We examine the QCD evolution of the helicity and transversity parton distribution functions when including also their dependence on transverse momentum. Using an appropriate definition of these polarized transverse momentum distributions (TMDs), we describe their dependence on the factorization scale and rapidity cutoff, which is essential for phenomenological applications.
The quark transversity distribution inside nucleon is less understood than the quark unpolarized and helicity distributions inside nucleon. In particular, it is important to know clearly why the quark helicity and transversity distributions are different. We investigate the origin of their discrepancy.
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 consider the quark and antiquark transversity distributions inside a polarized proton and we study how they are expected to be related to the corresponding helicity distributions, both in sign and magnitude. Our considerations lead to simple predictions in good agreement with their first determination for light quarks from experimental data. We also give our predictions for the light antiquarks transversity distributions, so far unknown.
We construct the spin formalism in order to deal in a direct and natural way with processes involving transversity which are now of increasing popularity. The helicity formalism which is more appropriate for collision processes of definite helicity has been so far used also to manage processes with transversity, but at the price of computing numerous helicity amplitudes generally involving unnecessary kinematical variables.In a second step we work out the correspondence between both formalisms and retrieve in another way all results of the helicity formalism but in simpler forms.We then comput…
We present the first lattice-QCD calculation of the isovector polarized parton distribution functions (both helicity and transversity) using the large-momentum effective field theory (LaMET) approach for direct Bjorken-$x$ dependence. We first review the detailed steps of the procedure in the unpolarized case, then generalize to the helicity and transversity cases. We also derive a new mass-correction formulation for all three cases. We then compare the effects of each finite-momentum correction using lattice data calculated at $M_π\approx 310$ MeV. Finally, we discuss the implications of thes…
It is shown that $Λ$-hyperon fragmentation in charged lepton deep inelastic scattering (DIS) on a polarized nucleon target can provide sensitive information concerning the quark helicity and transversity distributions for both nucleon and $Λ$-hyperon at large $x$. Numerical predictions are given for the spin transfers of the produced $Λ$, when the target nucleon is polarized either longitudinally or transversely, and with the nucleon and $Λ$ quark distributions evaluated both in an SU(6) quark-spectator-diquark model and in a perturbative QCD (pQCD) based model. It is also shown that the predi…
We study the polarization of hyperon in different processes in singly polarized $pp$ collisions, in particular its relation to the polarized parton distributions. We show that by measuring hyperon polarization in particularly chosen processes, one can extract useful information on these parton distributions. We show in particular that, by measuring the $Σ^+$ polarization in high $p_T$ direct photon production process, one can extract information on the gluon helicity distribution; and by measuring the transverse polarization of hyeprons with high $p_T$ in singly polarized reactions, one can ob…
An inventory is made of the experiments which can measure the transversely polarized quark distributions and fragmentation functions at leading twist. (Contribution to the 10th International Symposium on High Energy Spin Physics, Nagoya, Japan, Nov. 9-14, 1992)
Recent developments showed that light cone parton distributions can be studied by investigating the large momentum limit of the so-called quasiparton distributions, which are defined in terms of spacelike correlators, and therefore can be readily computed on the lattice. These two distributions can be connected to each other by a perturbative factorization formula or matching condition that allows one to convert the latter into the former. Here we present the one-loop matching condition for the transversity generalized quark distribution in the nonsinglet case
We present an exploratory study using generalized parton distributions of several observables related to transverse degrees of freedom in hadronic structure -- the nucleon transverse momentum, the transverse radius, or impact parameter, and the momentum transfer, $t$, dependence of the longitudinal variable $x$ -- in both nucleons and nuclei.
Transversity distribution is one of the three fundamental parton distributions that completely describe polarized spin 1/2 nucleon. Its chiral odd nature prevented for many years its experimental exploration, however presently we have obtained great deal of information about this distribution. This includes experimental data from Semi Inclusive Deep Inelastic Scattering, knowledge of scale dependence and phenomenological extractions. I will discuss main features of this distribution and indicate the future improvements of our knowledge.
Quark and gluon helicity flip generalized parton distributions (GPDs) encode the information on the nucleon structure in the transversity sector. In order to build a theoretically consistent phenomenological parametrization for these hadronic matrix element within the framework of the dual parametrization of GPDs (or with the equivalent approach of the SO(3) partial waves (PW) expansion with the Mellin-Barnes integral techniques) we establish the set of combinations of parton helicity flip GPDs suitable for the expansion in the cross channel SO(3) PWs.
Transversity generalized parton distributions (GPDs) appear as scalar functions in the decomposition of off-forward quark-quark and gluon-gluon correlators with a parton helicity flip. For a spin 1 hadron, we find 9 transversity GPDs for both quarks and gluons at leading twist 2. We study these twist-2 chiral odd quark transversity GPDs for the deuteron in a light cone convolution model, based on the impulse approximation, and using the lowest Fock-space state for the deuteron.
The role of transversity or helicity-flip generalized parton distributions (GPDs) in leptoproduction of vector mesons is investigated within the framework of the handbag approach. The transversity GPDs in combination with twist-3 meson wave functions, occur in the amplitudes for transitions from a transversely polarized virtual photon to a longitudinal polarized vector meson. The importance of the transversity GPDs can be examined in some of the spin density matrix elements and in transverse target spin asymmetries. Using suitable parametrizations of both helicity-flip and non-flip GPDs, which…
The transversity Generalized Parton Distributions (tGPDs) and related transversity form factors of the pion are evaluated in chiral quark models, both local (Nambu--Jona-Lasinio) and nonlocal, involving a momentum-dependent quark mass. The obtained tGPDs satisfy all a priori formal requirements, such as the proper support, normalization, and polynomiality. We evaluate generalized transversity form factors accessible from the recent lattice QCD calculations. These form factors, after the necessary QCD evolution, agree very well with the lattice data, confirming the fact that the spontaneously b…
We present a determination of the non-singlet transversity parton distribution function (PDF) of the nucleon, normalized with respect to the tensor charge at $μ^2=2$ GeV$^2$ from lattice quantum chromodynamics. We apply the pseudo-distribution approach, using a gauge ensemble with a lattice spacing of 0.094 fm and the light quark mass tuned to a pion mass of 358 MeV. We extract the transversity PDF from the analysis of the short-distance behavior of the Ioffe-time pseudo-distribution using the leading-twist next-to-leading order (NLO) matching coefficients calculated for transversity. We recon…
Exclusive pi0 electroproduction from nucleons can be related to transversity, the tensor charge, and other quantities related to transversity. This process isolates C-parity odd and chiral odd combinations of t-channel exchange quantum numbers. In a hadronic picture the meson production amplitudes for intermediate energy and Q are determined by C-odd Regge exchanges with final state interactions. The helicity structure for this C-odd process relates to the quark helicity flip, or chiral odd generalized parton distributions (GPDs).Various cross sections and asymmetries will be sensitive to the …
The chiral-odd transversity generalized parton distributions of the nucleon can be accessed experimentally through the exclusive photoproduction process gamma N -> pi rhoT N', with or without beam and target polarization, provided the vector meson is produced in a transversely polarized state. The kinematical domain of factorization is defined through a large invariant mass of the meson pair and a small transverse momentum of the final nucleon. We calculate perturbatively the scattering amplitude at leading order in alpha_s and build a simple model for the dominant transversity GPD H_T(x, xi, …
We present the general framework to calculate chiral-odd generalized parton distributions in the overlap representation using the Fock-state decomposition in the transverse spin basis. In the forward limit we derive the transversity distribution, the tensor charge and the angular momentum sum rule for quarks with transverse polarization in an unpolarized nucleon. Numerical results are obtained by applying the formalism to the case of light-cone wavefunctions of constituent quark models.
We present the first direct calculation of the transversity parton distribution function within the nucleon from lattice QCD. The calculation is performed using simulations with the light quark mass fixed to its physical value and at one value of the lattice spacing. Novel elements of the calculations are non-perturbative renormalization and extraction of a formula for the matching to light-cone PDFs. Final results are presented in the $\overline{\rm MS}$ scheme at a scale of $\sqrt{2}$ GeV.
Within the framework of light-cone quantization we derive the overlap representation of generalized parton distributions for transversely polarized quarks using the Fock-state decomposition in the transverse-spin basis. We apply this formalism to the case of light-cone wave functions in a constituent quark model giving numerical results for the four chiral-odd generalized parton distributions in a region where they describe the emission and reabsorption of a quark by the nucleon. With the transversity distribution obtained in the forward limit of the generalized distribution, we provide some p…
Impact parameter dependent parton distributions are transversely distorted when one considers transversely polarized nucleons and/or quarks. This provides a physical mechanism for the T-odd Sivers effect in semi-inclusive deep-inelastic scattering. The transverse distortion can also be related to Ji's sum rule for the angular momentum carried by the quarks. The distortion of chirally odd impact parameter dependent parton distributions is related to chirally odd GPDs. This result is used to provide a decomposition of the quark angular momentum w.r.t. quarks of definite transversity. Chirally od…
The chiral-odd transversity generalized parton distributions (GPDs) of the nucleon can be accessed experimentally through the exclusive photoproduction process gamma + N -> pi + rho + N', in the kinematics where the meson pair has a large invariant mass and the final nucleon has a small transverse momentum, provided the vector meson is produced in a transversally polarized state. We calculate perturbatively the scattering amplitude at leading order in alpha_s. We build a simple model for the dominant transversity GPD H_T(x,xi, t) based on the concept of double distribution. We estimate the unp…
Dynamical gluon effects in proton transversity and off-forward parton distributions from a light-front Hamiltonian approach
Institute of Modern Physics, Chinese Academy of Sciences（中国科学院近代物理研究所）；University of Chinese Academy of Sciences（中国科学院大学）；Iowa State University（爱荷华州立大学）
We present results on the quark unpolarized, helicity and transversity parton distributions functions of the nucleon. We use the quasi-parton distribution approach within the lattice QCD framework and perform the computation using an ensemble of twisted mass fermions with the strange and charm quark masses tuned to approximately their physical values and light quark masses giving pion mass of 260 MeV. We use hierarchical probing to evaluate the disconnected quark loops. We discuss identification of ground state dominance, the Fourier transform procedure and convergence with the momentum boost.…
We report on the extraction of dihadron fragmentation functions (DiFF) from the semiinclusive production of two hadron pairs in back-to-back jets in e+e- annihilation. A nonzero asymmetry in the correlation of azimuthal orientations of opposite $π^+π^-$ pairs is related to the transverse polarization of fragmenting quarks through a significant polarized DiFF. A combined analysis of this asymmetry and the spin asymmetry in the SIDIS process $ep^{\uparrow}\to e'(π^+π^-)X$ has led to the first extraction of the u and d-flavor transversity parton distribution function in the framework of collinear…
The forward limit of the chiral-odd generalized parton distributions (GPDs) and their lower moments are investigated within the framework of the chiral quark soliton model (CQSM), with particular emphasis upon the transversity decomposition of nucleon angular momentum proposed by Burkardt. A strong correlation between quark spin and orbital angular momentum inside the nucleon is manifest itself in the derived second moment sum rule within the CQSM, thereby providing with an additional support to the qualitative connection between chiral-odd GPDs and the Boer-Mulders effects. We further confirm…
Exclusive $π^0$ electroproduction from nucleons is suggested for extracting the tensor charge and other quantities related to transversity from experimental data. This process isolates C-parity odd and chiral odd combinations of t-channel exchange quantum numbers. In a hadronic picture it connects the meson production amplitudes to C-odd Regge exchanges with final state interactions. In a description based on partonic degrees of freedom, the helicity structure for this C-odd process relates to the quark helicity flip, or chiral odd generalized parton distributions.
Nucleon spin structure functions have been investigated mainly by longitudinally-polarized ones for finding the origin of the nucleon spin. Other types of spin structure functions are transversely-polarized ones. In particular, quark transversity distributions in the nucleons have very different properties from the longitudinally-polarized quark distribution functions, especially in scaling violation, because they are decoupled from the gluon transversity, due to the fact that they are helicity-flip (chiral-odd) distributions. Such studies are valuable for finding not only the origin of the nu…
Exclusive $π^o$ electroproduction and related processes are suggested to investigate the chiral odd transversity distributions of quarks in the transversely polarized nucleon, $h_1(x)$, and its first moment, the tensor charge. The connection between a description based on partonic degrees of freedom, given in terms of generalized parton distributions, and Regge phenomenology is explored.
The probabilistic model of parton distributions, previously developed by one of the authors, is generalized to include the transversity distribution. When interference effects are attributed to quark level only, the intrinsic quark motion produces the transversity, which is about twice as large as the usual polarized distribution. The applicability of such a picture is considered and possible corrections, accounting for interference effects at the parton-hadron transition stage are discussed.
We show that in hard exclusive electroproduction, ep-->eVp, the leading-twist hard-scattering coefficient for the production of a transversely polarized vector meson V vanishes to all orders of perturbation theory. This implies that this process cannot be used to measure the skewed transversity distribution of quarks in a hadron. In contrast, a recent calculation obtained a non-zero value at NLO. We show that this calculation is incorrect because it failed to include the necessary collinear subtractions. Our method of proof also applies to other processes whose hard-scattering coefficients are…
The QCD evolution of the transversity distributions is investigated and compared to that of the helicity distributions. It is shown that they differ largely in the small-$x$ region. It is also proved that the evolution preserves Soffer's inequality among the three leading-twist distribution functions.
We discuss the NLO evolution of quark transversity densities and of the parton distribution function for linearly polarized gluons in a linearly polarized hadron. A supersymmetric relation between the NLO evolution kernels for transversity and for linear polarization is found. We also study the implications of NLO evolution for Soffer's inequality and the prospects of measuring transversity densities in polarized Drell-Yan at RHIC.
Using overlap as well as Wilson fermions, we have computed the one-loop renormalization factors of ten non-singlet operators which measure the third moment of quark momentum and helicity distributions (the lowest two having been computed in a previous paper), as well as the lowest three moments of the $g_2$ structure function and the lowest two non-trivial moments of the $h_1$ transversity structure function (plus the tensor charge). These factors are needed to extract physical observables from Monte Carlo simulations of the corresponding matrix elements. An exact chiral symmetry is maintained…
Exclusive $π^0$ electroproduction from nucleons at large $Q^2$ can be described by Generalized Parton Distributions (GPDs), particularly the chiral odd subset related to transversity. These GPDs can be accessed experimentally from various cross sections and asymmetries. We calculate these GPDs in a spectator model, constrained by boundary functions. Alternatively, in a hadronic picture the meson production amplitudes correspond to C-odd Regge exchanges with final state interactions. The helicity structure provides relations between the partonic and the hadronic, Regge description of C-odd, chi…
We discuss polarized parton distributions and their effects on spin asymmetries at RHIC. In particular, transversity distributions and transverse spin asymmetry are studied. First, we show the $Q^2$ evolution difference between a transversity distribution and a corresponding longitudinally polarized distribution. The difference could be an important test of perturbative QCD in high-energy spin physics. Then, the transverse spin asymmetry $A_{TT}$ is calculated with possible transversity distributions. Next, we study antiquark flavor asymmetry $Δ_{_T} \bar u/ Δ_{_T} \bar d$ in the transversity …
The quark helicity measured in polarized deep inelastic scattering is different from the quark spin in the rest frame of the nucleon. We point out that the quark spin distributions $Δq_{RF}(x)$ are connected with the quark helicity distributions $Δq(x)$ and the quark transversity distributions $δq(x)$ by an approximate relation: $Δq_{RF}(x) + Δq(x)=2 δq(x)$. This relation will be useful in order to measure the rest frame (or quark model) spin distributions of the nucleon once the quark helicity distributions and quark transversity distributions are themselves measured. We also calculate the $x…
Two related issues are discussed, which might be easily explored by present and future COMPASS experiments. The first one deals with the new world of transversity, the fundamental polarized parton distribution so far totally unknown. The second issue concerns Lambda production in polarized semi-inclusive processes, with a measurement of the Lambda polarization, which might give novel information on distribution and fragmentation properties of polarized partons. In case of transverse polarization the detection of Lambda's gives access to a new way of measuring transversities. Also the interesti…
The feasibility of measuring chiral-odd parton distribution functions in polarized Drell-Yan and semi-inclusive experiments has renewed theoretical interest in their study. Models of hadron structure have proven succesful in describing the gross features of the chiral-even structure functions. Similar expectations support our study of the transversity parton distributions in the Isgur-Karl and MIT bag models. We confirm the diverse low x behavior of the transversity and spin structure functions at the experimental scale and show that it is fundamentally a consequence of the different behavior …
Exclusive meson leptoproduction from nucleons in the deeply virtual exchanged boson limit can be described by generalized parton distributions (GPDs). Including spin dependence in the description requires 8 independent quark-parton and gluon-parton functions. The chiral even subset of 4 quark-nucleon GPDs are related to nucleon form factors and to parton distribution functions. The chiral odd set of 4 quark-nucleon GPDs are related to transversity, the tensor charge, and other quantities related to transversity. Different meson or photon production processes access different combinations of GP…
I shall present a rather pedagogical discussion of the transversity distributions in the quark-parton model and, in particular, the role of perturbative QCD corrections. Among the topics I shall discuss are: LO and NLO evolution, the Soffer bound and so-called K factors in the Drell-Yan process. The main conclusion will be that, compared to unpolarised or even longitudinally polarised hadron scattering, the case of transverse spin should actually provide a far clearer window onto the workings of QCD and the interplay with the quark-parton model.
The specificities of transverse polarization with respect to helicity of ultrarelativistic fermions are pointed out. For massless fermions, a covariant transversity four-vector is defined, up to a kind of gauge transformation. The tranversity distribution of quarks in a nucleon is defined. Its possible connection to the magnetic or electric dipole moment of the baryon is conjectured. Consequences of the approximate chiral invariance on transverse spin asymmetries in hard processes are enumerated. The "sheared jet effect" introduced by Collins for measuring the transverse polarization of a fina…
We implement a Monte Carlo sampling strategy to extract helicity parton densities and their uncertainties from a reference set of longitudinally polarized scattering data, chosen to be that used in the DSSV14 global analysis. Instead of adopting the simplest possible functional forms for the helicity parton distributions and imposing certain restrictions on their parameter space in order to constrain them, we employ redundant, flexible parametrizations and fit them to a large number of Monte Carlo replicas of the existing data. The optimum fit and its uncertainty estimates are then assumed to …
The distribution of transversely polarized quarks inside a transversely polarized nucleon, known as transversity, encodes a basic piece of information on the nucleon structure, sharing the same status with the more familiar unpolarized and helicity distributions. I will review its properties and discuss different ways to access it, with highlights and limitations. Recent phenomenological extractions and perspectives are also presented.
Transversity quark light-cone momentum distributions are calculated for the nucleon. We utilize a modified Nambu--Jona-Lasinio model in which confinement is simulated by eliminating unphysical thresholds for nucleon decay into quarks. The nucleon bound state is obtained by solving the relativistic Faddeev equation in the quark-diquark approximation, where both scalar and axial-vector diquark channels are included. Particular attention is paid to comparing our results with the recent experimental extraction of the transversity distributions by Anselmino et al. We also compare our transversity r…
Transversity distribution, together with the unpolarized and the helicity distributions, represents a basic piece of information on the internal structure of nucleons. Its peculiar property of being a chiral-odd quantity implies that it can be accessed only in combination with another chiral-odd partner, making it much harder to measure. In this talk I will review its properties and describe the most relevant and feasible ways to access it. Recent phenomenological extractions, their highlights and limitations, as well as perspectives are discussed.
We present a calculation of the two-loop evolution kernels of the twist-two transversally polarized quark and linearly polarized gluon skewed parton distributions in the minimal subtraction scheme and discuss a solution of the evolution equations suitable for numerical implementations.
Generalized parton distributions with helicity flip are studied in the quark sector, within a simple version of the MIT bag model, assuming an SU(6) wave function for the proton target. In the framework under scrutiny it turns out that only the generalized transversity distribution, H_T^q, is non vanishing. For this quantity, the forward limit is properly recovered and numerical results are found to underestimate recent lattice data for its first moment. Positivity bounds recently proposed are fulfilled by the obtained distribution. The relevance of the analysis for the planning of measurement…
We present the first extraction of the transversity distribution based on the global analysis of pion-pair production in deep-inelastic scattering and in proton-proton collisions with one transversely polarized proton. The extraction relies on the knowledge of di-hadron fragmentation functions, which are taken from the analysis of electron-positron annihilation data. For the first time, the chiral-odd transversity is extracted from a global analysis similar to what is usually done for the chiral-even spin-averaged and helicity distributions. The knowledge of transversity is important among oth…
We present a calculation of the two-loop splitting functions for the evolution of the twist-2 `transversity' parton densities of transversely polarized nucleons. We study the implications of our results for Soffer's inequality for the case of valence quark densities.
A method is discussed to determine the hitherto unknown u-quark transversity distribution from a planned HERMES measurement of a single-spin asymmetry in semi-inclusive pion electroproduction off a transversely polarized target. Assuming u-quark dominance, the measurement yields the shapes of the transversity distribution and of the ratio of a polarized and the unpolarized u-quark fragmentation functions. The unknown relative normalization can be obtained by identifying the transversity distribution with the well-known helicity distribution at large x. The systematic uncertainty of the method …
We present a next-to-leading order QCD calculation of the cross section and longitudinal spin asymmetry in single-inclusive charged-lepton production, pp -> l X, at RHIC, where the lepton is produced in the decay of an electroweak gauge boson. Our calculation is presented in terms of a multi-purpose Monte-Carlo integration program that may be readily used to include experimental spin asymmetry data in a global analysis of helicity parton densities. We perform a toy global analysis, studying the impact of anticipated RHIC data on our knowledge about the polarized anti-quark distributions.
A short review of problems with parton distribution functions in nucleons, non-polarized and polarized, is given. The main part is devoted to the transversity distribution its possible measurement and its first experimental probe via spin asymmetry in semi-inclusive DIS. It is argued that the proton transversity distribution could be successfully measured in future DIS experiments with {\it longitudinally} polarized target.
