Abstract
To explore the interplay of NLO matching and next-to-leading logarithmic (NLL) parton showers, we consider the simplest case of γ* and Higgs-boson decays to \( q\overline{q} \) and gg respectively. Not only should shower NLL accuracy be retained across observables after matching, but for global event-shape observables and the two-jet rate, matching can augment the shower in such a way that it additionally achieves next-to-next-to-double-logarithmic (NNDL) accuracy, a first step on the route towards general NNLL. As a proof-of-concept exploration of this question, we consider direct application of multiplicative matrix-element corrections, as well as simple implementations of MC@NLO and POWHEG-style matching. We find that the first two straightforwardly bring NNDL accuracy, and that this can also be achieved with POWHEG, although particular care is needed in the handover between POWHEG and the shower. Our study involves both analytic and numerical components and we also touch on some phenomenological considerations.
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10 November 2023
An Erratum to this paper has been published: https://doi.org/10.1007/JHEP11(2023)060
References
S. Frixione and B.R. Webber, Matching NLO QCD computations and parton shower simulations, JHEP 06 (2002) 029 [hep-ph/0204244] [INSPIRE].
P. Nason, A New method for combining NLO QCD with shower Monte Carlo algorithms, JHEP 11 (2004) 040 [hep-ph/0409146] [INSPIRE].
S. Frixione, P. Nason and C. Oleari, Matching NLO QCD computations with Parton Shower simulations: the POWHEG method, JHEP 11 (2007) 070 [arXiv:0709.2092] [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].
S. Alioli, P. Nason, C. Oleari and E. Re, A general framework for implementing NLO calculations in shower Monte Carlo programs: the POWHEG BOX, JHEP 06 (2010) 043 [arXiv:1002.2581] [INSPIRE].
T. Ježo and P. Nason, On the Treatment of Resonances in Next-to-Leading Order Calculations Matched to a Parton Shower, JHEP 12 (2015) 065 [arXiv:1509.09071] [INSPIRE].
J. Bellm et al., Herwig 7.0/Herwig++ 3.0 release note, Eur. Phys. J. C 76 (2016) 196 [arXiv:1512.01178] [INSPIRE].
C. Reuschle et al., NLO efforts in Herwig++, PoS RADCOR2015 (2016) 050 [arXiv:1601.04101] [INSPIRE].
S. Hoche, F. Krauss, M. Schonherr and F. Siegert, Automating the POWHEG method in Sherpa, JHEP 04 (2011) 024 [arXiv:1008.5399] [INSPIRE].
Sherpa collaboration, Event Generation with Sherpa 2.2, SciPost Phys. 7 (2019) 034 [arXiv:1905.09127] [INSPIRE].
C.W. Bauer, F.J. Tackmann and J. Thaler, GenEvA. I. A New framework for event generation, JHEP 12 (2008) 010 [arXiv:0801.4026] [INSPIRE].
L. Lönnblad and S. Prestel, Merging Multi-leg NLO Matrix Elements with Parton Showers, JHEP 03 (2013) 166 [arXiv:1211.7278] [INSPIRE].
S. Jadach et al., Matching NLO QCD with parton shower in Monte Carlo scheme — the KrkNLO method, JHEP 10 (2015) 052 [arXiv:1503.06849] [INSPIRE].
M. Dasgupta et al., Logarithmic accuracy of parton showers: a fixed-order study, JHEP 09 (2018) 033 [Erratum ibid. 03 (2020) 083] [arXiv:1805.09327] [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 parton showers for hadron collisions: formulation and fixed-order studies, JHEP 11 (2022) 019 [arXiv:2205.02237] [INSPIRE].
M. van Beekveld et al., PanScales showers for hadron collisions: all-order validation, JHEP 11 (2022) 020 [arXiv:2207.09467] [INSPIRE].
J.R. Forshaw, J. Holguin and S. Plätzer, Building a consistent parton shower, JHEP 09 (2020) 014 [arXiv:2003.06400] [INSPIRE].
J. Holguin, J.R. Forshaw and S. Plätzer, Improvements on dipole shower colour, Eur. Phys. J. C 81 (2021) 364 [arXiv:2011.15087] [INSPIRE].
Z. Nagy and D.E. Soper, Summations of large logarithms by parton showers, Phys. Rev. D 104 (2021) 054049 [arXiv:2011.04773] [INSPIRE].
Z. Nagy and D.E. Soper, Summations by parton showers of large logarithms in electron-positron annihilation, arXiv:2011.04777 [DESY 20-182] [INSPIRE].
F. Herren et al., A new approach to color-coherent parton evolution, arXiv:2208.06057 [FERMILAB-PUB-22-556-T] [INSPIRE].
S. Catani, L. Trentadue, G. Turnock and B.R. Webber, Resummation of large logarithms in e+ e- event shape distributions, Nucl. Phys. B 407 (1993) 3 [INSPIRE].
S. Catani, F. Krauss, R. Kuhn and B.R. Webber, QCD matrix elements + parton showers, JHEP 11 (2001) 063 [hep-ph/0109231] [INSPIRE].
M. Bengtsson and T. Sjostrand, Coherent Parton Showers Versus Matrix Elements: Implications of PETRA - PEP Data, Phys. Lett. B 185 (1987) 435 [INSPIRE].
M.H. Seymour, Matrix element corrections to parton shower algorithms, Comput. Phys. Commun. 90 (1995) 95 [hep-ph/9410414] [INSPIRE].
W.T. Giele, D.A. Kosower and P.Z. Skands, A simple shower and matching algorithm, Phys. Rev. D 78 (2008) 014026 [arXiv:0707.3652] [INSPIRE].
P. Nason and G.P. Salam, Multiplicative-accumulative matching of NLO calculations with parton showers, JHEP 01 (2022) 067 [arXiv:2111.03553] [INSPIRE].
K. Hamilton, P. Nason, E. Re and G. Zanderighi, NNLOPS simulation of Higgs boson production, JHEP 10 (2013) 222 [arXiv:1309.0017] [INSPIRE].
P.F. Monni et al., MiNNLOP S: a new method to match NNLO QCD to parton showers, JHEP 05 (2020) 143 [Erratum ibid. 02 (2022) 031] [arXiv:1908.06987] [INSPIRE].
S. Alioli et al., Matching Fully Differential NNLO Calculations and Parton Showers, JHEP 06 (2014) 089 [arXiv:1311.0286] [INSPIRE].
S. Höche, Y. Li and S. Prestel, Drell-Yan lepton pair production at NNLO QCD with parton showers, Phys. Rev. D 91 (2015) 074015 [arXiv:1405.3607] [INSPIRE].
R. Corke and T. Sjostrand, Improved Parton Showers at Large Transverse Momenta, Eur. Phys. J. C 69 (2010) 1 [arXiv:1003.2384] [INSPIRE].
R. Medves, A. Soto-Ontoso and G. Soyez, Lund and Cambridge multiplicities for precision physics, JHEP 10 (2022) 156 [arXiv:2205.02861] [INSPIRE].
R. Medves, A. Soto-Ontoso and G. Soyez, Lund multiplicity in QCD jets, arXiv:2212.05076 [CERN-TH-2022-205] [INSPIRE].
P. Nason and B. Webber, Next-to-Leading-Order Event Generators, Ann. Rev. Nucl. Part. Sci. 62 (2012) 187 [arXiv:1202.1251] [INSPIRE].
S. Frixione, Z. Kunszt and A. Signer, Three jet cross-sections to next-to-leading order, Nucl. Phys. B 467 (1996) 399 [hep-ph/9512328] [INSPIRE].
S. Catani, B.R. Webber and G. Marchesini, QCD coherent branching and semiinclusive processes at large x, Nucl. Phys. B 349 (1991) 635 [INSPIRE].
A. Banfi, G.P. Salam and G. Zanderighi, Principles of general final-state resummation and automated implementation, JHEP 03 (2005) 073 [hep-ph/0407286] [INSPIRE].
S. Brandt, C. Peyrou, R. Sosnowski and A. Wroblewski, The Principal axis of jets. An Attempt to analyze high-energy collisions as two-body processes, Phys. Lett. 12 (1964) 57 [INSPIRE].
E. Farhi, A QCD Test for Jets, Phys. Rev. Lett. 39 (1977) 1587 [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].
B. Andersson, G. Gustafson, L. Lonnblad and U. Pettersson, Coherence Effects in Deep Inelastic Scattering, Z. Phys. C 43 (1989) 625 [INSPIRE].
M. Dasgupta, A. Fregoso, S. Marzani and G.P. Salam, Towards an understanding of jet substructure, JHEP 09 (2013) 029 [arXiv:1307.0007] [INSPIRE].
A.J. Larkoski, S. Marzani, G. Soyez and J. Thaler, Soft Drop, JHEP 05 (2014) 146 [arXiv:1402.2657] [INSPIRE].
R.K. Ellis, D.A. Ross and A.E. Terrano, The Perturbative Calculation of Jet Structure in e+ e- Annihilation, Nucl. Phys. B 178 (1981) 421 [INSPIRE].
G. Parisi, Super Inclusive Cross-Sections, Phys. Lett. B 74 (1978) 65 [INSPIRE].
J.F. Donoghue, F.E. Low and S.-Y. Pi, Tensor Analysis of Hadronic Jets in Quantum Chromodynamics, Phys. Rev. D 20 (1979) 2759 [INSPIRE].
F.A. Dreyer, G.P. Salam and G. Soyez, The Lund Jet Plane, JHEP 12 (2018) 064 [arXiv:1807.04758] [INSPIRE].
S. Mrenna and P. Skands, Automated Parton-Shower Variations in Pythia 8, Phys. Rev. D 94 (2016) 074005 [arXiv:1605.08352] [INSPIRE].
T. Sjostrand and P.Z. Skands, Transverse-momentum-ordered showers and interleaved multiple interactions, Eur. Phys. J. C 39 (2005) 129 [hep-ph/0408302] [INSPIRE].
L. Hartgring, E. Laenen and P. Skands, Antenna Showers with One-Loop Matrix Elements, JHEP 10 (2013) 127 [arXiv:1303.4974] [INSPIRE].
Y.L. Dokshitzer, G. Marchesini and G. Oriani, Measuring color flows in hard processes: Beyond leading order, Nucl. Phys. B 387 (1992) 675 [INSPIRE].
P. Cox and T. Melia, Independently Parameterised Momenta Variables and Monte Carlo IR Subtraction, JHEP 12 (2018) 038 [arXiv:1809.09325] [INSPIRE].
S. Catani, G. Turnock, B.R. Webber and L. Trentadue, Thrust distribution in e+ e- annihilation, Phys. Lett. B 263 (1991) 491 [INSPIRE].
A. Banfi, G.P. Salam and G. Zanderighi, Semi-numerical resummation of event shapes, JHEP 01 (2002) 018 [hep-ph/0112156] [INSPIRE].
T. Becher and G. Bell, NNLL Resummation for Jet Broadening, JHEP 11 (2012) 126 [arXiv:1210.0580] [INSPIRE].
S. Catani and B.R. Webber, Resummed C parameter distribution in e+ e- annihilation, Phys. Lett. B 427 (1998) 377 [hep-ph/9801350] [INSPIRE].
P. Richardson, Spin correlations in Monte Carlo simulations, JHEP 11 (2001) 029 [hep-ph/0110108] [INSPIRE].
N. Fischer, A. Lifson and P. Skands, Helicity Antenna Showers for Hadron Colliders, Eur. Phys. J. C 77 (2017) 719 [arXiv:1708.01736] [INSPIRE].
P. Richardson and S. Webster, Spin Correlations in Parton Shower Simulations, Eur. Phys. J. C 80 (2020) 83 [arXiv:1807.01955] [INSPIRE].
H. Chen, I. Moult and H.X. Zhu, Quantum Interference in Jet Substructure from Spinning Gluons, Phys. Rev. Lett. 126 (2021) 112003 [arXiv:2011.02492] [INSPIRE].
S. Frixione, A General approach to jet cross-sections in QCD, Nucl. Phys. B 507 (1997) 295 [hep-ph/9706545] [INSPIRE].
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Hamilton, K., Karlberg, A., Salam, G.P. et al. Matching and event-shape NNDL accuracy in parton showers. J. High Energ. Phys. 2023, 224 (2023). https://doi.org/10.1007/JHEP03(2023)224
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DOI: https://doi.org/10.1007/JHEP03(2023)224