Unpolarized Fragmentation Functions Research Articles

The Sivers asymmetry in charged Kaon and Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda $$\\end{document} hyperon produced SIDIS process at electron ion colliders

We investigate the single transverse-spin asymmetry with a sin(ϕh-ϕS)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sin (\\phi _h-\\phi _S)$$\\end{document} modulation in the charged Kaon produced and in Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda $$\\end{document} hyperon produced SIDIS process within the theoretical framework of transverse momentum dependent (TMD) factorization at the next-to-leading-logarithmic order. The asymmetry is contributed by the convolution of Sivers function and the unpolarized fragmentation function D1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$D_1$$\\end{document} for the produced hadron. The parametrization for the proton Qiu–Sterman function, which is closely related to the Sivers function, is adopted to numerically estimate the Sivers asymmetry at the kinematical region of Electron Ion Collider (EIC) and Electron Ion Collider in China (EicC). The TMD evolution of the TMD parton distribution functions are considered by employing the non-perturbative Sudakov form factor. It is found that the predicted Sivers asymmetries AUTsin(ϕh-ϕS)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$A_{UT}^{\\sin (\\phi _h-\\phi _S)}$$\\end{document} as functions of x, z and PhT\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$P_{hT}$$\\end{document} are sizable at the kinematical configurations of both EIC and EicC. The strange constituent of the produced charged Kaon and Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda $$\\end{document} hyperon in the final state can be a promising probe of the sea quark Sivers function as well as the flavor dependence in the proton target. Therefore, it is important to utilize the future EIC facilities to constrain the sea quark distribution functions as well as the validity of the generalized universality of the Sivers function.

Kotzinian-Mulders effect in semi-inclusive DIS within TMD factorization * *Supported by the National Natural Science Foundation of China (12075043)

In this study, we investigate the Kotzinian-Mulders effect under semi-inclusive deep inelastic scattering (SIDIS) within the framework of transverse momentum dependent (TMD) factorization. The asymmetry is contributed by the convolution of the Kotzinian-Mulders function and the unpolarized fragmentation function . As a TMD distribution, the Kotzinian-Mulders function in the coordinate space in the perturbative region can be represented as the convolution of the C-coefficients and the corresponding collinear correlation function. The Wandzura-Wilczek approximation is used to obtain this correlation function. We perform a detailed phenomenological numerical analysis of the Kotzinian-Mulders effect in the SIDIS process within TMD factorization at the kinematics of the HERMES and COMPASS experiments. We observe that the obtained -, -, and -dependent Kotzinian-Mulders effects are basically consistent with the HERMES and COMPASS measurements. We also make predictions at EIC and EicC kinematics.

The transverse polarization of Lambda hyperons in e^+e^-rightarrow Lambda ^uparrow h X processes within TMD factorization

We investigate the transverse polarization of the Lambda hyperon in the processes e^+e^-rightarrow Lambda ^uparrow pi ^pm X and e^+e^-rightarrow Lambda ^uparrow K^pm X within the framework of the transverse momentum dependent (TMD) factorization. The transverse polarization is contributed by the convolution of the transversely polarizing fragmentation function (PFF) D_{1T}^perp of the lambda hyperon and the unpolarized fragmentation function D_1 of pion/kaon. We adopt the spectator diquark model result for D_{1T}^{perp } to numerically estimate the transverse polarization in e^+e^-rightarrow Lambda ^uparrow h X process at the kinematical region of Belle Collaboration. To implement the TMD evolution formalism of the fragmentation functions, we apply two different parametrizations on the nonperturbative Sudakov form factors associated with the fragmentation functions of the Lambda , pion and kaon. It is found that our prediction on the polarization in the Lambda pi ^+ production and {bar{Lambda }} pi ^- is consistent with the recent Belle measurement in size and sign, while the model predictions on the polarizations in Lambda pi ^- and Lambda K^pm productions show strong disagreement with the Belle data. The reason for the discrepancies is discussed and possible approaches to improve the calculation in the future are also discussed.

Simultaneous extraction of fragmentation functions of light charged hadrons with mass corrections

Achieving the highest possible precision for theoretical predictions at the present and future high-energy lepton and hadron colliders requires a precise determination of fragmentation functions (FFs) of light and heavy charged hadrons from a global QCD analysis with great accuracy. We describe a simultaneous determination of unpolarized FFs of charged pions, charged kaons and protons/antiprotons from single-inclusive hadron production in electron-positron annihilation (SIA) data at next-to-leading order and next-to-next-to-leading order accuracy in perturbative QCD. A new set of FFs, called SGKS20, is presented. We include data for identified light charged hadrons (${\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}$, ${K}^{\ifmmode\pm\else\textpm\fi{}}$ and $p/\overline{p}$) as well as for unidentified light charged hadrons, ${h}^{\ifmmode\pm\else\textpm\fi{}}$ and show that these data have a significant impact on both size and uncertainties of the fragmentation functions. We examine the inclusion of higher-order perturbative QCD corrections and finite-mass effects. We compare the new SGKS20 FFs with other recent FFs available in the literature and find in general reasonable agreement, but also important differences for some parton species. We show that theoretical predictions obtained from our new FFs are in very good agreement with the analyzed SIA data, especially at small values of $z$. The SGKS20 FF sets presented in this work are available via the LHAPDF interface.

Transverse single spin asymmetry AUTsin(ϕh−ϕS) for single hadron production in semi-inclusive DIS

In this paper, we study the single spin asymmetry ${A}_{UT}^{\mathrm{sin}({\ensuremath{\phi}}_{h}\ensuremath{-}{\ensuremath{\phi}}_{S})}$ of a single hadron production in semi-inclusive deep inelastic scattering within the framework of transverse momentum dependent factorization up to the next-to-leading logarithmic order of QCD. The asymmetry is a contribution of the convolution of the Sivers function and the unpolarized fragmentation function. Specifically, the Sivers function in the coordinate space and perturbative region can represent the convolution of the $C$ coefficients and the corresponding collinear correlation functions, among which the Qiu-Sterman function is the most relevant one. We perform a detailed phenomenological analysis of the Sivers asymmetry at the kinematics of the HERMES and the COMPASS measurements. It is found that the obtained ${x}_{B}$-, ${z}_{h}$-, and ${P}_{h\ensuremath{\perp}}$-dependent asymmetries are basically consistent with the HERMES and the COMPASS measurements.

Towards small-z fragmentation functions of pion from QCD analysis of single-inclusive electron–positron annihilation

The present study aimed to explore the behavior of unpolarized fragmentation functions (FFs) of pion in the regions of small momentum fractions z. This study used a novel phenomenological QCD approach in the framework of fractal (or self-similar) behavior of FFs to quantify the small-z region. To this end, a simple parameterization for the pion fractal FFs is considered and small z experimental datasets on single inclusive pion production in electron–positron ($$e^+e^-$$) annihilation (SIA) for the range of $$10.54< Q < 91.28$$ GeV and $$z<0.1$$ are included in this analysis. The estimations of the uncertainty in the present analysis are carried out using the standard “Hessian” approach. In total, considering the overall value of $$\chi ^2/\mathrm{dof}$$ and theory/data comparisons, the results indicate excellent agreements between the experimental datasets and the theory predictions at small momentum fractions z. Finally, we present detailed comparisons between predictions for the relevant small-z observables obtained with various recent models of pion FFs available in literature. Considering the findings presented in this study, we discuss how our knowledge of pion FFs may be improved at small-z by future measurements.

Transverse momentum dependent of charged pion, kaon, and proton/antiproton fragmentation functions from e+e− annihilation process

The main aim of this paper is a new determination of transverse momentum dependence of unpolarized fragmentation function (TMD FFs) in single inclusive hadron production in electron-positron annihilation (SIA) process. Motivated by the need for a reliable and consistent determination of TMD FFs, we use the most recent TMD production cross sections of charged pions ($\pi^\pm$), kaons ($K^\pm$) and protons/antiprotons ($p/\bar{p}$) measured in inclusive $e^+e^-$ collisions by Belle Collaboration. These datasets are the first transverse momentum dependence of identified light charged hadron measurements SIA process. In this analysis, referred to as {\tt SK19 TMD FFs}, the common Gaussian distribution is used for the $P_{hT}$ dependent of the cross section. The uncertainties in the extraction of {\tt SK19 TMD FFs} are estimated using the standard "Hessian" technique. We study the quality of the TMD FFs determined in this analysis by comparing with the available recent Belle cross sections measurement. For all hadron species, we found a very good agreement between this particular set of experimental data and the corresponding theory calculations over a relatively wide range of transverse momentum $P_{hT}$. As a result of this study, suggestions are identified for possible future research considering the theory improvements and other available experimental observables.

Double Collins effect in e+e−→ΛΛ¯X and e+e−→ΛπX processes in a diquark spectator model

We study the Collins function $H^\perp_{1}$ of the $\Lambda$ hyperon, which describes the fragmentation of a transversely polarized quark into an unpolarized $\Lambda$ hyperon. We calculate $H^\perp_{1}$ for light quarks of the $\Lambda$ hyperon, in the diquark spectator model with a Gaussian form factor for the hyperon-quark-diquark vertex. The model calculation includes contributions from both the scalar diquark and vector diquark spectators. Using the model result, we estimate the weighted $\cos2\phi_0$ asymmetry in the process $e^+e^- \to \Lambda\bar{\Lambda}X$ contributed by the coupling of two Collins functions. The QCD evolution effects for the first $k_T$-moment of the Collins function and the unpolarized fragmentation function $D_1(z)$ are also included. The results show that asymmetry is sizable and measurable at the kinematical configurations of Belle and BaBar experiments. We also find that the evolution effects play an important role in the phenomenological analysis.

Transverse polarization of the Λ hyperon from unpolarized quark fragmentation in the diquark model

We investigate the spin-dependent (naive) T-odd fragmentation function $D^\perp_{1T}$, which can provide an explanation on the transverse polarization of the $\Lambda^0$ hyperon produced in an unpolarized process. We calculate $D^\perp_{1T}$ for light flavors in the spectator diquark model, with a Gaussian form factor at the hyperon-quark-diquark vertex. We include in the calculation both the scalar diquark and axial-vector diquark spectators. We determine the values of the model parameters by fitting the unpolarized fragmentation function $D^\Lambda_1$ to the DSV parametrization for $D^\Lambda_1$. In addition, we compute the longitudinal polarization fragmentation function $G^\Lambda_1$ and compare it with the known parametrization of $G^\Lambda_1$. We also estimate the transverse polarizations of $\Lambda$ production, in both semi-inclusive deep inelastic scattering and single inclusive $e^+e^-$ annihilation.

Power corrections and renormalons in Transverse Momentum Distributions

We study the power corrections to Transverse Momentum Distributions (TMDs) by analyzing renormalon divergences of the perturbative series. The renormalon divergences arise independently in two constituents of TMDs: the rapidity evolution kernel and the small-b matching coefficient. The renormalon contributions (and consequently power corrections and non-perturbative corrections to the related cross sections) have a non-trivial dependence on the Bjorken variable and the transverse distance. We discuss the consistency requirements for power corrections for TMDs and suggest inputs for the TMD phenomenology in accordance with this study. Both unpolarized quark TMD parton distribution function and fragmentation function are considered.

Double-spin asymmetryALTcosϕSin semi-inclusive DIS at CLAS12 and EIC within the collinear framework

We study the longitudinal-transverse double-spin asymmetry with a $\cos\phi_S$ modulation in semi-inclusive deep inelastic scattering for charged and neutral pions production. We consider the particular case in which the transverse momentum of the final state hadron is integrated out. The corresponding asymmetry may be contributed by two parts: one is the convolution of the twist-3 distribution function $g_{T}(x)$ and the unpolarized fragmentation function $D_1(z)$, the other is related to the coupling of the transversity distribution function $h_1(x)$ and the collinear twist-3 fragmentation function $\tilde{E}(z)$. We take into account both contributions to predict the $\cos\phi_S$ asymmetry at the kinematics of CLAS12 and a future Electron Ion Collider. We find that the asymmetry of pion production at CLAS12 is sizable, and $\tilde{E}(z)$ can play an important role in the asymmetry in the large-$z$ region.

Exploring the Flavor Dependence of Partonic Transverse Momentum

Using recently published HERMES data on multiplicities in semi-inclusive deep-inelastic scattering, we discuss the flavor dependence of unpolarized transverse-momentum dependent distribution and fragmentation functions. We find convincing indications that favored fragmentation into pions have smaller average transverse momentum than unfavored ones and fragmentation into kaons. We find weaker indications of flavor dependence in the transverse-momentum dependence of parton distributions.

Phenomenology from SIDIS ande+e−multiplicities: multiplicities and phenomenology - part I

This study is part of a project to investigate the transverse momentum dependence in parton dis- tribution and fragmentation functions, analyzing (semi-)inclusive high-energy processes within a proper QCD framework. We calculate the transverse-momentum-dependent (TMD) multiplicities for e + e − annihilation into two hadrons (considering different combinations of pions and kaons) aiming to investigate the impact of in- trinsic and radiative partonic transverse momentum and their mixing with flavor. Different descriptions of the non-perturbative evolution kernel (see, e.g., Refs. (1-5)) are available on the market and there are 200 sets of flavor configurations for the unpolarized TMD fragmentation functions (FFs) resulting from a Monte Carlo fit of Semi-Inclusive Deep-Inelastic Scattering (SIDIS) data at Hermes (see Ref. (6)). We build our predictions of e + e − multiplicities relying on this rich phenomenology. The comparison of these calculations with future experimental data (from Belle and BaBar collaborations) will shed light on non-perturbative aspects of hadron structure, opening important insights into the physics of spin, flavor and momentum structure of hadrons.

Fragmentation functions of pions and kaons in the nonlocal chiral quark model

We investigate the unpolarized pion and kaon fragmentation functions using the nonlocal chiral-quark model. In this model the interactions between the quarks and pseudoscalar mesons is manifested nonlocally. In addition, the explicit flavor SU(3) sym- metry breaking e ect is taken into account in terms of the current quark masses. The results of our model are evaluated to higher Q 2 value Q 2 = 4 GeV 2 by the DGLAP evo- lution. Then we compare them with the empirical parametrizations. We find that our results are in relatively good agreement with the empirical parametrizations and the other theoretical estimations.

FLAVOR DEPENDENCE OF UNPOLARIZED TMDS FROM SEMI-INCLUSIVE PION PRODUCTION

Recent data from semi-inclusive deep inelastic scattering collected by the HERMES collaboration allow for the first time to discuss how the transverse-momentum dependence of unpolarized distribution and fragmentation functions is affected by the flavor of the involved partons. A model built with flavor-dependent Gaussian transverse-momentum distributions fits data better than the same flavor-independent model. The current analysis is performed for totally unpolarized scattering of leptons off protons and deuterons, with detected pions in the final state. There are convincing indications of flavor dependence in the fragmentation functions, while for parton distribution functions the evidence is weaker.

TRANSVERSE MOMENTUM-WEIGHTED SIVERS ASYMMETRY IN SEMI-INCLUSIVE DEEP INELASTIC SCATTERING AT NEXT-TO-LEADING ORDER

We summarize the results of a recent study of next-to-leading order perturbative QCD corrections to the transverse momentum-weighted Sivers asymmetry in semi-inclusive hadron production in lepton-proton deep inelastic scattering. The corresponding differential cross section is evaluated as a convolution of a twist-three quark-gluon correlation function, often referred to as Qiu-Sterman function, the usual unpolarized fragmentation function, and a hard coefficient function. By studying the collinear divergence structure, we identify the evolution kernel for the Qiu-Sterman function. The hard coefficient function, which is finite and free of any divergence, is evaluated at one-loop order.

Transverse momentum-weighted Sivers asymmetry in semi-inclusive deep inelastic scattering at next-to-leading order

We study the next-to-leading order perturbative QCD corrections to the transverse momentum-weighted Sivers asymmetry in semi-inclusive hadron production in lepton-proton deep inelastic scattering. The corresponding differential cross section is evaluated as a convolution of a twist-three quark-gluon correlation function, often referred to as Qiu-Sterman function, the usual unpolarized fragmentation function, and a hard coefficient function. By studying the collinear divergence structure, we identify the evolution kernel for the Qiu-Sterman function. The hard coefficient function, which is finite and free of any divergence, is evaluated at one-loop order.

Unpolarized Fragmentation Function for the Pion and Kaon via the Nonlocal Chiral-Quark Model

In this talk we present our recent studies for the unpolarized fragmentation functions for the pion and kaon, employing the nonlocal chiral quark model, which manifests the nonlocal interaction between the quarks and pseudoscalar mesons, in the light-cone frame. It turns out that the nonlocal interaction produces considerable differences in comparison to typical local-interaction models.

Fragmentation functions and parton distribution functions for the pion with the nonlocal interactions

We study the unpolarized fragmentation functions and the parton distribution functions of the pion employing the nonlocal chiral quark model. This model manifests the nonlocal interactions between the quarks and pseudoscalar mesons in the light-cone coordinate. We find that the nonlocal interactions result in substantial differences in comparison to the result of typical models with only local couplings. We also perform the high ${Q}^{2}$-evolution for our results which is calculated at a relatively low-renormalization scale ${Q}^{2}\ensuremath{\approx}0.36\text{ }\text{ }{\mathrm{GeV}}^{2}$ and compare them with the experimental data. It has shown that our results after evolution are in qualitatively good agreement with those experimental data.

QCD evolution of naive-time-reversal-odd fragmentation functions

We study QCD evolution equations of the first transverse-momentum moment of the naive-time-reversal-odd fragmentation functions---the Collins function and the polarizing fragmentation function. We find for the Collins function case that the evolution kernel has a diagonal piece the same as that for the transversity fragmentation function, while for the polarizing fragmentation function case this piece is the same as that for the unpolarized fragmentation function. Our results might have important implications in the current global analysis of spin asymmetries.