Abstract
The implementation of a new final-state parton-shower algorithm in the Pythia event generator is described. The shower algorithm, dubbed Apollo, combines central aspects of the Vincia antenna shower with the global transverse-recoil scheme of the Alaric framework in order to achieve formal consistency with next-to-leading logarithmic (NLL) resummation. The shower algorithm is constructed in such a way that it facilitates a straightforward combination with fixed-order calculations. As an explicit proof of concept, a general scheme for matrix-element corrections (MECs) and two separate multiplicative next-to-leading order (NLO) matching schemes are outlined. It is argued that both matching schemes retain the logarithmic accuracy of the shower. The improved modelling of radiation is examined by contrasting the new algorithm with existing leading-logarithmic parton showers in Pythia.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
V.N. Gribov and L.N. Lipatov, Deep inelastic e p scattering in perturbation theory, Sov. J. Nucl. Phys. 15 (1972) 438 [INSPIRE].
G. Altarelli and G. Parisi, Asymptotic Freedom in Parton Language, Nucl. Phys. B 126 (1977) 298 [INSPIRE].
Y.L. Dokshitzer, Calculation of the Structure Functions for Deep Inelastic Scattering and e+e− Annihilation by Perturbation Theory in Quantum Chromodynamics, Sov. Phys. JETP 46 (1977) 641 [INSPIRE].
G. Marchesini and B.R. Webber, Simulation of QCD Jets Including Soft Gluon Interference, Nucl. Phys. B 238 (1984) 1 [INSPIRE].
S. Plätzer and S. Gieseke, Coherent Parton Showers with Local Recoils, JHEP 01 (2011) 024 [arXiv:0909.5593] [INSPIRE].
M. Bengtsson and T. Sjöstrand, A Comparative Study of Coherent and Noncoherent Parton Shower Evolution, Nucl. Phys. B 289 (1987) 810 [INSPIRE].
G. Gustafson and U. Pettersson, Dipole Formulation of QCD Cascades, Nucl. Phys. B 306 (1988) 746 [INSPIRE].
L. Lönnblad, ARIADNE version 4: A program for simulation of QCD cascades implementing the color dipole model, Comput. Phys. Commun. 71 (1992) 15 [INSPIRE].
J.-C. Winter and F. Krauss, Initial-state showering based on colour dipoles connected to incoming parton lines, JHEP 07 (2008) 040 [arXiv:0712.3913] [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].
W.T. Giele, D.A. Kosower and P.Z. Skands, Higher-Order Corrections to Timelike Jets, Phys. Rev. D 84 (2011) 054003 [arXiv:1102.2126] [INSPIRE].
N. Fischer, S. Prestel, M. Ritzmann and P. Skands, Vincia for Hadron Colliders, Eur. Phys. J. C 76 (2016) 589 [arXiv:1605.06142] [INSPIRE].
Z. Nagy and D.E. Soper, Matching parton showers to NLO computations, JHEP 10 (2005) 024 [hep-ph/0503053] [INSPIRE].
S. Schumann and F. Krauss, A Parton shower algorithm based on Catani-Seymour dipole factorisation, JHEP 03 (2008) 038 [arXiv:0709.1027] [INSPIRE].
S. Plätzer and S. Gieseke, Dipole Showers and Automated NLO Matching in Herwig++, Eur. Phys. J. C 72 (2012) 2187 [arXiv:1109.6256] [INSPIRE].
S. Höche and S. Prestel, The midpoint between dipole and parton showers, Eur. Phys. J. C 75 (2015) 461 [arXiv:1506.05057] [INSPIRE].
D.A. Kosower, Antenna factorization of gauge theory amplitudes, Phys. Rev. D 57 (1998) 5410 [hep-ph/9710213] [INSPIRE].
J.M. Campbell, M.A. Cullen and E.W.N. Glover, Four jet event shapes in electron-positron annihilation, Eur. Phys. J. C 9 (1999) 245 [hep-ph/9809429] [INSPIRE].
A. Gehrmann-De Ridder, T. Gehrmann and E.W.N. Glover, Antenna subtraction at NNLO, JHEP 09 (2005) 056 [hep-ph/0505111] [INSPIRE].
A. Daleo, T. Gehrmann and D. Maitre, Antenna subtraction with hadronic initial states, JHEP 04 (2007) 016 [hep-ph/0612257] [INSPIRE].
J. Currie, E.W.N. Glover and S. Wells, Infrared Structure at NNLO Using Antenna Subtraction, JHEP 04 (2013) 066 [arXiv:1301.4693] [INSPIRE].
T. Gehrmann, E.W.N. Glover and M. Marcoli, The colourful antenna subtraction method, JHEP 03 (2024) 114 [arXiv:2310.19757] [INSPIRE].
S. Catani and M.H. Seymour, The dipole formalism for the calculation of QCD jet cross-sections at next-to-leading order, Phys. Lett. B 378 (1996) 287 [hep-ph/9602277] [INSPIRE].
S. Catani and M.H. Seymour, A general algorithm for calculating jet cross-sections in NLO QCD, Nucl. Phys. B 485 (1997) 291 [hep-ph/9605323] [INSPIRE].
S. Catani, S. Dittmaier, M.H. Seymour and Z. Trocsanyi, The dipole formalism for next-to-leading order QCD calculations with massive partons, Nucl. Phys. B 627 (2002) 189 [hep-ph/0201036] [INSPIRE].
J.J. Lopez-Villarejo and P.Z. Skands, Efficient Matrix-Element Matching with Sector Showers, JHEP 11 (2011) 150 [arXiv:1109.3608] [INSPIRE].
H. Brooks, C.T. Preuss and P. Skands, Sector Showers for Hadron Collisions, JHEP 07 (2020) 032 [arXiv:2003.00702] [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].
A. Banfi, G. Corcella and M. Dasgupta, Angular ordering and parton showers for non-global QCD observables, JHEP 03 (2007) 050 [hep-ph/0612282] [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].
Z. Nagy and D.E. Soper, Summations of large logarithms by parton showers, Phys. Rev. D 104 (2021) 054049 [arXiv:2011.04773] [INSPIRE].
M. Dasgupta et al., Parton showers beyond leading logarithmic accuracy, Phys. Rev. Lett. 125 (2020) 052002 [arXiv:2002.11114] [INSPIRE].
S. Höche, D. Reichelt and F. Siegert, Momentum conservation and unitarity in parton showers and NLL resummation, JHEP 01 (2018) 118 [arXiv:1711.03497] [INSPIRE].
G. Bewick, S. Ferrario Ravasio, P. Richardson and M.H. Seymour, Logarithmic accuracy of angular-ordered parton showers, JHEP 04 (2020) 019 [arXiv:1904.11866] [INSPIRE].
J.R. Forshaw, J. Holguin and S. Plätzer, Building a consistent parton shower, JHEP 09 (2020) 014 [arXiv:2003.06400] [INSPIRE].
F. Herren et al., A new approach to color-coherent parton evolution, JHEP 10 (2023) 091 [arXiv:2208.06057] [INSPIRE].
G. Bewick, S. Ferrario Ravasio, P. Richardson and M.H. Seymour, Initial state radiation in the Herwig 7 angular-ordered parton shower, JHEP 01 (2022) 026 [arXiv:2107.04051] [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].
M. van Beekveld and S. Ferrario Ravasio, Next-to-leading-logarithmic PanScales showers for Deep Inelastic Scattering and Vector Boson Fusion, JHEP 02 (2024) 001 [arXiv:2305.08645] [INSPIRE].
S. Höche, F. Krauss and D. Reichelt, The alaric parton shower for hadron colliders, arXiv:2404.14360 [INSPIRE].
B. Assi and S. Höche, New approach to QCD final-state evolution in processes with massive partons, Phys. Rev. D 109 (2024) 114008 [arXiv:2307.00728] [INSPIRE].
K. Hamilton et al., Matching and event-shape NNDL accuracy in parton showers, JHEP 03 (2023) 224 [Erratum ibid. 11 (2023) 060] [arXiv:2301.09645] [INSPIRE].
S. Ferrario Ravasio et al., Parton Showering with Higher Logarithmic Accuracy for Soft Emissions, Phys. Rev. Lett. 131 (2023) 161906 [arXiv:2307.11142] [INSPIRE].
J.M. Campbell et al., Event Generators for High-Energy Physics Experiments, SciPost Phys. 16 (2024) 130 [arXiv:2203.11110] [INSPIRE].
S. Frixione and B.R. Webber, Matching NLO QCD computations and parton shower simulations, JHEP 06 (2002) 029 [hep-ph/0204244] [INSPIRE].
E. Norrbin and T. Sjöstrand, QCD radiation off heavy particles, Nucl. Phys. B 603 (2001) 297 [hep-ph/0010012] [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].
M. Bengtsson and T. Sjöstrand, Coherent Parton Showers Versus Matrix Elements: Implications of PETRA-PEP Data, Phys. Lett. B 185 (1987) 435 [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].
S. Catani, F. Krauss, R. Kuhn and B.R. Webber, QCD matrix elements + parton showers, JHEP 11 (2001) 063 [hep-ph/0109231] [INSPIRE].
L. Lönnblad, Correcting the color dipole cascade model with fixed order matrix elements, JHEP 05 (2002) 046 [hep-ph/0112284] [INSPIRE].
L. Lönnblad and S. Prestel, Matching Tree-Level Matrix Elements with Interleaved Showers, JHEP 03 (2012) 019 [arXiv:1109.4829] [INSPIRE].
C. Bierlich et al., A comprehensive guide to the physics and usage of PYTHIA 8.3, SciPost Phys. Codeb. 2022 (2022) 8 [arXiv:2203.11601] [INSPIRE].
O. Braun-White, N. Glover and C.T. Preuss, A general algorithm to build real-radiation antenna functions for higher-order calculations, JHEP 06 (2023) 065 [arXiv:2302.12787] [INSPIRE].
A. Gehrmann-De Ridder, M. Ritzmann and P.Z. Skands, Timelike Dipole-Antenna Showers with Massive Fermions, Phys. Rev. D 85 (2012) 014013 [arXiv:1108.6172] [INSPIRE].
T. Sjöstrand and P.Z. Skands, Transverse-momentum-ordered showers and interleaved multiple interactions, Eur. Phys. J. C 39 (2005) 129 [hep-ph/0408302] [INSPIRE].
M. Dinsdale, M. Ternick and S. Weinzierl, Parton showers from the dipole formalism, Phys. Rev. D 76 (2007) 094003 [arXiv:0709.1026] [INSPIRE].
Z. Nagy and D.E. Soper, Parton shower evolution with subleading color, JHEP 06 (2012) 044 [arXiv:1202.4496] [INSPIRE].
K. Hamilton et al., Colour and logarithmic accuracy in final-state parton showers, JHEP 03 (2021) 041 [arXiv:2011.10054] [INSPIRE].
H. Brooks and C.T. Preuss, Efficient multi-jet merging with the Vincia sector shower, Comput. Phys. Commun. 264 (2021) 107985 [arXiv:2008.09468] [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. Höche and D. Reichelt, Numerical resummation at subleading color in the strongly ordered soft gluon limit, Phys. Rev. D 104 (2021) 034006 [arXiv:2001.11492] [INSPIRE].
M. De Angelis, J.R. Forshaw and S. Plätzer, Resummation and Simulation of Soft Gluon Effects beyond Leading Color, Phys. Rev. Lett. 126 (2021) 112001 [arXiv:2007.09648] [INSPIRE].
M. Cacciari et al., Fully Differential Vector-Boson-Fusion Higgs Production at Next-to-Next-to-Leading Order, Phys. Rev. Lett. 115 (2015) 082002 [Erratum ibid. 120 (2018) 139901] [arXiv:1506.02660] [INSPIRE].
S. Höche, F. Krauss, M. Schonherr and F. Siegert, Automating the POWHEG method in Sherpa, JHEP 04 (2011) 024 [arXiv:1008.5399] [INSPIRE].
R. Corke and T. Sjöstrand, Improved Parton Showers at Large Transverse Momenta, Eur. Phys. J. C 69 (2010) 1 [arXiv:1003.2384] [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].
L. Magnea et al., Local analytic sector subtraction at NNLO, JHEP 12 (2018) 107 [Erratum ibid. 06 (2019) 013] [arXiv:1806.09570] [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].
L. Clavelli, Jet Invariant Mass in Quantum Chromodynamics, Phys. Lett. B 85 (1979) 111 [INSPIRE].
P.E.L. Rakow and B.R. Webber, Transverse Momentum Moments of Hadron Distributions in QCD Jets, Nucl. Phys. B 191 (1981) 63 [INSPIRE].
S. Catani, G. Turnock and B.R. Webber, Jet broadening measures in e+e− annihilation, Phys. Lett. B 295 (1992) 269 [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].
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].
S. Catani, B.R. Webber and G. Marchesini, QCD coherent branching and semiinclusive processes at large x, Nucl. Phys. B 349 (1991) 635 [INSPIRE].
C. Bierlich et al., Reweighting Monte Carlo Predictions and Automated Fragmentation Variations in Pythia 8, SciPost Phys. 16 (2024) 134 [arXiv:2308.13459] [INSPIRE].
C. Bierlich et al., Robust Independent Validation of Experiment and Theory: Rivet version 3, SciPost Phys. 8 (2020) 026 [arXiv:1912.05451] [INSPIRE].
DELPHI collaboration, Tuning and test of fragmentation models based on identified particles and precision event shape data, Z. Phys. C 73 (1996) 11 [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].
JADE and OPAL collaborations, QCD analyses and determinations of alpha(s) in e+e− annihilation at energies between 35-GeV and 189-GeV, Eur. Phys. J. C 17 (2000) 19 [hep-ex/0001055] [INSPIRE].
S. Catani et al., New clustering algorithm for multi-jet cross-sections in e+e− annihilation, Phys. Lett. B 269 (1991) 432 [INSPIRE].
N. Brown and W.J. Stirling, Jet cross-sections at leading double logarithm in e+e− annihilation, Phys. Lett. B 252 (1990) 657 [INSPIRE].
N. Brown and W.J. Stirling, Finding jets and summing soft gluons: A New algorithm, Z. Phys. C 53 (1992) 629 [INSPIRE].
W.J. Stirling, Hard QCD working group: Theory summary, J. Phys. G 17 (1991) 1567 [INSPIRE].
S. Bethke, Z. Kunszt, D.E. Soper and W.J. Stirling, New jet cluster algorithms: Next-to-leading order QCD and hadronization corrections, Nucl. Phys. B 370 (1992) 310 [INSPIRE].
A. Gehrmann-De Ridder, T. Gehrmann, E.W.N. Glover and G. Heinrich, NNLO corrections to event shapes in e+e− annihilation, JHEP 12 (2007) 094 [arXiv:0711.4711] [INSPIRE].
M. van Beekveld et al., Introduction to the PanScales framework, version 0.1, arXiv:2312.13275 [INSPIRE].
L. Lönnblad and S. Prestel, Merging Multi-leg NLO Matrix Elements with Parton Showers, JHEP 03 (2013) 166 [arXiv:1211.7278] [INSPIRE].
L. Lönnblad and S. Prestel, Unitarising Matrix Element + Parton Shower merging, JHEP 02 (2013) 094 [arXiv:1211.4827] [INSPIRE].
J.C. Collins, Spin Correlations in Monte Carlo Event Generators, Nucl. Phys. B 304 (1988) 794 [INSPIRE].
I.G. Knowles, Angular Correlations in QCD, Nucl. Phys. B 304 (1988) 767 [INSPIRE].
I.G. Knowles, A Linear Algorithm for Calculating Spin Correlations in Hadronic Collisions, Comput. Phys. Commun. 58 (1990) 271 [INSPIRE].
G. Gustafson, Multiplicity distributions in QCD cascades, Nucl. Phys. B 392 (1993) 251 [INSPIRE].
J.M. Campbell et al., Towards NNLO+PS matching with sector showers, Phys. Lett. B 836 (2023) 137614 [arXiv:2108.07133] [INSPIRE].
Acknowledgments
The author would like to thank Stefan Höche and Peter Skands for many helpful discussions and comments on the manuscript. Computations were carried out on the PLEIADES cluster at the University of Wuppertal, supported by the Deutsche Forschungsgemeinschaft (DFG, grant No. INST 218/78-1 FUGG) and the Bundesministerium für Bildung und Forschung (BMBF).
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: 2403.19452
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
Preuss, C.T. A partitioned dipole-antenna shower with improved transverse recoil. J. High Energ. Phys. 2024, 161 (2024). https://doi.org/10.1007/JHEP07(2024)161
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP07(2024)161