Open Access

QCD Theory Meets Information Theory

Benoît Assi ^1,2,*, Stefan Höche ^1,†, Kyle Lee ^3,‡, and Jesse Thaler ^3,4,§

¹Theory Division, Fermilab, Batavia, Illinois 60510, USA
²Department of Physics, University of Cincinnati, Cincinnati, Ohio 45221, USA
³Center for Theoretical Physics—A Leinweber Institute, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
⁴The NSF AI Institute for Artificial Intelligence and Fundamental Interactions, USA

^*Contact author: bassi@fnal.gov
^†Contact author: shoeche@fnal.gov
^‡Contact author: kylel@mit.edu
^§Contact author: jthaler@mit.edu

Phys. Rev. Lett. 135, 131901 – Published 22 September, 2025

DOI: https://doi.org/10.1103/gf42-qzd9

Abstract

We present a novel technique to incorporate precision calculations from quantum chromodynamics into fully differential particle-level Monte Carlo simulations. By minimizing an information-theoretic quantity subject to constraints, our reweighted Monte Carlo incorporates systematic uncertainties absent in individual Monte Carlo predictions, achieving consistency with the theory input in precision and its estimated systematic uncertainties. Our method can be applied to arbitrary observables known from precision calculations, including multiple observables simultaneously. It generates strictly positive weights, thus offering a clear path to statistically powerful and theoretically precise computations for current and future collider experiments. As a proof of concept, we apply our technique to event-shape observables at electron-positron colliders, leveraging existing precision calculations of thrust. Our analysis highlights the importance of logarithmic moments of event shapes, which have not been previously studied in the collider physics literature.

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References (114)

A. Buckley et al., General-purpose event generators for LHC physics, Phys. Rep. 504, 145 (2011).
R. K. Ellis et al., Physics briefing book: Input for the European strategy for particle physics update 2020, Report No. CERN-ESU-004, 2019.
M. Narain et al., The future of US particle physics—The Snowmass 2021 energy frontier report, Report No. FERMILAB-FN-1219-PPD-T, 2022.
J. N. Butler et al., Report of the 2021 U.S. community study on the future of particle physics (Snowmass 2021), 10.2172/1922503 (2023).
F. Maltoni et al., TF07 Snowmass report: Theory of collider phenomena, arXiv:2210.02591.
N. Craig et al., Snowmass theory frontier report, arXiv:2211.05772.
A. Huss, J. Huston, S. Jones, and M. Pellen, Les Houches 2021—Physics at TeV colliders: Report on the standard model precision wishlist, J. Phys. G 50, 043001 (2023).
J. M. Campbell et al., Event generators for high-energy physics experiments, SciPost Phys. 16, 130 (2024).
K. Hamilton, P. Nason, C. Oleari, and G. Zanderighi, Merging $H / W / Z + 0$ and 1 jet at NLO with no merging scale: A path to parton shower + NNLO matching, J. High Energy Phys. 05 (2013) 082.
K. Hamilton, P. Nason, E. Re, and G. Zanderighi, NNLOPS simulation of Higgs boson production, J. High Energy Phys. 10 (2013) 222.
S. Höche, Y. Li, and S. Prestel, Drell-Yan lepton pair production at NNLO QCD with parton showers, Phys. Rev. D 91, 074015 (2015).
A. Karlberg, E. Re, and G. Zanderighi, NNLOPS accurate Drell-Yan production, J. High Energy Phys. 09 (2014) 134.
K. Hamilton, P. Nason, and G. Zanderighi, Finite quark-mass effects in the NNLOPS POWHEG + MiNLO Higgs generator, J. High Energy Phys. 05 (2015) 140.
S. Alioli, C. W. Bauer, C. Berggren, F. J. Tackmann, and J. R. Walsh, Drell-Yan production at NNLL’+NNLO matched to parton showers, Phys. Rev. D 92, 094020 (2015).
W. Astill, W. Bizoń, E. Re, and G. Zanderighi, NNLOPS accurate associated HZ production with $H \to b \bar{b}$ decay at NLO, J. High Energy Phys. 11 (2018) 157.
E. Re, M. Wiesemann, and G. Zanderighi, NNLOPS accurate predictions for $W^{+} W^{-}$ production, J. High Energy Phys. 12 (2018) 121.
P. F. Monni, P. Nason, E. Re, M. Wiesemann, and G. Zanderighi, ${MiNNLO}_{P S}$ : A new method to match NNLO QCD to parton showers, J. High Energy Phys. 05 (2020) 143; 02 (2022) 031(E).
J. Mazzitelli, P. F. Monni, P. Nason, E. Re, M. Wiesemann, and G. Zanderighi, Next-to-next-to-leading order event generation for top-quark pair production, Phys. Rev. Lett. 127, 062001 (2021).
S. Alioli, A. Broggio, A. Gavardi, S. Kallweit, M. A. Lim, R. Nagar, D. Napoletano, and L. Rottoli, Precise predictions for photon pair production matched to parton showers in GENEVA, J. High Energy Phys. 04 (2021) 041.
J. Mazzitelli, P. F. Monni, P. Nason, E. Re, M. Wiesemann, and G. Zanderighi, Top-pair production at the LHC with ${MINNLO}_{P S}$ , J. High Energy Phys. 04 (2022) 079.
S. Alioli, A. Broggio, A. Gavardi, S. Kallweit, M. A. Lim, R. Nagar, D. Napoletano, C. W. Bauer, and L. Rottoli, Matching NNLO predictions to parton showers using N3LL color-singlet transverse momentum resummation in geneva, Phys. Rev. D 104, 094020 (2021).
J. M. Lindert, D. Lombardi, M. Wiesemann, G. Zanderighi, and S. Zanoli, $W^{\pm} Z$ production at NNLO QCD and NLO EW matched to parton showers with ${MiNNLO}_{P S}$ , J. High Energy Phys. 11 (2022) 036.
A. Gavardi, C. Oleari, and E. Re, NNLO + PS Monte Carlo simulation of photon pair production with ${MiNNLO}_{P S}$ , J. High Energy Phys. 09 (2022) 061.
S. Alioli, G. Billis, A. Broggio, A. Gavardi, S. Kallweit, M. A. Lim, G. Marinelli, R. Nagar, and D. Napoletano, Refining the GENEVA method for Higgs boson production via gluon fusion, J. High Energy Phys. 05 (2023) 128.
A. Gavardi, M. A. Lim, S. Alioli, and F. J. Tackmann, NNLO + PS $W^{+} W^{-}$ production using jet veto resummation at NNLL’, J. High Energy Phys. 12 (2023) 069.
S. Höche and S. Prestel, Triple collinear emissions in parton showers, Phys. Rev. D 96, 074017 (2017).
F. Dulat, S. Höche, and S. Prestel, Leading-color fully differential two-loop soft corrections to QCD dipole showers, Phys. Rev. D 98, 074013 (2018).
M. Dasgupta, F. A. Dreyer, K. Hamilton, P. F. Monni, G. P. Salam, and G. Soyez, Parton showers beyond leading logarithmic accuracy, Phys. Rev. Lett. 125, 052002 (2020).
G. Bewick, S. Ferrario Ravasio, P. Richardson, and M. H. Seymour, Logarithmic accuracy of angular-ordered parton showers, J. High Energy Phys. 04 (2020) 019.
J. R. Forshaw, J. Holguin, and S. Plätzer, Building a consistent parton shower, J. High Energy Phys. 09 (2020) 014.
Z. Nagy and D. E. Soper, Summations of large logarithms by parton showers, Phys. Rev. D 104, 054049 (2021).
Z. Nagy and D. E. Soper, Summations by parton showers of large logarithms in electron-positron annihilation, arXiv:2011.04777.
G. Bewick, S. Ferrario Ravasio, P. Richardson, and M. H. Seymour, Initial state radiation in the herwig 7 angular-ordered parton shower, J. High Energy Phys. 01 (2022) 026.
L. Gellersen, S. Höche, and S. Prestel, Disentangling soft and collinear effects in QCD parton showers, Phys. Rev. D 105, 114012 (2022).
M. van Beekveld, S. Ferrario Ravasio, G. P. Salam, A. Soto-Ontoso, G. Soyez, and R. Verheyen, PanScales parton showers for hadron collisions: formulation and fixed-order studies, J. High Energy Phys. 11 (2022) 019.
M. van Beekveld, S. Ferrario Ravasio, K. Hamilton, G. P. Salam, A. Soto-Ontoso, G. Soyez, and R. Verheyen, PanScales showers for hadron collisions: All-order validation, J. High Energy Phys. 11 (2022) 020.
F. Herren, S. Höche, F. Krauss, D. Reichelt, and M. Schönherr, A new approach to color-coherent parton evolution, J. High Energy Phys. 10 (2023) 091.
B. Assi and S. Höche, New approach to QCD final-state evolution in processes with massive partons, Phys. Rev. D 109, 114008 (2024).
S. Ferrario Ravasio, K. Hamilton, A. Karlberg, G. P. Salam, L. Scyboz, and G. Soyez, Parton showering with higher logarithmic accuracy for soft emissions, Phys. Rev. Lett. 131, 161906 (2023).
C. T. Preuss, A partitioned dipole-antenna shower with improved transverse recoil, J. High Energy Phys. 07 (2024) 161.
S. Höche, F. Krauss, and D. Reichelt, The alaric parton shower for hadron colliders, Phys. Rev. D 111, 094032 (2025).
M. van Beekveld et al., New standard for the logarithmic accuracy of parton showers, Phys. Rev. Lett. 134, 011901 (2025).
G. Gustafson, Multiplicity distributions in QCD cascades, Nucl. Phys. B392, 251 (1993).
W. T. Giele, D. A. Kosower, and P. Z. Skands, Higher-order corrections to timelike jets, Phys. Rev. D 84, 054003 (2011).
Z. Nagy and D. E. Soper, Parton shower evolution with subleading color, J. High Energy Phys. 06 (2012) 044.
S. Plätzer and M. Sjödahl, Subleading $N_{c}$ improved parton showers, J. High Energy Phys. 07 (2012) 042.
Z. Nagy and D. E. Soper, A parton shower based on factorization of the quantum density matrix, J. High Energy Phys. 06 (2014) 097.
Z. Nagy and D. E. Soper, Effects of subleading color in a parton shower, J. High Energy Phys. 07 (2015) 119.
S. Plätzer, M. Sjodahl, and J. Thorén, Color matrix element corrections for parton showers, J. High Energy Phys. 11 (2018) 009.
J. Isaacson and S. Prestel, Stochastically sampling color configurations, Phys. Rev. D 99, 014021 (2019).
Z. Nagy and D. E. Soper, Exponentiating virtual imaginary contributions in a parton shower, Phys. Rev. D 100, 074005 (2019).
Z. Nagy and D. E. Soper, Parton showers with more exact color evolution, Phys. Rev. D 99, 054009 (2019).
J. R. Forshaw, J. Holguin, and S. Plätzer, Parton branching at amplitude level, J. High Energy Phys. 08 (2019) 145.
S. Höche and D. Reichelt, Numerical resummation at subleading color in the strongly ordered soft gluon limit, Phys. Rev. D 104, 034006 (2021).
M. De Angelis, J. R. Forshaw, and S. Plätzer, Resummation and simulation of soft gluon effects beyond leading color, Phys. Rev. Lett. 126, 112001 (2021).
J. Holguin, J. R. Forshaw, and S. Plätzer, Improvements on dipole shower colour, Eur. Phys. J. C 81, 364 (2021).
K. Hamilton, R. Medves, G. P. Salam, L. Scyboz, and G. Soyez, Colour and logarithmic accuracy in final-state parton showers, J. High Energy Phys. 03 (2021) 041.
I. Moult, I. W. Stewart, G. Vita, and H. X. Zhu, First subleading power resummation for event shapes, J. High Energy Phys. 08 (2018) 013.
M. A. Ebert, I. Moult, I. W. Stewart, F. J. Tackmann, G. Vita, and H. X. Zhu, Power corrections for N-jettiness subtractions at $O (α_{s})$ , J. High Energy Phys. 12 (2018) 084.
Y. L. Dokshitzer and B. R. Webber, Calculation of power corrections to hadronic event shapes, Phys. Lett. B 352, 451 (1995).
E. Gardi, Perturbative and nonperturbative aspects of moments of the thrust distribution in $e^{+} e^{-}$ annihilation, J. High Energy Phys. 04 (2000) 030.
C. Lee and G. F. Sterman, Momentum flow correlations from event shapes: Factorized soft gluons and soft-collinear effective theory, Phys. Rev. D 75, 014022 (2007).
V. Mateu, I. W. Stewart, and J. Thaler, Power corrections to event shapes with mass-dependent operators, Phys. Rev. D 87, 014025 (2013).
A. Metz and A. Vossen, Parton fragmentation functions, Prog. Part. Nucl. Phys. 91, 136 (2016).
H.-M. Chang, M. Procura, J. Thaler, and W. J. Waalewijn, Calculating track thrust with track functions, Phys. Rev. D 88, 034030 (2013).
K. Lee and I. Moult, Joint track functions: Expanding the space of calculable correlations at colliders, arXiv:2308.01332.
R. Boussarie et al., TMD handbook, arXiv:2304.03302.
M. Cacciari and N. Houdeau, Meaningful characterisation of perturbative theoretical uncertainties, J. High Energy Phys. 09 (2011) 039.
F. J. Tackmann, Beyond scale variations: Perturbative theory uncertainties from nuisance parameters, J. High Energy Phys. 08 (2025) 098.
M. A. Lim and R. Poncelet, Robust estimates of theoretical uncertainties at fixed-order in perturbation theory, arXiv:2412.14910.
K. Desai, B. Nachman, and J. Thaler, Moment extraction using an unfolding protocol without binning, Phys. Rev. D 110, 116013 (2024).
K. Sharp and F. Matschinsky, Translation of Ludwig Boltzmann’s paper “On the relationship between the second fundamental theorem of the mechanical theory of heat and probability calculations regarding the conditions for thermal equilibrium” Sitzungberichte der Kaiserlichen Akademie der Wissenschaften. Mathematisch-Naturwissen Classe. Abt. II, LXXVI 1877, pp. 373–435 (Wien. Ber. 1877, 76:373–435). Reprinted in Wiss. Abhandlungen, Vol. II, reprint 42, pp. 164–223, Barth, Leipzig, 1909, Entropy 17, 1971 (2015).
E. T. Jaynes, Information theory and statistical mechanics, Phys. Rev. 106, 620 (1957).
E. T. Jaynes, Information theory and statistical mechanics. II, Phys. Rev. 108, 171 (1957).
In practice, we numerically determine the Lagrange multipliers $λ_{j}$ by inserting Eq. (4) into Eq. (2) and minimizing the loss $\sum_{j} {(c_{j} - d_{j} / c_{j} + d_{j})}^{2}$ . This balances the relative contributions of all constraints, allowing efficient optimization via Adam [76].
D. P. Kingma, Adam: A method for stochastic optimization, arXiv:1412.6980.
In general, the $G_{i j}$ depend on anomalous dimensions at different perturbative orders [78]. To better separate these orders, one could use the $v$ -dependent functions that multiply the anomalous dimensions. In practice, we find the logarithmic basis to be more practical and equally efficient for capturing resummation effects.
L. G. Almeida, S. D. Ellis, C. Lee, G. Sterman, I. Sung, and J. R. Walsh, Comparing and counting logs in direct and effective methods of QCD resummation, J. High Energy Phys. 04 (2014) 174.
E. Farhi, A QCD test for jets, Phys. Rev. Lett. 39, 1587 (1977).
S. Catani, L. Trentadue, G. Turnock, and B. R. Webber, Resummation of large logarithms in $e^{+} e^{-}$ event shape distributions, Nucl. Phys. B407, 3 (1993).
A. J. Larkoski and J. Thaler, Unsafe but calculable: Ratios of angularities in perturbative QCD, J. High Energy Phys. 09 (2013) 137.
A. J. Larkoski, S. Marzani, and J. Thaler, Sudakov safety in perturbative QCD, Phys. Rev. D 91, 111501(R) (2015).
P. Cal, K. Lee, F. Ringer, and W. J. Waalewijn, Jet energy drop, J. High Energy Phys. 11 (2020) 012.
P. Cal, K. Lee, F. Ringer, and W. J. Waalewijn, The soft drop momentum sharing fraction $z_{g}$ beyond leading-logarithmic accuracy, Phys. Lett. B 833, 137390 (2022).
R. Abbate, M. Fickinger, A. H. Hoang, V. Mateu, and I. W. Stewart, Precision thrust cumulant moments at $N^{3} LL$ , Phys. Rev. D 86, 094002 (2012).
Despite the appearance of $v^{- 1}$ in Eq. (8), it is preferable to compute moments with $m \geq 0$ . The reason is that the $v^{- 1}$ terms generated by $d / d v$ in Eq. (5) are well approximated by all but the most pathological MC priors, up to normalization effects. For fixed-order calculations without resummation, plain moments of $τ^{m}$ (i.e., $n = 0$ ) are recommended.
R. Abbate, M. Fickinger, A. H. Hoang, V. Mateu, and I. W. Stewart, Thrust at $N^{3} L L$ with power corrections and a precision global fit for $α_{s} (m Z)$ , Phys. Rev. D 83, 074021 (2011).
G. Bell, A. Hornig, C. Lee, and J. Talbert, $e^{+} e^{-}$ angularity distributions at ${NNLL}^{'}$ accuracy, J. High Energy Phys. 01 (2019) 147.
M. A. Benitez, A. H. Hoang, V. Mateu, I. W. Stewart, and G. Vita, On determining $α_{s} (m_{Z})$ from dijets in $e^{+} e^{-}$ thrust, J. High Energy Phys. 07 (2025) 249.
A. H. Hoang, D. W. Kolodrubetz, V. Mateu, and I. W. Stewart, $C$ -parameter distribution at $N^{3} L L^{'}$ including power corrections, Phys. Rev. D 91, 094017 (2015).
S. Höche and S. Prestel, The midpoint between dipole and parton showers, Eur. Phys. J. C 75, 461 (2015).
C. Bierlich et al., A comprehensive guide to the physics and usage of pythia 8.3, SciPost Phys. Codebases 2022, 8 (2022).
E. Bothmann et al. (Sherpa Collaboration), Event generation with sherpa 2.2, SciPost Phys. 7, 034 (2019).
E. Bothmann et al. (Sherpa Collaboration), Event generation with sherpa 3, J. High Energy Phys. 12 (2024) 156.
A. Buckley, J. Butterworth, D. Grellscheid, H. Hoeth, L. Lönnblad, J. Monk, H. Schulz, and F. Siegert, rivet user manual, Comput. Phys. Commun. 184, 2803 (2013).
C. Bierlich et al., Robust independent validation of experiment and theory: rivet version 4 release note, SciPost Phys. Codebases 36, 1 (2024).
A. H. Hoang, D. W. Kolodrubetz, V. Mateu, and I. W. Stewart, Precise determination of $α_{s}$ from the $C$ -parameter distribution, Phys. Rev. D 91, 094018 (2015).
P. E. L. Rakow and B. R. Webber, Transverse momentum moments of hadron distributions in QCD jets, Nucl. Phys. B191, 63 (1981).
J. D. Bjorken and S. J. Brodsky, Statistical model for electron-positron annihilation into hadrons, Phys. Rev. D 1, 1416 (1970).
ALEPH Collaboration, Studies of QCD at $e^{+} e^{-}$ centre-of-mass energies between 91-GeV and 209-GeV, Eur. Phys. J. C 35, 457 (2004).
S. Alioli, C. W. Bauer, C. J. Berggren, A. Hornig, F. J. Tackmann, C. K. Vermilion, J. R. Walsh, and S. Zuberi, Combining higher-order resummation with multiple NLO calculations and parton showers in GENEVA, J. High Energy Phys. 09 (2013) 120.
S. Catani, B. R. Webber, and G. Marchesini, QCD coherent branching and semiinclusive processes at large $x$ , Nucl. Phys. B349, 635 (1991).
S. Schumann and F. Krauss, A parton shower algorithm based on Catani-Seymour dipole factorisation, J. High Energy Phys. 03 (2008) 038.
G. S. Chahal and F. Krauss, Cluster hadronisation in sherpa, SciPost Phys. 13, 019 (2022).
C. L. Basham, L. S. Brown, S. D. Ellis, and S. T. Love, Energy correlations in electron—Positron annihilation: Testing QCD, Phys. Rev. Lett. 41, 1585 (1978).
C. L. Basham, L. S. Brown, S. D. Ellis, and S. T. Love, Energy correlations in electron-positron annihilation in quantum chromodynamics: Asymptotically free perturbation theory, Phys. Rev. D 19, 2018 (1979).
F. Aversa, P. Chiappetta, M. Greco, and J. P. Guillet, Higher order corrections to QCD Jets, Phys. Lett. B 210, 225 (1988).
S. D. Ellis, Z. Kunszt, and D. E. Soper, The one jet inclusive cross-section at order $α_{s}^{3}$ : Gluons only, Phys. Rev. Lett. 62, 726 (1989).
http://iaifi.org/
B. Assi, S. Hoeche, K. Lee, and J. Thaler, TBD, https://doi.org/10.5281/zenodo.16989934.
S. Catani and B. R. Webber, Infrared safe but infinite: Soft gluon divergences inside the physical region, J. High Energy Phys. 10 (1997) 005.
A. Bhattacharya, M. D. Schwartz, and X. Zhang, Sudakov shoulder resummation for thrust and heavy jet mass, Phys. Rev. D 106, 074011 (2022).
P. Nason and G. Zanderighi, Fits of $α_{s}$ using power corrections in the three-jet region, J. High Energy Phys. 06 (2023) 058.
Z. Ligeti, I. W. Stewart, and F. J. Tackmann, Treating the b quark distribution function with reliable uncertainties, Phys. Rev. D 78, 114014 (2008).

Phys. Rev. Lett. 135, 131901– Published 22 September, 2025

Vol. 135, Iss. 13 — 26 September 2025

Received 13 February 2025
Revised 8 August 2025
Accepted 26 August 2025

DOI: https://doi.org/10.1103/gf42-qzd9

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

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QCD Theory Meets Information Theory

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