Abstract
Power counting is a systematic strategy for organizing collider observables and their associated theoretical calculations. In this paper, we use power counting to characterize a class of jet substructure observables called energy flow polynomials (EFPs). EFPs provide an overcomplete linear basis for infrared-and-collinear safe jet observables, but it is known that in practice, a small subset of EFPs is often sufficient for specific jet analysis tasks. By applying power counting arguments, we obtain linear relationships between EFPs that hold for quark and gluon jets to a specific order in the power counting. We test these relations in the parton shower generator Pythia, finding excellent agreement. Power counting allows us to truncate the basis of EFPs without affecting performance, which we corroborate through a study of quark-gluon tagging and regression.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
M.H. Seymour, Tagging a heavy Higgs boson, in ECFA Large Hadron Collider (LHC) Workshop: Physics and Instrumentation, (1991), pp. 557–569.
M.H. Seymour, Searches for new particles using cone and cluster jet algorithms: A Comparative study, Z. Phys. C 62 (1994) 127 [INSPIRE].
J.M. Butterworth, B.E. Cox and J.R. Forshaw, WW scattering at the CERN LHC, Phys. Rev. D 65 (2002) 096014 [hep-ph/0201098] [INSPIRE].
J.M. Butterworth, J.R. Ellis and A.R. Raklev, Reconstructing sparticle mass spectra using hadronic decays, JHEP 05 (2007) 033 [hep-ph/0702150] [INSPIRE].
J.M. Butterworth, A.R. Davison, M. Rubin and G.P. Salam, Jet substructure as a new Higgs search channel at the LHC, Phys. Rev. Lett. 100 (2008) 242001 [arXiv:0802.2470] [INSPIRE].
D.E. Kaplan, K. Rehermann, M.D. Schwartz and B. Tweedie, Top Tagging: A Method for Identifying Boosted Hadronically Decaying Top Quarks, Phys. Rev. Lett. 101 (2008) 142001 [arXiv:0806.0848] [INSPIRE].
J. Thaler and L.-T. Wang, Strategies to Identify Boosted Tops, JHEP 07 (2008) 092 [arXiv:0806.0023] [INSPIRE].
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 (2009) 074017 [arXiv:0807.0234] [INSPIRE].
J. Thaler and K. Van Tilburg, Identifying Boosted Objects with N-subjettiness, JHEP 03 (2011) 015 [arXiv:1011.2268] [INSPIRE].
J. Gallicchio and M.D. Schwartz, Quark and Gluon Tagging at the LHC, Phys. Rev. Lett. 107 (2011) 172001 [arXiv:1106.3076] [INSPIRE].
J. Cogan, M. Kagan, E. Strauss and A. Schwarztman, Jet-Images: Computer Vision Inspired Techniques for Jet Tagging, JHEP 02 (2015) 118 [arXiv:1407.5675] [INSPIRE].
L.G. Almeida, M. Backović, M. Cliche, S.J. Lee and M. Perelstein, Playing Tag with ANN: Boosted Top Identification with Pattern Recognition, JHEP 07 (2015) 086 [arXiv:1501.05968] [INSPIRE].
P. Baldi, K. Bauer, C. Eng, P. Sadowski and D. Whiteson, Jet Substructure Classification in High-Energy Physics with Deep Neural Networks, Phys. Rev. D 93 (2016) 094034 [arXiv:1603.09349] [INSPIRE].
P.T. Komiske, E.M. Metodiev and M.D. Schwartz, Deep learning in color: towards automated quark/gluon jet discrimination, JHEP 01 (2017) 110 [arXiv:1612.01551] [INSPIRE].
D. Guest, J. Collado, P. Baldi, S.-C. Hsu, G. Urban and D. Whiteson, Jet Flavor Classification in High-Energy Physics with Deep Neural Networks, Phys. Rev. D 94 (2016) 112002 [arXiv:1607.08633] [INSPIRE].
G. Louppe, K. Cho, C. Becot and K. Cranmer, QCD-Aware Recursive Neural Networks for Jet Physics, JHEP 01 (2019) 057 [arXiv:1702.00748] [INSPIRE].
F.A. Dreyer, G.P. Salam and G. Soyez, The Lund Jet Plane, JHEP 12 (2018) 064 [arXiv:1807.04758] [INSPIRE].
A. Andreassen, I. Feige, C. Frye and M.D. Schwartz, JUNIPR: a Framework for Unsupervised Machine Learning in Particle Physics, Eur. Phys. J. C 79 (2019) 102 [arXiv:1804.09720] [INSPIRE].
P.T. Komiske, E.M. Metodiev and J. Thaler, Energy Flow Networks: Deep Sets for Particle Jets, JHEP 01 (2019) 121 [arXiv:1810.05165] [INSPIRE].
A.J. Larkoski, I. Moult and D. Neill, Power Counting to Better Jet Observables, JHEP 12 (2014) 009 [arXiv:1409.6298] [INSPIRE].
A.J. Larkoski, I. Moult and D. Neill, Building a Better Boosted Top Tagger, Phys. Rev. D 91 (2015) 034035 [arXiv:1411.0665] [INSPIRE].
A.J. Larkoski and I. Moult, The Singular Behavior of Jet Substructure Observables, Phys. Rev. D 93 (2016) 014017 [arXiv:1510.08459] [INSPIRE].
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 (2001) 114020 [hep-ph/0011336] [INSPIRE].
C.W. Bauer and I.W. Stewart, Invariant operators in collinear effective theory, Phys. Lett. B 516 (2001) 134 [hep-ph/0107001] [INSPIRE].
C.W. Bauer, D. Pirjol and I.W. Stewart, Soft collinear factorization in effective field theory, Phys. Rev. D 65 (2002) 054022 [hep-ph/0109045] [INSPIRE].
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 (2002) 014017 [hep-ph/0202088] [INSPIRE].
M. Beneke, A.P. Chapovsky, M. Diehl and T. Feldmann, Soft collinear effective theory and heavy to light currents beyond leading power, Nucl. Phys. B 643 (2002) 431 [hep-ph/0206152] [INSPIRE].
P.T. Komiske, E.M. Metodiev and J. Thaler, Energy flow polynomials: A complete linear basis for jet substructure, JHEP 04 (2018) 013 [arXiv:1712.07124] [INSPIRE].
P.T. Komiske, E.M. Metodiev and J. Thaler, An operational definition of quark and gluon jets, JHEP 11 (2018) 059 [arXiv:1809.01140] [INSPIRE].
A. Butter et al., The Machine Learning landscape of top taggers, SciPost Phys. 7 (2019) 014 [arXiv:1902.09914] [INSPIRE].
T. Faucett, J. Thaler and D. Whiteson, Mapping Machine-Learned Physics into a Human-Readable Space, Phys. Rev. D 103 (2021) 036020 [arXiv:2010.11998] [INSPIRE].
J. Collado, J.N. Howard, T. Faucett, T. Tong, P. Baldi and D. Whiteson, Learning to identify electrons, Phys. Rev. D 103 (2021) 116028 [arXiv:2011.01984] [INSPIRE].
J. Collado, K. Bauer, E. Witkowski, T. Faucett, D. Whiteson and P. Baldi, Learning to isolate muons, JHEP 21 (2020) 200 [arXiv:2102.02278] [INSPIRE].
B.M. Dillon, G. Kasieczka, H. Olischlager, T. Plehn, P. Sorrenson and L. Vogel, Symmetries, safety, and self-supervision, SciPost Phys. 12 (2022) 188 [arXiv:2108.04253] [INSPIRE].
Y. Lu, A. Romero, M.J. Fenton, D. Whiteson and P. Baldi, Resolving extreme jet substructure, JHEP 08 (2022) 046 [arXiv:2202.00723] [INSPIRE].
L. Bradshaw, S. Chang and B. Ostdiek, Creating simple, interpretable anomaly detectors for new physics in jet substructure, Phys. Rev. D 106 (2022) 035014 [arXiv:2203.01343] [INSPIRE].
J. Thaler and K. Van Tilburg, Maximizing Boosted Top Identification by Minimizing N-subjettiness, JHEP 02 (2012) 093 [arXiv:1108.2701] [INSPIRE].
I.W. Stewart, F.J. Tackmann and W.J. Waalewijn, N-Jettiness: An Inclusive Event Shape to Veto Jets, Phys. Rev. Lett. 105 (2010) 092002 [arXiv:1004.2489] [INSPIRE].
K. Datta and A. Larkoski, How Much Information is in a Jet?, JHEP 06 (2017) 073 [arXiv:1704.08249] [INSPIRE].
L. Moore, K. Nordström, S. Varma and M. Fairbairn, Reports of My Demise Are Greatly Exaggerated: N-subjettiness Taggers Take On Jet Images, SciPost Phys. 7 (2019) 036 [arXiv:1807.04769] [INSPIRE].
T. Sjöstrand et al., An introduction to PYTHIA 8.2, Comput. Phys. Commun. 191 (2015) 159 [arXiv:1410.3012] [INSPIRE].
P.T. Komiske, E.M. Metodiev and J. Thaler, Cutting Multiparticle Correlators Down to Size, Phys. Rev. D 101 (2020) 036019 [arXiv:1911.04491] [INSPIRE].
P. Cal, J. Thaler and W. Waalewijn, Power counting relations for Energy Flow Polynomials, Zenodo (2022) 6542205.
I. Moult, L. Necib and J. Thaler, New Angles on Energy Correlation Functions, JHEP 12 (2016) 153 [arXiv:1609.07483] [INSPIRE].
P. Komiske, E. Metodiev and J. Thaler, Pythia8 quark and gluon jets for energy flow, Zenodo (2019) 3164691.
M. Cacciari, G.P. Salam and G. Soyez, The anti-kt jet clustering algorithm, JHEP 04 (2008) 063 [arXiv:0802.1189] [INSPIRE].
M. Cacciari, G.P. Salam and G. Soyez, FastJet User Manual, Eur. Phys. J. C 72 (2012) 1896 [arXiv:1111.6097] [INSPIRE].
H.P. Nilles and K.H. Streng, Quark-Gluon Separation in Three Jet Events, Phys. Rev. D 23 (1981) 1944 [INSPIRE].
L.M. Jones, Tests for Determining the Parton Ancestor of a Hadron Jet, Phys. Rev. D 39 (1989) 2550 [INSPIRE].
Z. Fodor, How to See the Differences Between Quark and Gluon Jets, Phys. Rev. D 41 (1990) 1726 [INSPIRE].
L. Jones, Towards a systematic jet classification, Phys. Rev. D 42 (1990) 811 [INSPIRE].
L. Lönnblad, C. Peterson and T. Rognvaldsson, Using neural networks to identify jets, Nucl. Phys. B 349 (1991) 675 [INSPIRE].
J. Pumplin, How to tell quark jets from gluon jets, Phys. Rev. D 44 (1991) 2025 [INSPIRE].
J. Gallicchio and M.D. Schwartz, Quark and Gluon Jet Substructure, JHEP 04 (2013) 090 [arXiv:1211.7038] [INSPIRE].
B. Bhattacherjee, S. Mukhopadhyay, M.M. Nojiri, Y. Sakaki and B.R. Webber, Associated jet and subjet rates in light-quark and gluon jet discrimination, JHEP 04 (2015) 131 [arXiv:1501.04794] [INSPIRE].
D. Ferreira de Lima, P. Petrov, D. Soper and M. Spannowsky, Quark-Gluon tagging with Shower Deconstruction: Unearthing dark matter and Higgs couplings, Phys. Rev. D 95 (2017) 034001 [arXiv:1607.06031] [INSPIRE].
P. Gras et al., Systematics of quark/gluon tagging, JHEP 07 (2017) 091 [arXiv:1704.03878] [INSPIRE].
A.J. Larkoski, J. Thaler and W.J. Waalewijn, Gaining (Mutual) Information about Quark/Gluon Discrimination, JHEP 11 (2014) 129 [arXiv:1408.3122] [INSPIRE].
C. Frye, A.J. Larkoski, J. Thaler and K. Zhou, Casimir Meets Poisson: Improved Quark/Gluon Discrimination with Counting Observables, JHEP 09 (2017) 083 [arXiv:1704.06266] [INSPIRE].
J. Mo, F.J. Tackmann and W.J. Waalewijn, A case study of quark-gluon discrimination at NNLL’ in comparison to parton showers, Eur. Phys. J. C 77 (2017) 770 [arXiv:1708.00867] [INSPIRE].
A.J. Larkoski and E.M. Metodiev, A Theory of Quark vs. Gluon Discrimination, JHEP 10 (2019) 014 [arXiv:1906.01639] [INSPIRE].
E.M. Metodiev and J. Thaler, Jet Topics: Disentangling Quarks and Gluons at Colliders, Phys. Rev. Lett. 120 (2018) 241602 [arXiv:1802.00008] [INSPIRE].
T. Cheng, Recursive Neural Networks in Quark/Gluon Tagging, Comput. Softw. Big Sci. 2 (2018) 3 [arXiv:1711.02633] [INSPIRE].
H. Lüo, M.-x. Luo, K. Wang, T. Xu and G. Zhu, Quark jet versus gluon jet: fully-connected neural networks with high-level features, Sci. China Phys. Mech. Astron. 62 (2019) 991011 [arXiv:1712.03634] [INSPIRE].
G. Kasieczka, N. Kiefer, T. Plehn and J.M. Thompson, Quark-Gluon Tagging: Machine Learning vs Detector, SciPost Phys. 6 (2019) 069 [arXiv:1812.09223] [INSPIRE].
A.J. Larkoski, I. Moult and D. Neill, Toward Multi-Differential Cross Sections: Measuring Two Angularities on a Single Jet, JHEP 09 (2014) 046 [arXiv:1401.4458] [INSPIRE].
M. Procura, W.J. Waalewijn and L. Zeune, Resummation of Double-Differential Cross Sections and Fully-Unintegrated Parton Distribution Functions, JHEP 02 (2015) 117 [arXiv:1410.6483] [INSPIRE].
M. Procura, W.J. Waalewijn and L. Zeune, Joint resummation of two angularities at next-to-next-to-leading logarithmic order, JHEP 10 (2018) 098 [arXiv:1806.10622] [INSPIRE].
G. Lustermans, A. Papaefstathiou and W.J. Waalewijn, How much joint resummation do we need?, JHEP 10 (2019) 130 [arXiv:1908.07529] [INSPIRE].
A.J. Larkoski, I. Moult and D. Neill, Analytic Boosted Boson Discrimination, JHEP 05 (2016) 117 [arXiv:1507.03018] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2205.06818
Rights and permissions
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.
About this article
Cite this article
Cal, P., Thaler, J. & Waalewijn, W.J. Power counting energy flow polynomials. J. High Energ. Phys. 2022, 21 (2022). https://doi.org/10.1007/JHEP09(2022)021
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP09(2022)021