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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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Higher order QCD corrections to the transverse and longitudinal fragmentation functions in electron-positron annihilation

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NUCLEAR PHYSICS B 1997年第1-2期487卷 233-282页

作者： Rijken, PJ vanNeerven, WL Instituut Lorentz University of Leiden P.O. Box 9506 2300 RA Leiden The Netherlands

We present the calculation of the order alpha(s)(2) corrections to the coefficient functions contributing to the longitudinal (F-L(x,Q(2))) and traverse fragmentation functions (F-T(x,Q(2))) measured in electron-position annihilation. The effect of these higher order QCD corrections on the behaviour of the fragmentation functions and the corresponding longitudinal (d sigma(L)(x,Q(2))/dx) and transverse cross sections (d sigma(T)(x,Q(2))/dx) are studied. In particular we investigate the dependence of the above quantities on the mass factorization scale (M) and the various parameterizations chosen for the parton fragmentation densities D-p(H)(x,M(2)) (p = q,g;H = pi(+/-),K-+/-,P,(P) over bar). Our analysis reveals that the order alpha(s)(2) contributions to F-L(x,Q(2)) are large whereas these contributions to F-T(x,Q(2)) are small. From the above fragmentation functions one can also compute the integrated cross sections sigma(L) and sigma(T) in an independent way. The sum sigma(tot) = sigma(L) + sigma(T), corrected up to order alpha(s)(2), agrees with the well-known result in the literature providing us with an independent check on our calculations.

关键词： electron-positron annihilation fragmentation functions

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Momentum sum rules for fragmentation functions

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PHYSICS LETTERS B 2010年第3期690卷 296-303页

作者： Meissner, S. Metz, A. Pitonyak, D. Temple Univ Dept Phys Philadelphia PA 19122 USA Ruhr Univ Bochum Inst Theoret Phys 2 D-44780 Bochum Germany

Momentum sum rules for fragmentation functions are considered. In particular, we give a general proof of the Schafer-Teryaev sum rule for the transverse momentum dependent Collins function. We also argue that corresponding sum rules for related fragmentation functions do not exist. Our model-independent analysis is supplemented by calculations in a simple field-theoretical model. (c) 2010 Elsevier B.V. All rights reserved.

关键词： Transverse momentum dependent parton correlators fragmentation functions Sum rules

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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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Medium-modified DGLAP evolution of fragmentation functions from large to small x

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NUCLEAR PHYSICS B 2009年第1-2期819卷 306-318页

作者： Albino, S. Kniehl, B. A. Perez-Ramos, R. Univ Hamburg Inst Theoret Phys 2 D-22761 Hamburg Germany

The unified description of fragmentation function evolution from large to small x which was developed for the vacuum in previous publications is now generalized to the medium, and is studied for the case in which the complete contribution from the largest class of soft gluon logarithms. the double logarithms, are accounted for and with the fixed order part calculated to leading order. In this approach it proves possible to choose the remaining degrees of freedom related to the medium such that the distribution of produced hadrons is suppressed at large momenta while the production of soft radiation-induced charged hadrons at small momenta is enhanced, in agreement with experiment. Just as for the vacuum, our approach does not require further assumptions concerning fragmentation and is more complete than previous computations of evolution in the medium. (C) 2009 Elsevier B.V.. All rights reserved.

关键词： Perturbative quantum chromodynamics DGLAP evolution fragmentation functions Quark-gluon plasma

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Power corrections to fragmentation functions in flavour-singlet deep-inelastic scattering

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NUCLEAR PHYSICS B 1999年第1-2期549卷 263-279页

作者： Smye, E Univ Cambridge Cavendish Lab Cambridge CB3 0HE England

We investigate the power-suppressed corrections to fragmentation functions in flavour-singlet deep-inelastic lepton scattering, to complement the previous results for the non-singlet contribution. Our method is a dispersive approach based on an analysis of Feynman graphs containing massive gluons. As in non-singlet deep-inelastic scattering we find that the leading corrections are proportional to 1/Q(2). (C) 1999 Elsevier Science B.V. All rights reserved.

关键词： QCD deep-inelastic scattering power corrections fragmentation functions

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fragmentation functions of neutral mesons π⁰ and κ⁰ with Laplace transform approach

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INTERNATIONAL JOURNAL OF MODERN PHYSICS A 2016年第17期31卷

作者： Taghavi-Shahri, F. Tehrani, S. Atashbar Zarei, M. Ferdowsi Univ Mashhad Dept Phys POB 1436 Mashhad Iran POB 1149-8834413 Tehran Iran

With an analytical solutions of DGLAP evolution equations based on the Laplace transform method, we find the fragmentation functions (FFs) of neutral mesons, pi(0) and kappa(0) at NLO approximation. We also calculated the total fragmentation functions of these mesons and compared them with experimental data and those from global fits. The results show a good agreement between our solutions and other models and they are compatible with experimental data.

关键词： Laplace transform fragmentation functions natural meson

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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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Measurement of jet fragmentation functions and of their moments in pp collisions at √s =2.76 TeV with ALICE at the LHC

Measurement of jet fragmentation functions and of their mome...

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作者： Mengliang WANG Central China Normal University

学位级别：博士

A cross-over between ordinary nuclear matter and a state of decon? ned quarks and gluons, the Quark Gluon Plasma (QGP), is predicted by lattice QCD calculations at low chemical potential and high temperature in the nuclear phase diagram. Ex- perimentally, ultra-relativistic heavy ion collisions are used to produce and study the hot and dense QGP medium. Produced in a hard scattering at the early stage of the collision a highly ener- getic parton is? rst expected to lose energy in the medium before fragmenting into a hadronic spray of particles called jet. A detailed study of the modi? cation of the jet structure and of its fragmentation pattern in vacuum and in medium should provide insights into the QGP properties. The jet fragmentation functions describe the momentum distribution of hadrons inside a reconstructed jet. In proton-proton (pp) collisions their measurement is important for understanding the mechanisms of parton fragmentation. Such measurements also provide a test of perturbative Quantum Chromo Dynamics (pQCD) as well as a baseline for similar measurements in p-A collisions (revealing potential cold nuclear matter e? ects) or in A-A colli- sions (shedding light on the energy loss mechanisms in presence of a hot and dense medium). However, in heavy-ion collisions the presence of a large underlying event and of its event-by-event? uctuations makes the measurement of jet fragmentation functions a challenging task. The use of the fragmentation function moments has been proposed in [1] as a way to overcome this di? culty. The ALICE detector at the Large Hadron Collider (LHC) has unique tracking capabilities enabling to measure charged particles down to transverse momenta as low as 150 ∼ MeV/c. This allows assessing possible modi? cations of the jet structure and helps constraining the jet fragmentation functions. The ALICE Electromagnetic Calorimeter (EMCal) can also be used to measure hard probes of the initial collision, including jets, high p T photons, n

关键词： pp collisions ultra-relativistic heavy-ion collisions QGP ALICE jets fragmentation functions fragmentation function moments electromagnetic calorimeters EMCal DCal

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