Abstract
We compute the average Lund multiplicity of high-energy QCD jets. This extends an earlier calculation, done for event-wide multiplicity in e+e− collisions [1], to the large energy range available at the LHC. Our calculation achieves next-to-next-to-double logarithmic (NNDL) accuracy. Our results are split into a universal collinear piece, common to the e+e− calculation, and a non-universal large-angle contribution. The latter amounts to 10–15% of the total multiplicity. We provide accurate LHC predictions by matching our resummed calculation to fixed-order NLO results and by incorporating non-perturbative corrections via Monte Carlo simulations. Including NNDL terms leads to a 50% reduction of the theoretical uncertainty, with non-perturbative corrections remaining below 5% down to transverse momentum scales of a few GeV. This proves the suitability of Lund multiplicities for robust theory-to-data comparisons at the LHC.
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References
R. Medves, A. Soto-Ontoso and G. Soyez, Lund and Cambridge multiplicities for precision physics, JHEP 10 (2022) 156 [arXiv:2205.02861] [INSPIRE].
J. Gallicchio and M.D. Schwartz, Quark and Gluon Tagging at the LHC, Phys. Rev. Lett. 107 (2011) 172001 [arXiv:1106.3076] [INSPIRE].
ATLAS collaboration, Light-quark and gluon jet discrimination in pp collisions at \( \sqrt{s} \) = 7 TeV with the ATLAS detector, Eur. Phys. J. C 74 (2014) 3023 [arXiv:1405.6583] [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].
F.A. Dreyer and H. Qu, Jet tagging in the Lund plane with graph networks, JHEP 03 (2021) 052 [arXiv:2012.08526] [INSPIRE].
R. Kogler et al., Jet Substructure at the Large Hadron Collider: Experimental Review, Rev. Mod. Phys. 91 (2019) 045003 [arXiv:1803.06991] [INSPIRE].
A.J. Larkoski, I. Moult and B. Nachman, Jet Substructure at the Large Hadron Collider: A Review of Recent Advances in Theory and Machine Learning, Phys. Rept. 841 (2020) 1 [arXiv:1709.04464] [INSPIRE].
T. Lapsien, R. Kogler and J. Haller, A new tagger for hadronically decaying heavy particles at the LHC, Eur. Phys. J. C 76 (2016) 600 [arXiv:1606.04961] [INSPIRE].
D. Krohn, J. Thaler and L.-T. Wang, Jets with Variable R, JHEP 06 (2009) 059 [arXiv:0903.0392] [INSPIRE].
A. Tripathee et al., Jet Substructure Studies with CMS Open Data, Phys. Rev. D 96 (2017) 074003 [arXiv:1704.05842] [INSPIRE].
A. Larkoski et al., Exposing the QCD Splitting Function with CMS Open Data, Phys. Rev. Lett. 119 (2017) 132003 [arXiv:1704.05066] [INSPIRE].
ATLAS collaboration, Measurement of the Soft-Drop Jet Mass in pp Collisions at \( \sqrt{s} \) = 13 TeV with the ATLAS Detector, Phys. Rev. Lett. 121 (2018) 092001 [arXiv:1711.08341] [INSPIRE].
CMS collaboration, Measurement of the Splitting Function in pp and Pb-Pb Collisions at \( \sqrt{s_{NN}} \) = 5.02 TeV, Phys. Rev. Lett. 120 (2018) 142302 [arXiv:1708.09429] [INSPIRE].
CMS collaboration, Measurement of jet substructure observables in \( t\overline{t} \) events from proton-proton collisions at \( \sqrt{s} \) = 13 TeV, Phys. Rev. D 98 (2018) 092014 [arXiv:1808.07340] [INSPIRE].
CMS collaboration, Measurement of the groomed jet mass in PbPb and pp collisions at \( \sqrt{s_{NN}} \) = 5.02 TeV, JHEP 10 (2018) 161 [arXiv:1805.05145] [INSPIRE].
ATLAS collaboration, Measurement of soft-drop jet observables in pp collisions with the ATLAS detector at \( \sqrt{s} \) = 13 TeV, Phys. Rev. D 101 (2020) 052007 [arXiv:1912.09837] [INSPIRE].
ATLAS collaboration, Measurement of jet-substructure observables in top quark, W boson and light jet production in proton-proton collisions at \( \sqrt{s} \) = 13 TeV with the ATLAS detector, JHEP 08 (2019) 033 [arXiv:1903.02942] [INSPIRE].
ATLAS collaboration, Measurement of the Lund Jet Plane Using Charged Particles in 13 TeV Proton-Proton Collisions with the ATLAS Detector, Phys. Rev. Lett. 124 (2020) 222002 [arXiv:2004.03540] [INSPIRE].
STAR collaboration, Measurement of groomed jet substructure observables in p + p collisions at \( \sqrt{s} \) = 200 GeV with STAR, Phys. Lett. B 811 (2020) 135846 [arXiv:2003.02114] [INSPIRE].
A Large Ion Collider Experiment and ALICE collaborations, Measurement of the groomed jet radius and momentum splitting fraction in pp and Pb Pb collisions at \( \sqrt{s_{NN}} \) = 5.02 TeV, Phys. Rev. Lett. 128 (2022) 102001 [arXiv:2107.12984] [INSPIRE].
ALICE collaboration, Measurements of the groomed jet radius and momentum splitting fraction with the soft drop and dynamical grooming algorithms in pp collisions at \( \sqrt{s} \) = 5.02 TeV, arXiv:2204.10246 [INSPIRE].
ALICE collaboration, Measurements of groomed-jet substructure of charm jets tagged by D0 mesons in proton-proton collisions at \( \sqrt{s} \) = 13 TeV, arXiv:2208.04857 [INSPIRE].
M. Dasgupta, K. Khelifa-Kerfa, S. Marzani and M. Spannowsky, On jet mass distributions in Z + jet and dijet processes at the LHC, JHEP 10 (2012) 126 [arXiv:1207.1640] [INSPIRE].
D. Napoletano and G. Soyez, Computing N-subjettiness for boosted jets, JHEP 12 (2018) 031 [arXiv:1809.04602] [INSPIRE].
P. Cal, F. Ringer and W.J. Waalewijn, The jet shape at NLL’, JHEP 05 (2019) 143 [arXiv:1901.06389] [INSPIRE].
A. Lifson, G.P. Salam and G. Soyez, Calculating the primary Lund Jet Plane density, JHEP 10 (2020) 170 [arXiv:2007.06578] [INSPIRE].
D. Reichelt et al., Phenomenology of jet angularities at the LHC, JHEP 03 (2022) 131 [arXiv:2112.09545] [INSPIRE].
N. Ziani, K. Khelifa-Kerfa and Y. Delenda, Jet mass distribution in Higgs/vector boson + jet events at hadron colliders with kt clustering, Eur. Phys. J. C 81 (2021) 570 [arXiv:2104.11060] [INSPIRE].
S. Caletti et al., Jet angularities in Z + jet production at the LHC, JHEP 07 (2021) 076 [arXiv:2104.06920] [INSPIRE].
K. Lee, B. Meçaj and I. Moult, Conformal Colliders Meet the LHC, arXiv:2205.03414 [INSPIRE].
E. Craft, K. Lee, B. Meçaj and I. Moult, Beautiful and Charming Energy Correlators, arXiv:2210.09311 [INSPIRE].
S. Marzani, L. Schunk and G. Soyez, The jet mass distribution after Soft Drop, Eur. Phys. J. C 78 (2018) 96 [arXiv:1712.05105] [INSPIRE].
Z.-B. Kang, K. Lee, X. Liu and F. Ringer, The groomed and ungroomed jet mass distribution for inclusive jet production at the LHC, JHEP 10 (2018) 137 [arXiv:1803.03645] [INSPIRE].
Z.-B. Kang et al., The soft drop groomed jet radius at NLL, JHEP 02 (2020) 054 [arXiv:1908.01783] [INSPIRE].
P. Cal, D. Neill, F. Ringer and W.J. Waalewijn, Calculating the angle between jet axes, JHEP 04 (2020) 211 [arXiv:1911.06840] [INSPIRE].
D. Anderle et al., Groomed jet mass as a direct probe of collinear parton dynamics, Eur. Phys. J. C 80 (2020) 827 [arXiv:2007.10355] [INSPIRE].
P. Cal, K. Lee, F. Ringer and W.J. Waalewijn, Jet energy drop, JHEP 11 (2020) 012 [arXiv:2007.12187] [INSPIRE].
P. Cal, K. Lee, F. Ringer and W.J. Waalewijn, The soft drop momentum sharing fraction zg beyond leading-logarithmic accuracy, Phys. Lett. B 833 (2022) 137390 [arXiv:2106.04589] [INSPIRE].
C. Frye, A.J. Larkoski, M.D. Schwartz and K. Yan, Factorization for groomed jet substructure beyond the next-to-leading logarithm, JHEP 07 (2016) 064 [arXiv:1603.09338] [INSPIRE].
Z.-B. Kang, K. Lee, X. Liu and F. Ringer, Soft drop groomed jet angularities at the LHC, Phys. Lett. B 793 (2019) 41 [arXiv:1811.06983] [INSPIRE].
M. Dasgupta, B.K. El-Menoufi and J. Helliwell, QCD resummation for groomed jet observables at NNLL + NLO, JHEP 01 (2023) 045 [arXiv:2211.03820] [INSPIRE].
H.S. Hannesdottir, A. Pathak, M.D. Schwartz and I.W. Stewart, Prospects for strong coupling measurement at hadron colliders using soft-drop jet mass, arXiv:2210.04901 [INSPIRE].
E. Gerwick, S. Schumann, B. Gripaios and B. Webber, QCD Jet Rates with the Inclusive Generalized kt Algorithms, JHEP 04 (2013) 089 [arXiv:1212.5235] [INSPIRE].
B. Bhattacherjee et al., Associated jet and subjet rates in light-quark and gluon jet discrimination, JHEP 04 (2015) 131 [arXiv:1501.04794] [INSPIRE].
P. Caucal, A. Soto-Ontoso and A. Takacs, Dynamical Grooming meets LHC data, JHEP 07 (2021) 020 [arXiv:2103.06566] [INSPIRE].
A.J. Larkoski, S. Marzani and J. Thaler, Sudakov Safety in Perturbative QCD, Phys. Rev. D 91 (2015) 111501 [arXiv:1502.01719] [INSPIRE].
F.A. Dreyer, G.P. Salam and G. Soyez, The Lund Jet Plane, JHEP 12 (2018) 064 [arXiv:1807.04758] [INSPIRE].
F.A. Dreyer, G. Soyez and A. Takacs, Quarks and gluons in the Lund plane, JHEP 08 (2022) 177 [arXiv:2112.09140] [INSPIRE].
S. Catani, Y.L. Dokshitzer, F. Fiorani and B.R. Webber, Average number of jets in e+e− annihilation, Nucl. Phys. B 377 (1992) 445 [INSPIRE].
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 the proceedings of the Workshop on Monte Carlo Generators for HERA Physics (Plenary Starting Meeting), Hamburg Germany, April 27–30 April (1998), pp. 270–279 [hep-ph/9907280] [INSPIRE].
A.J. Larkoski, D. Neill and J. Thaler, Jet Shapes with the Broadening Axis, JHEP 04 (2014) 017 [arXiv:1401.2158] [INSPIRE].
M. Cacciari, G.P. Salam and G. Soyez, The anti-kt jet clustering algorithm, JHEP 04 (2008) 063 [arXiv:0802.1189] [INSPIRE].
R.K. Ellis, G. Marchesini and B.R. Webber, Soft Radiation in Parton Parton Scattering, Nucl. Phys. B 286 (1987) 643 [Erratum ibid. 294 (1987) 1180] [INSPIRE].
Y. Hatta, E. Iancu, A.H. Mueller and D.N. Triantafyllopoulos, Resumming double non-global logarithms in the evolution of a jet, JHEP 02 (2018) 075 [arXiv:1710.06722] [INSPIRE].
M. Cacciari, G.P. Salam and G. Soyez, FastJet User Manual, Eur. Phys. J. C 72 (2012) 1896 [arXiv:1111.6097] [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].
Z. Nagy, Next-to-leading order calculation of three jet observables in hadron hadron collision, Phys. Rev. D 68 (2003) 094002 [hep-ph/0307268] [INSPIRE].
A. Banfi, G.P. Salam and G. Zanderighi, Accurate QCD predictions for heavy-quark jets at the Tevatron and LHC, JHEP 07 (2007) 026 [arXiv:0704.2999] [INSPIRE].
PDF4LHC Working Group collaboration, The PDF4LHC21 combination of global PDF fits for the LHC Run III, J. Phys. G 49 (2022) 080501 [arXiv:2203.05506] [INSPIRE].
S. Bright-Thonney and B. Nachman, Investigating the Topology Dependence of Quark and Gluon Jets, JHEP 03 (2019) 098 [arXiv:1810.05653] [INSPIRE].
M. Cacciari et al., The t anti-t cross-section at 1.8 TeV and 1.96 TeV: A Study of the systematics due to parton densities and scale dependence, JHEP 04 (2004) 068 [hep-ph/0303085] [INSPIRE].
C. Bierlich et al., A comprehensive guide to the physics and usage of PYTHIA 8.3, arXiv:2203.11601 [https://doi.org/10.21468/SciPostPhysCodeb.8] [INSPIRE].
P. Skands, S. Carrazza and J. Rojo, Tuning PYTHIA 8.1: the Monash 2013 Tune, Eur. Phys. J. C 74 (2014) 3024 [arXiv:1404.5630] [INSPIRE].
R. Corke and T. Sjostrand, Interleaved Parton Showers and Tuning Prospects, JHEP 03 (2011) 032 [arXiv:1011.1759] [INSPIRE].
ATLAS collaboration, ATLAS Pythia 8 tunes to 7 TeV data, ATL-PHYS-PUB-2014-021, CERN, Geneva (2014) [INSPIRE].
J. Bellm et al., Herwig 7.0/Herwig++ 3.0 release note, Eur. Phys. J. C 76 (2016) 196 [arXiv:1512.01178] [INSPIRE].
Sherpa collaboration, Event Generation with Sherpa 2.2, SciPost Phys. 7 (2019) 034 [arXiv:1905.09127] [INSPIRE].
S. Abreu et al., Leading-color two-loop QCD corrections for three-jet production at hadron colliders, JHEP 07 (2021) 095 [arXiv:2102.13609] [INSPIRE].
M. Czakon, A. Mitov and R. Poncelet, Next-to-Next-to-Leading Order Study of Three-Jet Production at the LHC, Phys. Rev. Lett. 127 (2021) 152001 [Erratum ibid. 129 (2022) 119901] [arXiv:2106.05331] [INSPIRE].
ATLAS collaboration, Measurement of the charged-particle multiplicity inside jets from \( \sqrt{s} \) = 8 TeV pp collisions with the ATLAS detector, Eur. Phys. J. C 76 (2016) 322 [arXiv:1602.00988] [INSPIRE].
CMS collaboration, Study of quark and gluon jet substructure in Z + jet and dijet events from pp collisions, JHEP 01 (2022) 188 [arXiv:2109.03340] [INSPIRE].
ATLAS collaboration, Jet energy scale measurements and their systematic uncertainties in proton-proton collisions at \( \sqrt{s} \) = 13 TeV with the ATLAS detector, Phys. Rev. D 96 (2017) 072002 [arXiv:1703.09665] [INSPIRE].
M. Dasgupta et al., Parton showers beyond leading logarithmic accuracy, Phys. Rev. Lett. 125 (2020) 052002 [arXiv:2002.11114] [INSPIRE].
K. Hamilton et al., Colour and logarithmic accuracy in final-state parton showers, JHEP 03 (2021) 041 [arXiv:2011.10054] [INSPIRE].
A. Karlberg, G.P. Salam, L. Scyboz and R. Verheyen, Spin correlations in final-state parton showers and jet observables, Eur. Phys. J. C 81 (2021) 681 [arXiv:2103.16526] [INSPIRE].
K. Hamilton et al., Soft spin correlations in final-state parton showers, JHEP 03 (2022) 193 [arXiv:2111.01161] [INSPIRE].
M. van Beekveld et al., PanScales showers for hadron collisions: all-order validation, JHEP 11 (2022) 020 [arXiv:2207.09467] [INSPIRE].
M. van Beekveld et al., PanScales parton showers for hadron collisions: formulation and fixed-order studies, JHEP 11 (2022) 019 [arXiv:2205.02237] [INSPIRE].
F. Herren et al., A new approach to color-coherent parton evolution, arXiv:2208.06057 [INSPIRE].
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Medves, R., Soto-Ontoso, A. & Soyez, G. Lund multiplicity in QCD jets. J. High Energ. Phys. 2023, 104 (2023). https://doi.org/10.1007/JHEP04(2023)104
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DOI: https://doi.org/10.1007/JHEP04(2023)104