leading-order tests of NRQCD factorization with J/ψ yield and polarization, Mod. Phys. Lett. A 28 (2013) 1350027 [arXiv:1212.2037] [INSPIRE].
A. Buckley et al., Rivet user manual, Comput. Phys. Commun. 184 (2013) 2803 [arXiv:1003.0694] [INSPIRE].
C. Lee and G.F. Sterman, Momentum Flow Correlations from Event Shapes: Factorized Soft Gluons and Soft-Collinear Effective Theory, Phys. Rev. D 75 (2007) 014022 [hep-ph/0611061] [INSPIRE].
A. Hornig, C. Lee and G. Ovanesyan, Effective Predictions of Event Shapes: Factorized, Resummed and Gapped Angularity Distributions, JHEP 05 (2009) 122 [arXiv:0901.3780] [INSPIRE].
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Bain, R., Dai, L., Hornig, A. et al. Analytic and Monte Carlo studies of jets with heavy mesons and quarkonia. J. High Energ. Phys. 2016, 121 (2016). https://doi.org/10.1007/JHEP06(2016)121
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DOI: https://doi.org/10.1007/JHEP06(2016)121