Abstract
One of the key tasks of any particle collider is measurement. In practice, this is often done by fitting data to a simulation, which depends on many parameters. Sometimes, when the effects of varying different parameters are highly correlated, a large ensemble of data may be needed to resolve parameter-space degeneracies. An important example is measuring the top-quark mass, where other physical and unphysical parameters in the simulation must be profiled when fitting the top-quark mass parameter. We compare four different methodologies for top-quark mass measurement: a classical histogram fit similar to one commonly used in experiment augmented by soft-drop jet grooming; a 2D profile likelihood fit with a nuisance parameter; a machine-learning method called DCTR; and a linear regression approach, either using a least-squares fit or with a dense linearly-activated neural network. Despite the fact that individual events are totally uncorrelated, we find that the linear regression methods work most effectively when we input an ensemble of events sorted by mass, rather than training them on individual events. Although all methods provide robust extraction of the top-quark mass parameter, the linear network does marginally best and is remarkably simple. For the top study, we conclude that the Monte-Carlo-based uncertainty on current extractions of the top-quark mass from LHC data can be reduced significantly (by perhaps a factor of 2) using networks trained on sorted event ensembles. More generally, machine learning from ensembles for parameter estimation has broad potential for collider physics measurements.
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T. Sjöstrand et al., An introduction to PYTHIA 8.2, Comput. Phys. Commun. 191 (2015) 159 [arXiv:1410.3012] [INSPIRE].
S.R. Coleman and E.J. Weinberg, Radiative corrections as the origin of spontaneous symmetry breaking, Phys. Rev. D 7 (1973) 1888 [INSPIRE].
G. Isidori, G. Ridolfi and A. Strumia, On the metastability of the standard model vacuum, Nucl. Phys. B 609 (2001) 387 [hep-ph/0104016] [INSPIRE].
G. Degrassi et al., Higgs mass and vacuum stability in the standard model at NNLO, JHEP 08 (2012) 098 [arXiv:1205.6497] [INSPIRE].
A. Andreassen, W. Frost and M.D. Schwartz, Scale invariant instantons and the complete lifetime of the standard model, Phys. Rev. D 97 (2018) 056006 [arXiv:1707.08124] [INSPIRE].
M. Czakon, A. Mitov, M. Papucci, J.T. Ruderman and A. Weiler, Closing the stop gap, Phys. Rev. Lett. 113 (2014) 201803 [arXiv:1407.1043] [INSPIRE].
T. Eifert and B. Nachman, Sneaky light stop, Phys. Lett. B 743 (2015) 218 [arXiv:1410.7025] [INSPIRE].
ATLAS collaboration, Measurement of the t\( \overline{t} \) production cross-section using eμ events with b-tagged jets in pp collisions at \( \sqrt{s} \) = 7 and 8 TeV with the ATLAS detector, Eur. Phys. J. C 74 (2014) 3109 [Addendum ibid. 76 (2016) 642] [arXiv:1406.5375] [INSPIRE].
T. Cohen, W. Hopkins, S. Majewski and B. Ostdiek, Magnifying the ATLAS Stealth Stop Splinter: impact of spin correlations and finite widths, JHEP 07 (2018) 142 [arXiv:1804.00111] [INSPIRE].
T. Cohen, S. Majewski, B. Ostdiek and P. Zheng, On the ATLAS top mass measurements and the potential for stealth stop contamination, JHEP 06 (2020) 019 [arXiv:1909.09670] [INSPIRE].
ATLAS collaboration, Measurements of top-quark pair spin correlations in the eμ channel at \( \sqrt{s} \) = 13 TeV using pp collisions in the ATLAS detector, Eur. Phys. J. C 80 (2020) 754 [arXiv:1903.07570] [INSPIRE].
CMS collaboration, Measurement of the t\( \overline{t} \) production cross section, the top quark mass, and the strong coupling constant using dilepton events in pp collisions at \( \sqrt{s} \) = 13 TeV, Eur. Phys. J. C 79 (2019) 368 [arXiv:1812.10505].
CMS collaboration, Measurement of the t\( \overline{t} \) production cross section in the e-μ channel in proton-proton collisions at \( \sqrt{s} \) = 7 and 8 TeV, JHEP 08 (2016) 029 [arXiv:1603.02303] [INSPIRE].
CMS collaboration, Measurement of the t\( \overline{t} \) production cross section, the top quark mass, and the strong coupling constant using dilepton events in pp collisions at \( \sqrt{s} \) = 13 TeV, Eur. Phys. J. C 79 (2019) 368 [arXiv:1812.10505] [INSPIRE].
ATLAS collaboration, Measurement of the t\( \overline{t} \) production cross-section and lepton differential distributions in eμ dilepton events from pp collisions at \( \sqrt{s} \) = 13 TeV with the ATLAS detector, Eur. Phys. J. C 80 (2020) 528 [arXiv:1910.08819].
ATLAS collaboration, Measurement of lepton differential distributions and the top quark mass in t\( \overline{t} \) production in pp collisions at \( \sqrt{s} \) = 8 TeV with the ATLAS detector, Eur. Phys. J. C 77 (2017) 804 [arXiv:1709.09407] [INSPIRE].
CMS collaboration, Measurement of t\( \overline{\mathrm{t}} \) normalised multi-differential cross sections in pp collisions at \( \sqrt{s} \) = 13 TeV, and simultaneous determination of the strong coupling strength, top quark pole mass, and parton distribution functions, Eur. Phys. J. C 80 (2020) 658 [arXiv:1904.05237] [INSPIRE].
ATLAS collaboration, Measurement of the top quark mass in the t\( \overline{t} \) → dilepton channel from \( \sqrt{s} \) = 8 TeV ATLAS data, Phys. Lett. B 761 (2016) 350 [arXiv:1606.02179] [INSPIRE].
ATLAS collaboration, Top-quark mass measurement in the all-hadronic t\( \overline{t} \) decay channel at \( \sqrt{s} \) = 8 TeV with the ATLAS detector, JHEP 09 (2017) 118 [arXiv:1702.07546] [INSPIRE].
ATLAS collaboration, Measurement of the top quark mass in the t\( \overline{t} \) → lepton+jets channel from \( \sqrt{s} \) = 8 TeV ATLAS data and combination with previous results, Eur. Phys. J. C 79 (2019) 290 [arXiv:1810.01772] [INSPIRE].
CMS collaboration, Measurement of the top quark mass with lepton+jets final states using pp collisions at \( \sqrt{s} \) = 13 TeV, Eur. Phys. J. C 78 (2018) 891 [arXiv:1805.01428] [INSPIRE].
CMS collaboration, Measurement of the top quark mass in the all-jets final state at \( \sqrt{s} \) = 13 TeV and combination with the lepton+jets channel, Eur. Phys. J. C 79 (2019) 313 [arXiv:1812.10534] [INSPIRE].
A.H. Hoang, S. Plätzer and D. Samitz, On the cutoff dependence of the quark mass parameter in angular ordered parton showers, JHEP 10 (2018) 200 [arXiv:1807.06617] [INSPIRE].
S. Fleming, A.H. Hoang, S. Mantry and I.W. Stewart, Jets from massive unstable particles: top-mass determination, Phys. Rev. D 77 (2008) 074010 [hep-ph/0703207] [INSPIRE].
A.H. Hoang and I.W. Stewart, Top mass measurements from jets and the tevatron top-quark mass, Nucl. Phys. B Proc. Suppl. 185 (2008) 220 [arXiv:0808.0222] [INSPIRE].
M. Butenschoen, B. Dehnadi, A.H. Hoang, V. Mateu, M. Preisser and I.W. Stewart, Top quark mass calibration for Monte Carlo event generators, Phys. Rev. Lett. 117 (2016) 232001 [arXiv:1608.01318] [INSPIRE].
A.H. Hoang, S. Mantry, A. Pathak and I.W. Stewart, Extracting a short distance top mass with light grooming, Phys. Rev. D 100 (2019) 074021 [arXiv:1708.02586] [INSPIRE].
A.H. Hoang, What is the top quark mass?, Ann. Rev. Nucl. Part. Sci. 70 (2020) 225 [arXiv:2004.12915] [INSPIRE].
J. Kieseler, K. Lipka and S.-O. Moch, Calibration of the top-quark Monte Carlo mass, Phys. Rev. Lett. 116 (2016) 162001 [arXiv:1511.00841] [INSPIRE].
A. Andreassen and M.D. Schwartz, Reducing the top quark mass uncertainty with jet grooming, JHEP 10 (2017) 151 [arXiv:1705.07135] [INSPIRE].
A.J. Larkoski, S. Marzani, G. Soyez and J. Thaler, Soft drop, JHEP 05 (2014) 146 [arXiv:1402.2657] [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].
A. Andreassen, I. Feige, C. Frye and M.D. Schwartz, Binary JUNIPR: an interpretable probabilistic model for discrimination, Phys. Rev. Lett. 123 (2019) 182001 [arXiv:1906.10137] [INSPIRE].
A. Andreassen and B. Nachman, Neural networks for full phase-space reweighting and parameter tuning, Phys. Rev. D 101 (2020) 091901 [arXiv:1907.08209] [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].
M. Zaheer et al., Deep sets, in Advances in Neural Information Processing Systems, I. Guyon et al. eds., Curran Associates, U.S.A. (2017).
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].
M.J. Fenton, A. Shmakov, T.-W. Ho, S.-C. Hsu, D. Whiteson and P. Baldi, Permutationless many-jet event reconstruction with symmetry preserving attention networks, arXiv:2010.09206 [INSPIRE].
ATLAS collabroation, ATLAS Pythia 8 tunes to 7 TeV data, ATL-PHYS-PUB-2014-021 (2014).
J. Pumplin, D.R. Stump, J. Huston, H.L. Lai, P.M. Nadolsky and W.K. Tung, New generation of parton distributions with uncertainties from global QCD analysis, JHEP 07 (2002) 012 [hep-ph/0201195] [INSPIRE].
G. Watt and R.S. Thorne, Study of Monte Carlo approach to experimental uncertainty propagation with MSTW 2008 PDFs, JHEP 08 (2012) 052 [arXiv:1205.4024] [INSPIRE].
S. Carrazza, S. Forte and J. Rojo, Parton distributions and event generators, arXiv:1311.5887 [INSPIRE].
A.M. Cooper-Sarkar, HERAPDF1.5LO PDF Set with Experimental Uncertainties, PoS DIS2014 (2014) 032 [INSPIRE].
S. Argyropoulos and T. Sjöstrand, Effects of color reconnection on t\( \overline{t} \) final states at the LHC, JHEP 11 (2014) 043 [arXiv:1407.6653] [INSPIRE].
P.Z. Skands and D. Wicke, Non-perturbative QCD effects and the top mass at the Tevatron, Eur. Phys. J. C 52 (2007) 133 [hep-ph/0703081] [INSPIRE].
F. Chollet et al., Keras, https://keras.io (2015).
D.P. Kingma and J. Ba, Adam: a method for stochastic optimization, arXiv:1412.6980 [INSPIRE].
S.D. Ellis, A. Hornig, T.S. Roy, D. Krohn and M.D. Schwartz, Qjets: a non-deterministic approach to tree-based jet substructure, Phys. Rev. Lett. 108 (2012) 182003 [arXiv:1201.1914] [INSPIRE].
Y.-T. Chien, Telescoping jets: Probing hadronic event structure with multiple R’s, Phys. Rev. D 90 (2014) 054008 [arXiv:1304.5240] [INSPIRE].
Y.-T. Chien, D. Farhi, D. Krohn, A. Marantan, D. Lopez Mateos and M. Schwartz, Quantifying the power of multiple event interpretations, JHEP 12 (2014) 140 [arXiv:1407.2892] [INSPIRE].
F. Pedregosa et al., Scikit-learn: machine learning in Python, J. Mach. Learn. Res. 12 (2011) 2825.
P. Baldi, K. Cranmer, T. Faucett, P. Sadowski and D. Whiteson, Parameterized neural networks for high-energy physics, Eur. Phys. J. C 76 (2016) 235 [arXiv:1601.07913] [INSPIRE].
K. Cranmer, J. Pavez and G. Louppe, Approximating likelihood ratios with calibrated discriminative classifiers, arXiv:1506.02169 [INSPIRE].
J. Brehmer, K. Cranmer, G. Louppe and J. Pavez, Constraining effective field theories with machine learning, Phys. Rev. Lett. 121 (2018) 111801 [arXiv:1805.00013] [INSPIRE].
J. Brehmer, K. Cranmer, G. Louppe and J. Pavez, A guide to constraining effective field theories with machine learning, Phys. Rev. D 98 (2018) 052004 [arXiv:1805.00020] [INSPIRE].
J. Brehmer, G. Louppe, J. Pavez and K. Cranmer, Mining gold from implicit models to improve likelihood-free inference, Proc. Nat. Acad. Sci. 117 (2020) 5242 [arXiv:1805.12244] [INSPIRE].
M. Stoye, J. Brehmer, G. Louppe, J. Pavez and K. Cranmer, Likelihood-free inference with an improved cross-entropy estimator, arXiv:1808.00973 [INSPIRE].
J. Brehmer, F. Kling, I. Espejo and K. Cranmer, MadMiner: machine learning-based inference for particle physics, Comput. Softw. Big Sci. 4 (2020) 3 [arXiv:1907.10621] [INSPIRE].
A. Andreassen, P.T. Komiske, E.M. Metodiev, B. Nachman and J. Thaler, OmniFold: a method to simultaneously unfold all observables, Phys. Rev. Lett. 124 (2020) 182001 [arXiv:1911.09107] [INSPIRE].
M. Erdmann et al., Adversarial Neural Network-based data-simulation corrections for jet-tagging at CMS, J. Phys. Conf. Ser. 1525 (2020) 012094.
J. Hollingsworth and D. Whiteson, Resonance searches with machine learned likelihood ratios, arXiv:2002.04699 [INSPIRE].
F.A. Di Bello et al., Efficiency parameterization with neural networks, Comput. Softw. Big Sci. 5 (2021) 14 [arXiv:2004.02665] [INSPIRE].
A. Andreassen, B. Nachman and D. Shih, Simulation assisted likelihood-free anomaly detection, Phys. Rev. D 101 (2020) 095004 [arXiv:2001.05001] [INSPIRE].
A. Andreassen, S.-C. Hsu, B. Nachman, N. Suaysom and A. Suresh, Parameter estimation using neural networks in the presence of detector effects, Phys. Rev. D 103 (2021) 036001 [arXiv:2010.03569] [INSPIRE].
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Flesher, F., Fraser, K., Hutchison, C. et al. Parameter inference from event ensembles and the top-quark mass. J. High Energ. Phys. 2021, 58 (2021). https://doi.org/10.1007/JHEP09(2021)058
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DOI: https://doi.org/10.1007/JHEP09(2021)058