We present a thorough phenomenological analysis of the experimental data from Belle Collaboration for the transverse $Λ$ and $\barΛ$ polarisation, measured in $e^+e^-$ annihilation processes, for the case of inclusive (plus a jet) and associated production with a light charged hadron. This allows for the first ever extraction of the quark polarising fragmentation function for a $Λ$ hyperon, a transverse momentum dependent distribution giving the probability that an unpolarised quark fragments into a transversely polarised spin-1/2 hadron.
The surprising polarisation of Lambdas and other hyperons measured in many unpolarised hadronic processes, p N --> Lambda X, has been a long standing challenge for QCD phenomenology. One possible explanation was suggested, related to non perturbative properties of the quark hadronisation process, and encoded in the so-called Polarising Fragmentation Function (PFF). Recent Belle data have shown a non zero Lambda polarisation also in unpolarised e+ e- processes, e+ e- --> Lambda X and e+ e- --> Lambda h X. We consider the single inclusive case and the role of the PFFs. Adopting a simplified kine…
Experimental data from Belle Collaboration for the transverse polarization of $Λ$'s measured in $e^+ e^-$ annihilation processes are used to extract the polarizing fragmentation function (FF) within a TMD approach. We consider both associated and inclusive $Λ$ production, showing a quite consistent scenario. Good separation in flavor is obtained, leading to four independent FFs. Predictions for SIDIS processes at the EIC, crucial for understanding their universality and evolution properties, are also presented.
A new formalism for the factorization of the cross section for single hadron production in $e^+e^-$ annihilations, differential in $z_h$, $P_T$ and thrust, is applied to the phenomenological analysis of data recently measured by the BELLE Collaboration. Within this scheme the $e^+e^- \to hX$ cross section can be recast in the convolution of a perturbatively calculable coefficient and a universal transverse momentum dependent fragmentation function. While performing a next-to-leading order calculation of the perturbative part of the process to next-to-leading logarithmic accuracy, we examine an…
Data from the Belle Collaboration for associated production (with a light unpolarized hadron) and single-inclusive production of transversely polarized $Λ$-hyperons in $e^+e^-$ annihilation processes allowed to extract within a TMD approach, for the first time, the $Λ$ polarizing fragmentation function. Recent theoretical developments on the computation of cross sections for single-inclusive hadron production in $e^+e^-$ annihilation processes, within a Soft Collinear Effective Theory approach, combined with the CSS formalism for the double-hadron production case, can be used to perform a rene…
Recently, the {\it Belle} and {\it BABAR} Collaborations published the single-inclusive electron-positron annihilation data at the center of mass energies ($\sqrt{s}$) of $10.52$ GeV and $10.54$ GeV, respectively. These new data offer one the possibility to determine the nonperturbative initial conditions of fragmentation functions much more accurately. In our previous work \cite{Soleymaninia:2013cxa}, we extracted the fragmentation functions for $π^\pm$ and $K^\pm$ particles at next-to-leading order (NLO) including these new data, for the first time. These new data are in the regions of large…
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…
We investigate the transverse polarization of the $Λ$ hyperon in the processes $e^+e^-\toΛ^\uparrow π^\pm X$ and $e^+e^-\toΛ^\uparrow K^\pm X$ 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 $e^+e^-\toΛ^\uparrow h X$ process at…
We investigate the role of heavy quarks in the production of light flavored hadrons and in the determination of the corresponding non perturbative hadronization probabilities. We define a general mass variable flavor number scheme for fragmentation functions that accounts for heavy quark mass effects, and perform a global QCD analysis to an up-to-date data set including very precise Belle and BaBar results. We show that the mass dependent picture provides a much more accurate and consistent description of data.
We make a systematic study of the isospin symmetry of fragmentation functions by taking decay contributions into account. We assume the isospin symmetry in strong interactions and show that in the unpolarized case the isospin symmetry is held for fragmentation functions of $Λ$ and only tiny violations are allowed for other hadrons such as nucleon and pions due to the contributions from weak decays. We present a rough estimate of the magnitudes of such violations. In the polarized case, we show that the isospin symmetry violation for $Λ$ production should be tiny and the recent Belle data on th…
We study inclusive $Λ_c^{\pm}$-baryon production in $pp$ collisions in the general-mass variable-flavor number scheme and compare with data from the LHCb, ALICE and CMS collaborations. We perform a new fit of the $c \to Λ_c^+$ fragmentation function combining $e^+e^-$ data from OPAL and Belle. The agreement with LHC data is slightly worse compared with a calculation using an older fragmentation function, and the tension between different determinations of $Λ_c^{\pm}$ production cross sections from the LHC experimental collaborations is not resolved. The ratio of data for $Λ_c^+$-baryon and $D^…
The Belle II physics potential for hadron spectroscopy, inputs to g-2, fragmentation functions, proton form factors, measurements of $α_s$ and hadronic $τ$ decays is outlined.
We present the complete structure of the azimuthal dependences and polarization observables for two-hadron production in $e^+e^-$ annihilation processes within a transverse momentum dependent (TMD) approach adopting the helicity formalism. The leading-twist TMD fragmentation functions (TMD-FFs) for spin-1/2 hadrons are fully accounted for. The role of the polarizing FF, together with its extraction from Belle data for the transverse polarization of $Λ$'s, are discussed as well. Finally, predictions for SIDIS processes at EIC are presented.
Factorizing the cross section for single hadron production in $e^+e^-$ annihilations, differential in $z_h$, $P_T$ and thrust, is a highly non trivial task. We have devised a factorization scheme that allows us to recast the $e^+e^- \to hX$ cross section in the convolution of a perturbatively calculable coefficient and a universal Transverse Momentum Dependent (TMD) Fragmentation Function (FF). The predictions obtained from our NLO-NLL perturbative computation, together with a simple ansatz to model the non-perturbative part of the TMD, are applied to the experimental measurements of the BELLE…
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 dete…
The dominant mechanism to produce hadronic bound states with large transverse momentum is fragmentation, that is the splitting of a high energy parton into a hadronic state and other partons. We review the present schemes to calculate the heavy quark fragmentation functions (FFs) and drive an exact analytical expression of FF which includes most of the kinematical and dynamical properties of the process. Using the perturbative QCD, we calculate the FF for c-quark to split into S-wave D-meson to leading order in the QCD coupling constant. Our result is compared with the current well-known pheno…
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…
We present the first open-source analysis of fragmentation functions (FFs) of charged pions (entitled IPM-xFitter) computed at next-to-leading order (NLO) and next-to-next-to-leading order (NNLO) accuracy in perturbative QCD using the xFitter framework. This study incorporates a comprehensive and up-to-date set of pion production data from single-inclusive annihilation (SIA) processes, as well as the most recent measurements of inclusive cross-sections of single pion by the BELLE collaboration. The determination of pion FFs along with their theoretical uncertainties is performed in the Zero-Ma…
Charm-quark fragmentation with an effective coupling constant
我们使用最近提出的一个非微扰模型，基于一个有效的强耦合常数和自由的可调参数，研究e+e-湮灭中的c味强子产生。在微扰碎裂函数的框架下描述了粲夸克的产生，包括NLO系数函数、NLL非单重态的DGPs演化和NNLL大尺度的再确认。我们通过在NNLO近似下的有效耦合常数来模拟强子化效应，并将我们的结果与在Z 0极点和Upperdance（4S）共振下的实验数据进行了比较。我们发现，在实验和理论的不确定性范围内，当x<1-Lambda/m_c时，我们的模型能够给出ALEPH D ~*~+介子谱的合理描述。当与BELLE和CLEO在x空间中的D和D^* 数据进行比较时，出现了更严重的差异。在误差范围内，我们的模型仍然能够再现所有考虑的数据集的前十个梅林时刻。然而，相当大的理论不确定性要求一个完整的NNLO/NNLL分析。
Through data analysis, we present new sets of nonperturbative fragmentation functions (FFs) for $Λ_c^+$ baryon both at leading and next-to-leading order (NLO) and, for the first time, at next-to-next-to-leading order (NNLO) in the minimal subtraction factorization scheme with five massless quarks. The FFs are determined by fitting all available data of inclusive single $Λ_c^+$ baryon production in $e^+e^-$ annihilation taken by the OPAL Collaboration at CERN LEP1 and Belle Collaboration at KEKB. We also estimate the uncertainties in the $Λ_c^+$ FFs as well as in the corresponding observables. …
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 ($π^\pm$), 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 measure…
We perform a re-analysis of Belle data for the transverse $Λ$ and $\barΛ$ polarization in $e^+ e^-$ annihilation processes within a transverse momentum dependent (TMD) factorization approach. We consider two data sets, one referring to the associated production of $Λ$'s with a light unpolarized hadron in an almost back-to-back configuration, and one for the inclusive $Λ$ production, with the reconstruction of the thrust axis. We adopt the Collins-Soper-Sterman framework and employ the recent formulation on the factorization of single-inclusive hadron production. This extends a previous phenome…
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 present calculations of next-to-leading order and resummed QCD corrections for semi-inclusive deep-inelastic scattering and single-inclusive e+e- annihilation. The resummation is performed to next-to-leading logarithmic accuracy. Knowing these QCD corrections is important in order to extract parton distribution functions and fragmentation functions from present and future data for these reactions. We present comparisons of our results to recent data by the COMPASS, HERMES, Belle, and BaBar experiments.
We present multiple results on the production of loosely-bound molecules in bottomonium annihilations and $e^+e^-$ collisions at $\sqrt{s} = 10.58$ GeV. We perform the first comprehensive test of several models for deuteron production against all the existing data in this energy region. We fit the free parameters of the models to reproduce the observed cross sections, and we predict the deuteron spectrum and production and the cross section for the $e^+e^- \to d\bar{d} + X$ process both at the $Υ(1,2,3S)$ resonances and at $\sqrt{s}=10.58$ GeV. The predicted spectra show differences but are al…
We study the transverse momentum dependent (TMD) evolution of the Collins azimuthal asymmetries in $e^+e^-$ annihilations and semi-inclusive hadron production in deep inelastic scattering (SIDIS) processes. All the relevant coefficients are calculated up to the next-to-leading logarithmic (NLL) order accuracy. By applying the TMD evolution at the approximate NLL order in the Collins-Soper-Sterman (CSS) formalism, we extract transversity distributions for $u$ and $d$ quarks and Collins fragmentation functions from current experimental data by a global analysis of the Collins asymmetries in back…
This study is part of a project to investigate the transverse momentum dependence in parton distribution 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 intrinsic and radiative partonic transverse momentum and their mixing with flavor. Different descriptions of the non-perturbative evolution kernel are available on the market and ther…
We demonstrate that spontaneous transverse polarization of Lambda baryon ($Λ$) production in $e^+e^-$ annihilation can be described using the transverse momentum dependent polarizing fragmentation functions (TMD PFFs). Using a simple Gaussian model, we perform an extraction of the TMD PFFs by fitting the BELLE collaboration's recent measurement of the $Λ$ transverse polarization in back-to-back $Λ+h$ production in $e^+ e^-$ collisions, $e^{-} + e^{+} \rightarrow Λ^{\uparrow}+h+X$. We find that this simple model accurately describes the experimental data for $Λ$ production associated with pions…
We study the differential cross section of the single inclusive $e^+e^-$ annihilation to the hadrons via $γ$-production, in the different ${k_{t}}$-factorization frameworks. In order to take into account the transverse momenta of the incoming partons, for the first time, we apply the Kimber et al (KMR) method to calculate the unintegrated parton fragmentation functions (UFFs) from the ordinary integrated one, i.e., the parton fragmentation functions (FFs), which satisfy the similar DGLAP evolution equations, such as those of parton distribution functions (PDFs). Also, by utilizing the differen…
We present preliminary results for an updated extraction of the transversity parton distribution based on the analysis of pion-pair production in deep-inelastic scattering off transversely polarized targets in collinear factorization. Data for proton and deuteron targets by HERMES and COMPASS allow for a flavor separation of the valence components of transversity, while di-hadron fragmentation functions are taken from the semi-inclusive production of two pion pairs in back-to-back jets in $e^+ e^-$ annihilation. The latter data from Belle have been reanalyzed using the replica method and a mor…
In this paper we study transverse polarization of $Λ$ hyperons in single-inclusive leptonic annihilation. We show that when the transverse momentum of the $Λ$ baryon is measured with respect to the thrust axis, a transverse momentum dependent (TMD) factorization formalism is required and the polarization is generated by the TMD polarizing fragmentation function (TMD PFF), $D_{1T}^\perp$. However, when the transverse momentum of the $Λ$ baryon is measured with respect to the momentum of the initial leptons, a collinear twist-3 formalism is required and the polarization is generated by the intri…
We study the Collins function $H^\perp_{1}$ of the $Λ$ hyperon, which describes the fragmentation of a transversely polarized quark into an unpolarized $Λ$ hyperon. We calculate $H^\perp_{1}$ for light quarks of the $Λ$ 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 $\cos2ϕ_0$ asymmetry in the process $e^+e^- \to Λ\barΛX$ contributed by the coupling of two Collins functions. The QCD e…
We calculate the transverse momentum dependence in the production of two back-to-back hadrons in electron-positron annihilations at the medium/large energy scales of BES-III and BELLE experiments. We use the parameters of the transverse-momentum-dependent (TMD) fragmentation functions that were recently extracted from the semi-inclusive deep-inelastic-scattering multiplicities at low energy from HERMES. TMD evolution is applied according to different approaches and using different parameters for the nonperturbative part of the evolution kernel, thus exploring the sensitivity of our results to …
Probing Quark Electromagnetic Properties via Entangled Quark Pairs in Fragmentation Hadrons at Lepton Colliders
Peking University（北京大学）；Zhengzhou University（郑州大学）；Institute of High Energy Physics, Chinese Academy of Sciences（中国科学院高能物理研究所）；University of Chinese Academy of Sciences（中国科学院大学）；China Center of Advanced Science and Technology（中国高等科学技术中心）
This preprint has been superseded by (A. Courtoy, A. S. Miramontes, H. Avakian, M. Mirazita, and S. Pisano, Phys. Rev. D 106, 014027 (2022), 2203.14975). The latter should be consulted and referred to for the extraction of the $e(x)$ PDF. We present the extraction of the twist-3 PDF, $e(x)$, through the analysis of the preliminary data for the $\sinϕ$-moment of the beam-spin asymmetry for di-hadron Semi-Inclusive DIS at CLAS at 6 GeV. Pion-pair production off unpolarized target in the DIS regime provide an access to the higher-twist Parton Distribution Functions $e(x)$ and to Di-hadron Fragmen…
We make a systematic study of $Λ$ hyperon polarizations in unpolarized lepton induced semi-inclusive reactions such as $e^-N\to e^-ΛX$ and $e^+e^-\toΛh X$. We present the general form of cross sections in terms of structure functions obtained from a general kinematic analysis. This already shows that the produced hyperons can be polarized in three orthogonal directions, i.e., the longitudinal direction along the hyperon momentum, the normal direction of the production plane, and the transverse direction in the production plane. We present the parton model results at the leading twist and leadi…
Factorizing the cross section for single hadron production in $e^+e^-$ annihilations is a highly non trivial task when the transverse momentum of the outgoing hadron with respect to the thrust axis is taken into account. We work in a scheme that allows to factorize the $e^+e^- \to HX$ cross section as a convolution of a calculable hard coefficient and a Transverse Momentum Dependent (TMD) fragmentation function. The result, differential in $z_h$, $P_T$ and thrust, will be given to all orders in perturbation theory and explicitly computed to Next to Leading Order (NLO) and Next to Leading Log (…
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 present a new proposal to study the helicity-dependent dihadron fragmentation functions (DiFF), which describe the correlations of the longitudinal polarization of a fragmenting quark with the transverse momenta of the produced hadron pair. Recent experimental searches for this DiFF via azimuthal asymmetries in back-to-back hadron pair production in $e^+e^-$ annihilation by the ${\tt BELLE}$ Collaboration did not yield a signal. Here we propose a new way to access this DiFF in $e^+e^-$ annihilation, motivated by the recently recalculated cross section of this reaction, which explains why th…
Internal structure of exotic hadron candidate $f_0$(980) by using fragmentation functions
Quark Matter Research Center, Institute of Modern Physics, Chinese Academy of Sciences（中国科学院近代物理研究所夸克物质研究中心）；Southern Center for Nuclear Science Theory, Institute of Modern Physics, Chinese Academy of Sciences（中国科学院近代物理研究所南方核科学理论中心）；KEK Theory Center, Institute of Particle and Nuclear Studies, KEK（高能加速器研究机构粒子与核研究本部理论中心）
