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Inferring interpretable models of fragmentation functions using symbolic regression

MACHINE LEARNING-SCIENCE AND TECHNOLOGY 2025年第2期6卷 025003-025003页

作者： Makke, Nour Chawla, Sanjay HBKU Qatar Comp Res Inst Doha Qatar

Machine learning is rapidly making its path into the natural sciences, including high-energy physics. We present the first study that infers, directly from experimental data, a functional form of fragmentation functions. The latter represent a key ingredient to describe physical observables measured in high-energy physics processes that involve hadron production, and predict their values at different energies. fragmentation functions cannot be calculated in theory and have to be determined instead from data. Traditional approaches rely on global fits of experimental data to learn the parameters of a pre-assumed functional form inspired from phenomenological models of hadron production. This novel approach uses an ML technique, namely symbolic regression (SR), to learn an analytical model from measured charged hadron multiplicities. The function studied by SR resembles the Lund string function and describes the data well, thus representing a potential candidate for use in global FFs fits.

关键词： symbolic regression model discovery hadron production in HEP fragmentation functions

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Flavor dependence of charged pion fragmentation functions

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PHYSICS LETTERS B 2025年 865卷

作者： Bhatt, H. Bosted, P. Jia, S. Armstrong, W. Dutta, D. Ent, R. Gaskell, D. Kinney, E. Mkrtchyan, H. Ali, S. Ambrose, R. Androic, D. Gayoso, C. Ayerbe Bandari, A. Berdnikov, V. Bhetuwal, D. Biswas, D. Boer, M. Brash, E. Camsonne, A. Cardona, M. Chen, J. P. Chen, J. Chen, M. Christy, E. M. Danagoulian, S. Covrig, S. Duran, B. Elaasar, M. Elliot, C. Fenker, H. Fuchey, E. Hansen, J. O. Hauenstein, F. Diefenthaler, M. Horn, T. Huber, G. M. Jones, M. K. Kabir, M. L. Karki, A. Karki, B. Kay, S. J. D. Keppel, C. Kumar, V. Lashley-Colthirst, N. Li, W. B. Mack, D. Malace, S. Markowitz, P. McCaughan, M. McClellan, E. Meekins, D. Michaels, R. Mkrtchyan, A. Niculescu, G. Niculescu, I. Pandey, B. Park, S. Pooser, E. Sawatzky, B. Smith, G. R. Szumila-Vance, H. Tadepalli, A. S. Tadevosyan, V. Trotta, R. Voskanyan, H. Wood, S. A. Ye, Z. Yero, C. Zheng, X. Mississippi State Univ Mississippi State MS 39762 USA Coll William & Mary Williamsburg VA 23185 USA Temple Univ Philadelphia PA 19122 USA Argonne Natl Lab Lemont IL 60439 USA Thomas Jefferson Natl Accelerator Facil Newport News VA 23606 USA Univ Colorado Boulder Boulder CO 80309 USA Yerevan Phys Inst AI Alikhanyan Natl Sci Lab Yerevan 0036 Armenia Catholic Univ Amer Washington DC 20064 USA Univ Regina Regina SK S4S 0A2 Canada Univ Zagreb Zagreb Croatia Hampton Univ Hampton VA 23668 USA Christopher Newport Univ Newport News VA 23606 USA Univ Virginia Charlottesville VA 22903 USA North Carolina A&T State Univ Greensboro NC 27411 USA Southern Univ New Orleans New Orleans LA 70126 USA Univ Tennessee Knoxville TN 37996 USA Univ Connecticut Storrs CT 06269 USA Old Dominion Univ Norfolk VA 23529 USA Ohio Univ Athens OH 45701 USA Univ York York Y010 5DD England Florida Int Univ University Pk FL 33199 USA James Madison Univ Harrisonburg VA 22807 USA Virginia Mil Inst Lexington VA 24450 USA SUNY Stony Brook Stony Brook NY 11794 USA Tsinghua Univ Beijing 100084 Peoples R China

We have measured the flavor dependence of multiplicities for pi(+ )and pi(-) production in semi-inclusive deep-inelastic scattering (SIDIS) on proton and deuteron to explore a possible charge symmetry violation in fragmentation functions. The experiment used an electron beam with energies of 10.2 and 10.6 GeV at Jefferson Lab and the Hall-C spectrometers. The electron kinematics spanned the range 0.3< x <0.6, 2< Q( 2)<5.5 GeV2, and 2.2< W <3.2 GeV. The pion fractional momentum range was 0.3< z <0.7, and the transverse momentum range was 0< p(T) <0.25 GeV/c. Assuming factorization and allowing for isospin breaking, the results can be described by two "favored" and two "unfavored" effective low p(T) fragmentation functions that are flavor-dependent. We find each pair converges to a common flavor-independent fragmentation function at the highest W, where factorization is most applicable.

关键词： Charged pion multiplicities fragmentation functions Charge symmetry violation Higher twist corrections

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fragmentation functions for Ξ^-/(Ξ)over-bar⁺ using neural networks

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NUCLEAR PHYSICS A 2023年 1029卷

作者： Soleymaninia, Maryam Hashamipour, Hadi Khanpour, Hamzeh Spiesberger, Hubert Inst Res Fundamental Sci IPM Sch Particles & Accelerators POB 19395-5531 Tehran Iran Univ Udine Dipartimento Politecn Ingn & Architettura Via Sci 206 I-33100 Udine Italy Abdus Salaam Int Ctr Theoret Phys Str Costiera 11 I-34151 Trieste Italy Univ Sci & Technol Mazandaran Dept Phys POB 48518-78195 Behshahr Iran Johannes Gutenberg Univ Mainz Inst Phys PRISMA Cluster Excellence Staudinger Weg 7 D-55099 Mainz Germany

We present a determination of fragmentation functions (FFs) for the octet baryon Xi(-)/(Xi) over bar (+) from data for single inclusive electron-positron annihilation. Our parametrization in this QCD analysis is provided in terms of a Neural Network (NN). We determine fragmentation functions for Xi(-)/(Xi) over bar (+) at next-to-leading order and for the first time at next-to-next-to-leading order in perturbative QCD. We discuss the improvement of higher-order QCD corrections, the quality of fit, and the comparison of our theoretical results with the fitted datasets. As an application of our new set of fragmentation functions, named SHKS22, we present predictions for Xi(-)/(Xi) over bar (+) baryon production in proton-proton collisions at the LHC experiments. (c) 2022 Published by Elsevier B.V.

关键词： QCD fragmentation functions Hadronization

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Simultaneous Determination of fragmentation functions and Test on Momentum Sum Rule

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Physical Review Letters 2024年第26期132卷 261903-261903页

作者： Jun Gao ChongYang Liu XiaoMin Shen Hongxi Xing Yuxiang Zhao INPAC Shanghai Key Laboratory for Particle Physics and Cosmology and School of Physics and Astronomy Key Laboratory for Particle Astrophysics and Cosmology (MOE) Shanghai 200240 China Notkestr. 85 22607 Hamburg Germany Key Laboratory of Atomic and Subatomic Structure and Quantum Control (MOE) Guangdong Basic Research Center of Excellence for Structure and Fundamental Interactions of Matter Institute of Quantum Matter Guangdong-Hong Kong Joint Laboratory of Quantum Matter Guangdong Provincial Key Laboratory of Nuclear Science Southern Nuclear Science Computing Center Southern Center for Nuclear-Science Theory (SCNT) Beijing 100049 China Key Laboratory of Quark and Lepton Physics (MOE) and Institute of Particle Physics

We perform a simultaneous global analysis of hadron fragmentation functions (FFs) to various charged hadrons (π±, K±, and p/p¯) at next-to-leading order in QCD. The world data include results from electron-positron single-inclusive annihilation, semi-inclusive deep inelastic scattering, as well as proton-proton collisions including jet fragmentation measurements for the first time, which lead to strong constraints on the gluon fragmentations. By carefully selecting hadron kinematics to ensure the validity of QCD factorization and the convergence of perturbative calculations, we achieve a satisfying best fit with χ2/d.o.f.=0.90. The total momentum of u, d quarks and gluon carried by light charged hadrons have been determined precisely, urging precision determinations of FFs to neutral hadrons for a test of fundamental sum rules in QCD fragmentation.

关键词： fragmentation functions fragmentation into hadrons Perturbative QCD Quantum chromodynamics

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Number Density Interpretation of Dihadron fragmentation functions

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Physical Review Letters 2024年第1期132卷 011902-011902页

作者： D. Pitonyak C. Cocuzza A. Metz A. Prokudin N. Sato Department of Physics Lebanon Valley College Annville Pennsylvania 17003 USA Department of Physics SERC Temple University Philadelphia Pennsylvania 19122 USA Division of Science Penn State University Berks Reading Pennsylvania 19610 USA Jefferson Lab Newport News Virginia 23606 USA

We present a new quantum field-theoretic definition of fully unintegrated dihadron fragmentation functions (DiFFs) as well as a generalized version for n-hadron fragmentation functions. We demonstrate that this definition allows certain sum rules to be satisfied, making it consistent with a number density interpretation. Moreover, we show how our corresponding so-called extended DiFFs that enter existing phenomenological studies are number densities and also derive their evolution equations. Within this new framework, DiFFs extracted from experimental measurements will have a clear physical meaning.

关键词： fragmentation functions Quantum chromodynamics

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Determination of KS0 fragmentation functions including BESIII measurements and using neural networks

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Physical Review D 2024年第1期110卷 014019-014019页

作者： Maryam Soleymaninia Hadi Hashamipour Maral Salajegheh Hamzeh Khanpour Hubert Spiesberger Ulf-G. Meißner School of Particles and Accelerators I-87036 Arcavacata di Rende Cosenza Italy Helmholtz-Institut für Strahlen-und Kernphysik and Bethe Center for Theoretical Physics Faculty of Physics and Applied Computer Science Al. Mickiewicza 30 30-055 Kraków Poland Department of Physics PRISMA Institute for Advanced Simulation (IAS-4) 0186 Tbilisi Georgia

In this study, we revisit the extraction of parton-to-KS0 hadron fragmentation functions, named FF24-KS0, focusing on both next-to-leading-order and next-to-next-to-leading-order accuracy in perturbative QCD. Our approach involves the analysis of single inclusive electron-positron annihilation (SIA) data. The two key improvements are, on the one hand, the incorporation of the latest experimental data from the BESIII experiment and, on the other hand, the adoption of neural networks in the fitting procedure. To address experimental uncertainties, the Monte Carlo method is employed. Our investigation also explores the impact of hadron mass corrections on the description of SIA data, spanning a broad kinematic regime with a particular emphasis on the range of small z values. The theory prediction for KS0 production at both NLO and NNLO accuracy exhibits good agreement with experimental data within their respective uncertainties.

关键词： fragmentation functions Perturbative QCD QCD phenomenology

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Information entropy and fragmentation functions

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NUCLEAR PHYSICS A 2023年 1036卷

作者： Benito-Calvino, Guillermo Garcia-Olivares, Javier Llanes-Estrada, Felipe J. Univ Complutense Madrid Fac Ciencias Fis Dept Fis Teor Plaza Ciencias 1 Madrid 28040 Spain Univ Complutense Madrid Fac Ciencias Fis IPARCOS Plaza Ciencias 1 Madrid 28040 Spain

Several groups have recently investigated the flow of information in high-energy collisions, from the entanglement entropy of the proton yielding classical Shannon entropy of its parton distribution functions (pdfs), through jet splitting generating entropy, to the entropy distribution in hadron *** in the literature is a discussion of the information entropy of fragmentation functions (FFs) in the instances where they can be considered as probability distributions, and we here provide it. We find that this entropy is a single, convenient number to characterize future progress in the extraction of fragmentation *** also deploy the related Kullback-Leibler divergence between two distributions to assess existing relations among FFs and parton distribution functions (pdfs) such as that of Barone, Drago and Ma. From a couple of current parametrizations of FFs, we do not find supporting empirical evidence for the relation, although it is possible that FFs and pdfs have similar power-laws near the x = 1 endpoint.(c) 2023 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons .org /licenses /by -nc -nd /4 .0/).

关键词： fragmentation functions Parton distribution functions Shannon entropy Classical information entropy Kullback-Leibler divergence Barone-Drago-Ma relation

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Tests of the parametrizations of fragmentation functions using data on inclusive pion and kaon production in unpolarized pp collisions from the STAR collaboration and at the NICA project

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INTERNATIONAL JOURNAL OF MODERN PHYSICS A 2023年第21期38卷

作者： Kotlorz, D. Christova, E. Leader, E. Bogoliubov Lab Theoret Phys Joint Inst Nucl Res Dubna 141980 Russia Bulgarian Acad Sci Inst Nucl Res & Nucl Energy Tzarigradsko chaussee 72 Sofia 1784 Bulgaria Imperial Coll London London SW7 2AZ England

The goal of this study is to check which, if any, of the published versions of the pion and kaon fragmentation functions (FFs) is compatible with the STAR data on semi-inclusive pion and kaon production in proton-proton collisions, and on the basis of this analysis to make reliable predictions for the p(T) spectra of the pions and kaons in inclusive pion and kaon production at the future NICA proton-proton collider. The calculations are carried out in next-to-leading order (NLO) of perturbative quantum chromodynamics (pQCD), using the well-tested CTEQ6 parton distributions. We consider the following pion and kaon FFs - DSEHS-14 [D. de Florian, R. Sassot, M. Epele, R. J. Hernandez-Pinto and M. Stratmann, Phys. Rev. D 91, 014035 (2015), 1410.6027], DSEHS-17 [D. de Florian, M. Epele, R. J. Hernandez-Pinto, R. Sassot and M. Stratmann, Phys. Rev. D 95, 094019 (2017), 1702.06353], LSS-15 [E. Leader, A. V. Sidorov and D. B. Stamenov, Phys. Rev. D 93, 074026 (2016), 1506.06381], HKNS-07 [M. Hirai, S. Kumano, T. H. Nagai and K. Sudoh, Phys. Rev. D 75, 094009 (2007), hep-ph/0702250] and AKK-08 [S. Albino, B. A. Kniehl and G. Kramer, Nucl. Phys. B 803, 42 (2008), 0803.2768]. Our analysis shows that within the experimental errors all tested sets of FFs provide a good fit to STAR data at the c.m. energy root S=200GeV, and the best ones are both LSS-15 and DSEHS-14 for pions and DSEHS-17 for kaons. From comparison of the LO and NLO results it is clear that the latter fit data much better, specially in the region of small p(T). The NLO cross-sections are also less scale-Q2 dependent, where pT/2 <= Q <= 2p(T), than the LO ones. In order to make predictions for NICA energies, we compare the NLO pQCD results with the existing experimental BES STAR data on semi-inclusive hadron production in the most peripheral Au+Au collisions where the nuclear effects can be neglected. The comparison for lower energy scales, like at NICA, shows that a purely pQCD approach is inadequate and suggests

关键词： High energy physics phenomenological aspects of field theory particle interactions quark model perturbative quantum chromodynamics strong interaction fragmentation functions semi-inclusive hadron production pp collisions

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Jet fragmentation functions for Z-tagged jets

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PHYSICS LETTERS B 2019年 798卷 134978-000页

作者： Kang, Zhong-Bo Lee, Kyle Terry, John Xing, Hongxi Univ Calif Los Angeles Dept Phys & Astron Los Angeles CA 90095 USA Univ Calif Los Angeles Mani Bhaum Inst Theoret Phys Los Angeles CA 90095 USA SUNY Stony Brook CN Yang Inst Theoret Phys Stony Brook NY 11794 USA SUNY Stony Brook Dept Phys & Astron Stony Brook NY 11794 USA South China Normal Univ Inst Quantum Matter Guangzhou 510006 Guangdong Peoples R China South China Normal Univ Sch Phys & Telecommun Engn Guangzhou 510006 Guangdong Peoples R China

Recently the LHCb collaboration has measured both longitudinal and transverse momentum distribution of hadrons produced inside Z-tagged jets in proton-proton collisions at the Large Hadron Collider. These distributions are commonly referred to as jet fragmentation functions and are characterized by the longitudinal momentum fraction z(h) of the jet carried by the hadron and the transverse momentum j(perpendicular to) with respect to the jet direction. We derive a QCD formalism within Soft-Collinear Effective Theory to describe these distributions and find that the z(h)-dependence provides information on standard collinear fragmentation functions, while j(perpendicular to)-dependence probes transverse momentum dependent (TMD) fragmentation functions. We perform theoretical calculations and compare our results with the LHCb data. We find good agreement for the intermediate z(h) region. For j(perpendicular to)-dependence, we suggest binning in both z(h) and j(perpendicular to), which would lead to a more direct probing of TMD fragmentation functions. (C) 2019 The Author(s). Published by Elsevier B.V.

关键词： Jets fragmentation functions Perturbative QCD Soft Collinear Effective Theory

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Extracting α_s from scaling violations in light-hadron fragmentation functions

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MODERN PHYSICS LETTERS A 2016年第8期31卷

作者： Kniehl, Bernd A. Univ Hamburg Inst Theoret Phys 2 Luruper Chaussee 149 D-22761 Hamburg Germany

We review the status of extracting the strong-coupling constant alpha(s) from the scaling violations in fragmentation functions (FFs) by fitting the latter to experimental data of the inclusive production of single light hadrons in e(+)e(-) annihilation. We also discuss the analogous analysis based on the average hadron multiplicities in gluon and quark jets, which correspond to the first Mellin moments of the respective FFs. We then assess the prospects of such alpha(s) determinations at future high-luminosity e(+)e(-) colliders such alpha(s) the CERN Future Circular Collider operated in the e(+)e(-) annihilation mode (FCC-ee).

关键词： fragmentation functions scaling violations strong-coupling constant

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