Parton Fragmentation Functions

Abstract

This chapter provides a pedagogical and comprehensive introduction to parton fragmentation functions (FFs), the essential non-perturbative quantities in Quantum Chromodynamics (QCD) that describe the universal process of hadronization, the transition of quarks and gluons into observable hadrons. Formally defined as gauge-invariant matrix elements, the determination of FFs is achieved through global QCD analyses that synthesize world data from three primary processes: electron-positron annihilation, semi-inclusive deep inelastic scattering, and proton-proton collisions. This chapter covers the theoretical foundations of FFs, including their operator definitions and properties, the experimental probes used to constrain them, and the methodologies of modern global analyses. The discussion is extended to more advanced topics, including dihadron FFs, the three-dimensional picture of hadronization provided by spin- and transverse-momentum-dependent FFs, and the modification of fragmentation in a nuclear medium, which is key to probe their fundamental properties.

20 Pages, 5 figures. Invited article for the Encyclopedia of Particle Physics

References in corpus (110)

• Event generation with SHERPA 1.1
• Herwig++ Physics and Manual
• Fragmentation of Transversely Polarized Quarks Probed in Transverse Momentum Distributions
• The complete tree-level result up to order $1/Q$ for polarized deep-inelastic leptoproduction
• Semi-inclusive deep inelastic scattering at small transverse momentum
• Multiple Parton Scattering in Nuclei: Parton Energy Loss
• Global analysis of fragmentation functions for pions and kaons and their uncertainties
• Multiple Scattering, Parton Energy Loss and Modified Fragmentation Functions in Deeply Inelastic eA Scattering
• Uncertainties of predictions from parton distribution functions II: the Hessian method
• APFEL: A PDF Evolution Library with QED corrections
• Fragmentation Functions from Flavour-inclusive and Flavour-tagged e^+e^- Annihilations
• First Measurement of the Transverse Spin Asymmetries of the Deuteron in Semi-Inclusive Deep Inelastic Scattering
• A Higher Order Perturbative Parton Evolution Toolkit (HOPPET)
• QCDNUM: Fast QCD Evolution and Convolution
• Observation of a Single-Spin Azimuthal Asymmetry in Semi-Inclusive Pion Electro-Production
• AKK Update: Improvements from New Theoretical Input and Experimental Data
• Global Analysis of Fragmentation Functions for Protons and Charged Hadrons
• Production of charged pions, kaons and protons at large transverse momenta in pp and Pb-Pb collisions at $\sqrt{s_{\mathrm{NN}}}$ = 2.76 TeV
• Parton-to-Pion Fragmentation Reloaded
• Production of charged pions, kaons and (anti-)protons in Pb-Pb and inelastic pp collisions at $\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV
• Efficient evolution of unpolarized and polarized parton distributions with QCD-PEGASUS
• Identified charged hadron production in p+p collisions at sqrt(s)=200 and 62.4 GeV
• Extraction of Quark Transversity Distribution and Collins Fragmentation Functions with QCD Evolution
• Determination of fragmentation functions and their uncertainties
• Measuring transversity densities in singly polarized hadron-hadron and lepton-hadron collisions
• Parton Fragmentation Functions
• Next-to-leading order QCD corrections to high-p_T pion production in longitudinally polarized pp collisions
• QCD Analysis of Unpolarized and Polarized Lambda - Baryon Production in Leading and Next-to-Leading Order
• A determination of the fragmentation functions of pions, kaons, and protons with faithful uncertainties
• Measurement of Azimuthal Asymmetries in Inclusive Production of Hadron Pairs in e+e- Annihilation at \sqrt{s} = 10.58 GeV
• Single-spin Azimuthal Asymmetries in Electroproduction of Neutral Pions in Semi-inclusive Deep-inelastic Scattering
• Centrality Dependence of pi^0 and eta Production at Large Transverse Momentum in sqrt(s_NN) = 200 GeV d+Au Collisions
• Multiplicity dependence of charged pion, kaon, and (anti)proton production at large transverse momentum in p-Pb collisions at $\sqrt{{\text{s}}_{\mathrm{NN}}}$ = 5.02 TeV
• Next-to-Next-to-Leading Order Evolution of Non-Singlet Fragmentation Functions
• Parton energy loss limits and shadowing in Drell-Yan dimuon production
• Pion, kaon, proton and anti-proton transverse momentum distributions from p+p and d+Au collisions at $\sqrt{s_{NN}}=200$ GeV
• Measurement of Beam-Spin Asymmetries for Deep Inelastic ${\pi }^{+}$ Electroproduction
• Multivariate Fitting and the Error Matrix in Global Analysis of Data
• Higher order QCD corrections to the transverse and longitudinal fragmentation functions in electron-positron annihilation
• Hadronization in semi-inclusive deep-inelastic scattering on nuclei
• Simultaneous Monte Carlo analysis of parton densities and fragmentation functions
• Production of pi+, K+, K0, K*0, phi, p and Lambda-0 in Hadronic Z0 Decays
• Parton-to-Kaon Fragmentation Revisited
• On Third-Order Timelike Splitting Functions and Top-Mediated Higgs Decay into Hadrons
• Asymmetry of Lambda Baryons in Hadronic Z^0 Decays
• QCD Corrections to Semi-Inclusive Hadron Production in Electron-Positron Annihilation at Two Loops
• On the Next-to-Next-to-Leading Order Evolution of Flavour-Singlet Fragmentation Functions
• Jet Quenching from QCD Evolution
• Observation of transverse polarization asymmetries of charged pion pairs in e+e- annihilation near sqrt s=10.58 GeV
• Measurement of Collins asymmetries in inclusive production of charged pion pairs in e^+e^- annihilation at BABAR
• Polarized $q\to \Lambda$ Fragmentation Functions from $e^{+}{e}^{-}\to \Lambda +X^{\ast }$
• Identified hadron compositions in p+p and Au+Au collisions at high transverse momenta at $\sqrt{s_{{}_{NN}}}=200$ GeV
• Polarized Lambdas in the Current Fragmentation Region
• Measurement of Charged Particle Transverse Momentum Spectra in Deep Inelastic Scattering
• $O({\alpha }_s^2)$ Contributions to the longitudinal fragmentation function in $e^{+}{e}^{-}$ annihilation
• Measurement of the jet fragmentation function and transverse profile in proton-proton collisions at a center-of-mass energy of 7 TeV with the ATLAS detector
• Next-to-Leading Order Evolution of Polarized and Unpolarized Fragmentation Functions
• Collins functions for pions from SIDIS and new e+e- data: a first glance at their transverse momentum dependence
• First extraction of Interference Fragmentation Functions from e+e- data
• Production of charged pions, kaons and protons in e+e- annihilations into hadrons at sqrt{s} = 10.54 GeV
• The dihadron fragmentation function and its evolution
• Production of pi+, pi-, K+, K-, p and p-bar in Light (uds), c and b Jets from Z0 Decays
• Production of light-flavor hadrons in pp collisions at $\sqrt{s}$ = 7 and $\sqrt{s}$ = 13 TeV
• $Z$ boson production in $p+$Pb collisions at $\sqrt{s_{NN}}=5.02$ TeV measured with the ATLAS detector
• Transverse momentum broadening of hadrons produced in semi-inclusive deep-inelastic scattering on nuclei
• Precision measurement of charged pion and kaon differential cross sections in electron-positron annihilation at Q = 10.52 GeV
• Study of Z boson production in pPb collisions at sqrt(s[NN]) = 5.02 TeV
• First Monte Carlo analysis of fragmentation functions from single-inclusive $e^{+}{e}^{-}$ annihilation
• Hadron Transverse Momentum Distributions in Muon Deep Inelastic Scattering at 160 GeV/$c$
• Global Analysis of Fragmentation Functions for Eta Mesons
• The transverse momentum distribution of hadrons within jets
• Measurement of azimuthal asymmetries in inclusive charged dipion production in $e^{+}{e}^{-}$ annihilations at $\sqrt{s}$ = 3.65 GeV
• Pion and kaon fragmentation functions at next-to-next-to-leading order
• Observation of medium induced modifications of jet fragmentation in PbPb collisions at $\sqrt{s_{\mathrm{NN}}}=$ 5.02 TeV using isolated-photon-tagged jets
• $O({\alpha }_s^2)$ Contributions to the asymmetric fragmentation function in $e^{+}{e}^{-}$ annihilation
• Fragmentations Functions in Nuclear Media
• A determination of unpolarised pion fragmentation functions using semi-inclusive deep-inelastic-scattering data: MAPFF1.0
• Flavor hierarchy of jet quenching in relativistic heavy-ion collisions
• Analytic Continuation and Reciprocity Relation for Collinear Splitting in QCD
• Multiplicities of charged pions and unidentified charged hadrons from deep-inelastic scattering of muons off an isoscalar target
• The hadronization of partons
• QCD resummation for semi-inclusive hadron production processes
• Towards a Global QCD Analysis of Fragmentation Functions at Next-To-Next-To-Leading Order Accuracy
• Azimuthal transverse single-spin asymmetries of inclusive jets and charged pions within jets from polarized-proton collisions at $\sqrt{s}=500$ GeV
• Measurement of the Longitudinal Spin Transfer to Lambda and Anti-Lambda Hyperons in Polarised Muon DIS
• Longitudinal Spin Transfer to the $\Lambda$ Hyperon in Semi-Inclusive Deep-Inelastic Scattering
• Observation of Transverse Spin-Dependent Azimuthal Correlations of Charged Pion Pairs in $p^{\uparrow }+p$ at $\sqrt{s}=200$ GeV
• Evolution of the parton dihadron fragmentation functions
• Semi-inclusive deep-inelastic scattering at NNLO in QCD
• Collins asymmetries in inclusive charged $KK$ and $K\pi$ pairs produced in $e^{+}{e}^{-}$ annihilation
• First global QCD analysis of charged hadron fragmentation functions and their uncertainties at next-to-next-to-leading order
• Pion Fragmentation Functions at High Energy Colliders
• Global analysis of fragmentation functions to charged hadrons with high-precision data from the LHC
• Jet fragmentation functions for $Z$-tagged jets
• Transverse spin-dependent azimuthal correlations of charged pion pairs measured in p${}^{\uparrow }$+p collisions at $\sqrt{s}$ = 500 GeV
• Transversity distributions and tensor charges of the nucleon: extraction from dihadron production and their universal nature
• Probing fragmentation functions from same-side hadron-jet momentum correlations in p-p collisions
• Measurement of charged-pion production in deep-inelastic scattering off nuclei with the CLAS detector
• First simultaneous global QCD analysis of dihadron fragmentation functions and transversity parton distribution functions
• Transverse momentum dependent production cross sections of charged pions, kaons and protons produced in inclusive $e^{+}{e}^{-}$ annihilation at $\sqrt{s}=$ 10.58 GeV
• Simultaneous Determination of Fragmentation Functions and Test on Momentum Sum Rule
• Transverse Polarization of Lambda and Lambda-bar Hyperons in Quasireal Photoproduction
• Invariant-mass and fractional-energy dependence of inclusive production of di-hadrons in $e^{+}{e}^{-}$ annihilation at $\sqrt{s}=$ 10.58 GeV
• Multidifferential study of identified charged hadron distributions in $Z$-tagged jets in proton-proton collisions at $\sqrt{s}=$13 TeV
• Improved measurement of the longitudinal spin transfer to $\Lambda$ and $\bar{\Lambda }$ hyperons in polarized proton-proton collisions at $\sqrt{s}$ = 200 GeV
• Automated calculation of Jet fragmentation at NLO in QCD
• Nuclear modification factor of neutral pions in the forward and backward regions in $p$-Pb collisions
• Hadron-in-jet production at partonic threshold
• Longitudinal and transverse spin transfer to $\Lambda$ and $\overline{\Lambda }$ hyperons in polarized $p$+$p$ collisions at $\sqrt{s}=200$ GeV
• Measurements of Normalized Differential Cross Sections of Inclusive $\eta$ Production in $e^{+}{e}^{-}$ Annihilation at Energy from 2.0000 to 3.6710 GeV