Fragmentation functions are determined for the pion and kaon by global analyses of charged-hadron production data in electron-positron annihilation. Accurate measurements were reported by the Belle and BaBar collaborations for the fragmentation functions at the center-of-mass energies of 10.52 GeV and 10.54 GeV, respectively, at the KEK and SLAC B factories, whereas other available $e^+e^-$ measurements were mostly done at higher energies, mainly at the $Z$ mass of 91.2 GeV. There is a possibility that gluon fragmentation functions, as well as quark fragmentation functions, are accurately determined by scaling violation. We report our global analysis of the fragmentation functions especially to show impacts of the B-factory measurements on the fragmentation function determination. Our results indicate that the fragmentation functions are determined more accurately not only by the scaling violation but also by high-statistical nature of the Belle and BaBar data. However, there are some tensions between the Belle and BaBar data in comparison with previous measurements. We also explain how the flavor dependence of quark fragmentation functions and the gluon function are separated by using measurements at different $Q^2$ values. In particular, the electric and weak changes are different depending on the quark type, so that a light-quark flavor separation also became possible in principle due to the precise data at both $\sqrt{s}\simeq 10.5$ GeV and 91.2 GeV.
We briefly review the hadronization pictures adopted in the LUND String Fragmentation Model(LSFM), Webber Cluster Fragmentation Model(WCFM) and Quark Combination Model(QCM), respectively. Predictions of hadron multiplicity, baryon to meson ratios and baryon-antibaryon flavor correlations, especially related to heavy hadrons at $Z^0$ factory obtained by LSFM and QCM are reported.
The description of the polarized quark hadronization process is one of the most challenging problems in the physics of strong interactions. The various single hadron and dihadron fragmentation functions, that quantify this process, are determined by analyzing the inclusive production of hadrons in electron-positron semi-inclusive annihilation process (SIA). These, in turn, are used to extract the transverse momentum dependent parton distribution functions from the experiments on semi-inclusive deep inelastic scattering process (SIDIS), elucidating the spin-orbit correlations in nucleon. Here w…
We study fragmentation in electron-positron annihilation assuming a di-jet situation, using variables defined independent of any frame. In a collinear situation some of the variables are centered around zero with the small deviations attributed to intrinsic transverse momenta and large deviations attributed to additional hard subprocesses. Of course there is a gradual transition. Our modest goal is to show that covariantly defined variables are well suited to get a feeling for the magnitude of intrinsic transverse momenta.
When high-energy single-hadron production takes place inside an identified jet, there are important correlations between the fragmentation and phase-space cuts. For example, when one-hadron yields are measured in on-resonance B-factory data, a cut on the thrust event shape T is required to remove the large b-quark contribution. This leads to a dijet final state restriction for the light-quark fragmentation process. Here we complete our analysis of unpolarized fragmentation of (light) quarks and gluons to a light hadron h with energy fraction z in e+ e- -> dijet + h at the center-of-mass energy…
In electron positron annihilation, changing quarks into the final hadron states is being described by fragmentation function. Based on the scaling hypothesis, this function will be independent from the center of mass energy. Gluon radiation violates the scaling feature. Transverse momentum distribution plays an important role in scaling violation of fragmentation functions. In this article, by the use of data resulted from the annihilation process of electron positron in AMY detector at 60 GeV center of mass energy, first, charged particles multiplicity distribution will be obtained and it wil…
We propose the characterization of fragmentation functions by the energy fraction x, a hadron takes away from the energy of the jet measured in the frame co-moving with the jet. Besides, we propose the usage of the jet mass as the fragmentation scale Q. We show that these two Lorentz-invariant variables emerge naturally in a microcanonical ensemble with conserved fourmomentum. Then, we construct a statistical hadronisation model, in which, two features of the hadronic final states in various high-energy reactions (power law spectra and negative-binomial multiplicity distributions) can be conne…
The field of fragmentation functions of light quarks and gluons is reviewed. In addition to integrated fragmentation functions, attention is paid to the dependence of fragmentation functions on transverse momenta and on polarization degrees of freedom. Higher-twist and di-hadron fragmentation functions are considered as well. Moreover, the review covers both theoretical and experimental developments in single-inclusive hadron production in electron-positron annihilation, deep-inelastic lepton-nucleon scattering, and proton-proton collisions.
We consider the annihilation process of an electron-positron pair into a pair of heavier fermions when the initial electron and position beams are polarized. By calculating the polarization of the final-state particles, we discuss in detail the effect due to the produced particle masses in the $τ$-charm energy region at BEPC/BES, and also compare the effect with that at the B-factory. Such a study is useful for the design of possible polarization investigation at the BEPC/BES facility and the B-factory.
Transverse momentum asymmetry in the semi-inclusive electron positron annihilation process
College of Nuclear Equipment and Nuclear Engineering, Yantai University（烟台大学核装备与核工程学院）；School of Physics and Optoelectronic Engineering, Shandong University of Technology（山东理工大学物理与光电工程学院）；Southern Center for Nuclear-Science Theory (SCNT), Institute of Modern Physics, Chinese Academy of Sciences（中国科学院现代物理研究所南方核科学理论中心）；Key Laboratory of Particle Physics and Particle Irradiation (MOE), Institute of Frontier and Interdisciplinary Science, Shandong University（山东大学前沿交叉科学高等研究中心粒子物理与粒子辐照教育部重点实验室）
We present the framework for obtaining precise predictions for the transverse momentum of hadrons with respect to the thrust axis in $e^+e^-$ collisions. This will enable a precise extraction of transverse momentum dependent (TMD) fragmentation functions from a recent measurement by the Belle Collaboration. Our analysis takes into account, for the first time, the nontrivial interplay between the hadron transverse momentum and the cut on the thrust event shape. To this end, we identify three different kinematic regions, derive the corresponding factorization theorems within Soft Collinear Effec…
We study the production of polarized $Λ$-hyperons in electron-positron annihilation. We are particularly interested in the transverse-spin dependence of the cross section for unpolarized incident electron-positron pairs. At high energies this process may be described in the collinear twist-3 framework, where the hadronization transition of partons into a transversely polarized $Λ$-hyperon can be written in terms of collinear twist-3 fragmentation matrix elements. We calculate the hard partonic cross sections and interference terms in perturbative QCD to next-to-leading order accuracy. We find …
We present new functional form of pion and kaon fragmentation functions up to next-to-leading order obtained through a global fit to single-inclusive electron-positron annihilation data and also employ, the semi-inclusive deep inelastic scattering asymmetry data from HERMES and COMPASS to determine fragmentation functions. Also we apply very recently electron-positron annihilation data from BaBar and Belle at $\sqrt{s}=10.54$ GeV and $\sqrt{s}=10.52$ GeV, respectively. In this analysis we consider the impression of semi-inclusive deep inelastic scattering asymmetry data on the fragmentation fu…
The forward-backward asymmetry is an important measurable quantity which can enable independent determination of the neutral-current couplings of fermions. In this paper, we extend the definition of the asymmetry from the partonic level to the hadronic level by calculating this asymmetry of the hadron pair in the semi-inclusive electron position annihilation process. Semi-inclusive implies that a back-to-back jet is also measured in addition to the hadron pair. Due to the limitation of the factorization theorem, we calculate this process up to leading order twist-4 level by applying the collin…
We present a novel global QCD analysis of charged $D^{*}$-meson fragmentation functions at next-to-leading order accuracy. This is achieved by making use of the available data for single-inclusive $D^{*}$-meson production in electron-positron annihilation, hadron-hadron collisions, and, for the first time, in-jet fragmentation in proton-proton scattering. It is shown how to include all relevant processes efficiently and without approximations within the Mellin moment technique, specifically for the in-jet fragmentation cross section. The presented technical framework is generic and can be stra…
We present NNFF1.1h, a new determination of unidentified charged-hadron fragmentation functions (FFs) and their uncertainties. Experimental measurements of transverse-momentum distributions for charged-hadron production in proton-(anti)proton collisions at the Tevatron and at the LHC are used to constrain a set of FFs originally determined from electron-positron annihilation data. Our analysis is performed at next-to-leading order in perturbative quantum chromodynamics. We find that the hadron-collider data is consistent with the electron-positron data and that it significantly constrains the …
We have derived the coefficients of the highest three 1/x-enhanced small-x logarithms of all timelike splitting functions and the coefficient functions for the transverse fragmentation function in one-particle inclusive e^+e^- annihilation at (in principle) all orders in massless perturbative QCD. For the longitudinal fragmentation function we present the respective two highest contributions. These results have been obtained from KLN-related decompositions of the unfactorized fragmentation functions in dimensional regularization and their structure imposed by the mass-factorization theorem. Th…
A method for measuring the average longitudinal polarization of the electron beam at an electron-positron collider operating near the $J/ψ$ resonance is proposed. The method utilizes the differential cross-section of $J/ψ\to [Λ\to pπ^-][\barΛ\to\bar{p}π^+]$ decay. It can be used to measure the average longitudinal polarization of electrons with the statistical precision better than $10^{-3}$ at a Super Charm-Tau factory operating at the luminosity of $10^{35}~\mathrm{cm}{}^{-2}\mathrm{s}{}^{-1}$. The method is discussed in the context of the weak mixing angle measurement in the same experiment…
I present a first determination of a set of collinear fragmentation functions of charged pions using the NNPDF methodology. The analysis is based on a wide set of single-inclusive electron-positron annihilation data, including recent measurements from $B$-factory experiments, and is performed up to next-to-next-to-leading order accuracy in perturbative quantum chromodynamics. I discuss the results of the fits, highlighting their quality in the description of the data, their stability upon the inclusion of higher-order corrections, and their comparison to other sets of fragmentation functions.
We present first observations of the transversity parton distribution based on an analysis of pion-pair production in deep inelastic scattering off transversely polarized targets. The extraction of transversity relies on the knowledge of dihadron fragmentation functions, which we take from electron-positron annihilation measurements. This is the first attempt to determine the transversity distribution in the framework of collinear factorization.
We briefly report our recent progress on the study of the polarized fragmentation functions of $Λ$ hyperon in unpolarized semi-inclusive deep-inelastic scatterings and electron-positron annihilations at low energies. In particular, we present a simple but practical method on how to measure the azimuthal-angle-dependent longitudinal polarization and the transverse polarization inside the production plane and bridge these observables to the corresponding structure functions and fragmentation functions at the leading twist. Our work diversifies the high energy reactions that can probe the polariz…
The fragmentation functions for $c$ or $\bar{b}$ quark to $B_c$ or $B_c^*$ meson are derived up to QCD next-to-leading order (NLO). They are further computed numerically and presented in figures precisely. In order to reach a higher accuracy, we have also tried properly to apply them to estimating the $B_c$ and $B_c^*$ production at a $Z$-factory (an $e^+e^-$ collider running at the energy of the $Z$-boson pole).
We present a new determination of unpolarised charged pion and kaon fragmentation functions from a set of single-inclusive electron-positron annihilation and lepton-nucleon semi-inclusive deep-inelastic scattering data. The determination includes next-to-next-to-leading order QCD corrections to both processes, and is carried out in a framework that combines a neural-network parametrisation of fragmentation functions with a Monte Carlo representation of their uncertainties. We discuss the quality of the determination, in particular its dependence on higher order corrections.
We discuss studies on determination of fragmentation functions and an application to exotic-hadron search by using characteristic differences between favored and disfavored functions. The optimum fragmentation functions are determined for pion, kaon, and proton in the leading order (LO) and next-to-leading order (NLO) of the running coupling constant alpha_s by global analyses of hadron-production data in electron-positron annihilation. Various parametrization results are much different in disfavored-quark and gluon fragmentation functions; however, we show that they are within uncertainties o…
The fragmentation of a colored parton directly into a pair of colorless hadrons is a non-perturbative mechanism that offers important insights into the nucleon structure. Di-hadron fragmentation functions can be extracted from semi-inclusive electron-positron annihilation data. They also appear in observables describing the semi-inclusive production of two hadrons in deep-inelastic scattering of leptons off nucleons or in hadron-hadron collisions. When a target nucleon is transversely polarized, a specific chiral-odd di-hadron fragmentation function can be used as the analyzer of the net densi…
A new framework is sketched for the treatment of the hadronisation of a highly-virtual quark and anti-quark jet pair created in electron-positron annihilations. As in such a case, factorization theorem does not work, a new scale-evolution equation is proposed for the fragmentation functions. In this approach, the virtuality of the leading parton (taken to be equal to the mass of the jet it induces) is used as fragmentation scale.
We study the production of two almost back-to-back hadrons from the annihilation of an electron and a positron, allowing for the polarization of all particles involved. In particular, we conduct a general (model-independent) structure function decomposition of the cross section for the case $e^+e^- \to γ^* \to h_ah_bX$. Moreover, using the parton model we calculate the relevant structure functions in terms of twist-2 transverse momentum dependent (TMD) fragmentation functions (FFs). We also give results for the situation $e^+e^- \to Z^* \to h_ah_bX$ (including $γ$-$Z$ interference) within this…
The violation of CP symmetry at the electro-weak scale is one of the essential ingredients for electro-weak baryogenesis. It is therefore of great interest to map the CP properties of the Higgs sector in as much detail as possible. A linear electron-positron Higgs factory collider will provide many opportunities to probe the CP nature of the Higgs sector, thanks to access to several Higgs production processes at a wide range of centre-of-mass energies. In this paper we report on two studies based on full simulation of detector response and realistic reconstruction algorithms: 1) a study of $h …
The scaling of charged hadron fragmentation functions to the Tsallis distribution for $0.01 \lessapprox x \lessapprox 0.2$ is presented for various $e^+e^-$ collision energies. A possible microcanonical generalisation of the Tsallis distribution is proposed, which gives good agreement with measured data up to $x\approx1$. The proposal is based on superstatistics and a $KNO$ like scaling of multiplicity distributions in $e^+e^-$ experiments.
We present a new, comprehensive global analysis of parton-to-pion fragmentation functions at next-to-leading order accuracy in QCD. The obtained results are based on the latest experimental information on single-inclusive pion production in electron-positron annihilation, lepton-nucleon deep-inelastic scattering, and proton-proton collisions. An excellent description of all data sets is achieved, and the remaining uncertainties in parton-to-pion fragmentation functions are estimated based on the Hessian method. Extensive comparisons to the results from our previous global analysis are performe…
Observations of the transversity parton distribution based on an analysis of pion-pair production in deep inelastic scattering off transversely polarized targets are presented. This extraction relies on the knowledge of dihadron fragmentation functions, which are obtained from electron-positron annihilation measurements. This is the first attempt to determine the transversity distribution in the framework of collinear factorization.
Fragmentation functions for eta mesons are extracted at next-to-leading order accuracy of QCD in a global analysis of data taken in electron-positron annihilation and proton-proton scattering experiments. The obtained parametrization is in good agreement with all data sets analyzed and can be utilized, for instance, in future studies of double-spin asymmetries for single-inclusive eta production. The Lagrange multiplier technique is used to estimate the uncertainties of the fragmentation functions and to assess the role of the different data sets in constraining them.
We revisit the global QCD analysis of parton-to-kaon fragmentation functions at next-to-leading order accuracy using the latest experimental information on single-inclusive kaon production in electron-positron annihilation, lepton-nucleon deep-inelastic scattering, and proton-proton collisions. An excellent description of all data sets is achieved, and the remaining uncertainties in parton-to-kaon fragmentation functions are estimated and discussed based on the Hessian method. Extensive comparisons to the results from our previous global analysis are made.
We carry out a global QCD analysis of parton-to-pion fragmentation functions at next-to-next-to-leading order (NNLO) accuracy by performing a fit to the combined set of single-inclusive electron-positron annihilation and, for the first time, semi-inclusive deep-inelastic scattering (SIDIS) multiplicity data. For the latter, we utilize the approximate NNLO QCD corrections that were derived recently within the threshold resummation formalism. We explore the impact of the NNLO corrections on the description of the SIDIS data sets in various kinematic regimes and on the resulting pion fragmentatio…
We present a first analysis of parton-to-pion fragmentation functions at next-to-next-to-leading order accuracy in QCD based on single-inclusive pion production in electron-positron annihilation. Special emphasis is put on the technical details necessary to perform the QCD scale evolution and cross section calculation in Mellin moment space. We demonstrate how the description of the data and the theoretical uncertainties are improved when next-to-next-to-leading order QCD corrections are included.
Determination of Fragmentation Functions from Charge Asymmetries in Hadron Production
State Key Laboratory of Dark Matter Physics, Shanghai Key Laboratory for Particle Physics and Cosmology, Key Laboratory for Particle Astrophysics and Cosmology (MOE), School of Physics and Astronomy, Shanghai Jiao Tong University（上海交通大学物理与天文学院，粒子天体物理与宇宙学教育部重点实验室，暗物质物理全国重点实验室，粒子物理与宇宙学上海市重点实验室）
We consider accretion of matter onto a low mass black hole surrounded by ionized medium. We show that, because of higher mobility of protons than electrons, the black hole would acquire positive electric charge. If the black hole's mass is about or below $10^{20}$ g, the electric field at the horizon can reach the critical value which leads to vacuum instability and electron--positron pair production by the Schwinger mechanism. Since the positrons are ejected by the emergent electric field, while electrons are back--captured, the black hole operates as an antimatter factory which effectively c…
In this document, we present the global QCD analysis of parton-to-kaon fragmentation functions at next-to-leading order accuracy using the latest experimental information on single-inclusive kaon production in electron-positron annihilation, lepton-nucleon deep-inelastic scattering, and proton-proton collisions. An extended analysis of this work can be found in Ref.[1].
