In recent years information on the transversity distribution $h_1$ has been obtained combining the Collins asymmetry results from semi-inclusive deep inelastic scattering (SIDIS) data on transversely polarized nucleon targets with the information on the fragmentation function of a transversely polarized quark from the asymmetries measured in $e^+e^-$ annihilation into hadrons. An alternative method was proposed long time ago, which does not require the $e^+e^-$ data, but allows one to get ratios of the $u$ and $d$ quark transversity distributions from the SIDIS data alone. The method utilizes the ratio of the difference of the Collins asymmetries of positively and negatively charged hadrons produced on transversely polarized proton and deuteron targets. We have applied this method to the COMPASS proton and deuteron data, and extracted the ratio $h_1^d/h_1^u$. The results are compared to those obtained in a previous point--by--point extraction based both on SIDIS and $e^+e^-$ data.
The theoretical aspects of two leading twist transversity single spin asymmetries, one arising from the Collins effect and one from the interference fragmentation functions, are reviewed. Issues of factorization, evolution and Sudakov factors for the relevant observables are discussed. These theoretical considerations pinpoint the most realistic scenarios towards measurements of transversity.
A pedagogical introduction to single-spin asymmetries (SSA's) and transversity is presented. Discussion in some detail is made of certain aspects of (SSA's) in lepton-nucleon and in hadron-hadron scattering and the role of pQCD and evolution in the context of transversity.
Ways to access transversity through asymmetry measurements are reviewed. The recent first extraction and possible near future extractions are discussed.
A short review of single spin asymmetries in deep inelastic semi-inclusive processes, connected with prediction of chiral quark-soliton model for the nucleon transversity distributions, its possible theoretical understanding in the framework of QCD-induced approach and arising difficulties is given.
We give upper bounds for transverse double-spin asymmetries in polarized proton-proton collisions by saturating the positivity constraint for the transversity densities at a low hadronic resolution scale. We consider prompt photon, jet, pion, and heavy flavor production at the BNL Relativistic Heavy Ion Collider (RHIC). Estimates of the expected statistical accuracy for such measurements are presented, taking into account the acceptance of the RHIC detectors.
A review is given on single spin asymmetries in deep inelastic semi-inclusive scattering (SIDIS) and their possible theoretical understanding in the framework of QCD-induced factorization approach, wherefore predictions for transversity from the chiral quark soliton model are used. Arising difficulties to interpret most recent SIDIS data, and the possibility to access the transversity distribution in the Drell-Yan process are discussed.
We discuss the quark transversity distribution function and a possible way to access it through the measurement of single spin azimuthal asymmetry in semi-inclusive single pion electroproduction on a transversely polarized target.
We present the principles of the measurement of the quark transversity distributions in semi-inclusive deep inelastic electron scattering, which form the basis of HELP and one of the ELFE proposals. A string model for Collins-type asymmetry in polarized quark fragmentation function is proposed. A possible role of the Collins effect in the single spin asymmetries observed by experiment E 704 at Fermilab is suggested.
The transverse spin of interacting light quarks is described by two independent non-perturbative inputs, twist-2 transversity and twist-3 quark-gluon correlators, while for free massive quarks they are related by the equations of motion. Similar relation emerges also in a model, where quark-hadron transition is treated in a probabilistic way. The single spin asymmerty in SIDIS appears due to the interplay of transverity with Collins fragmentation function, which appears to be of twist 3, when defined in a Lorentz invariant way.
We study double transverse spin asymmetries in the Drell-Yan process at measured transverse momentum of the lepton pair. Contrary to what a collinear factorization approach would suggest, a nonzero double transverse spin asymmetry in the laboratory frame a priori does not imply nonzero transversity. TMD effects, such as the double Sivers effect, in principle form a background. Using the current knowledge of the relevant TMDs we estimate their contribution in the laboratory frame for Drell-Yan and W production at RHIC and point out a cross check asymmetry measurement to bound the TMD contributi…
We consider the leading twist $T$-odd contributions as the dominant source of the azimuthal and transverse single spin asymmetries in SIDIS and dilepton production in Drell-Yan Scattering. These asymmetries contain information on the distribution of quark transverse spin in (un)polarized protons. In the spectator framework we estimate these asymmetries at HERMES kinematics and at $50\ {\rm GeV}$ for the proposed experiments at GSI, where an anti-proton beam is ideal for studying the transversity properties of quarks due to the dominance of {\em valence} quark effects.
In this talk it is reported on an analysis of hard exclusive pion electroproduction within the handbag approach. Particular emphasis is laid on single-spin asymmetries. It is argued that a recent HERMES measurement of asymmetries measured with a transversely polarized target clearly indicate the occurrence of strong contributions from transversely polarized photons. Within the handbag approach such gamma_T --> pion transitions are described by the transversity GPDs accompanied by a twist-3 pion wave function. It is shown that this approach leads to results on cross sections and single-spin asy…
A major experimental program is presently underway to determine the Sivers, Boer-Mulders and transversity distributions, vital for understanding the internal structure of the nucleon. To this end we consider the Sivers, Boer-Mulders and transversity azimuthal asymmetries of the difference cross sections of hadrons with opposite charges in SIDIS reactions with unpolarized and transversely polarized target l+N\to l'+h+X, h=π^\pm, K^\pm, h^\pm. We show that on deuteron target these asymmetries are particularly simple and determine the sum of the valence-quark Q_V=u_V+d_V transverse momentum depen…
The transversity distribution for $u$ and $d$ quarks is usually extracted from data on spin asymmetries in Semi Inclusive Deep Inelastic Scattering (SIDIS): however, due to its chiral odd nature, it has to be coupled to another chiral odd function, typically the Collins or the di-hadron fragmentation function. A recent suggestion of considering SIDIS data involving ratios of spin asymmetries and avoiding a knowledge of the Collins function, is briefly discussed. New measurements, involving ratios of cross sections, are suggested. They would allow a direct extraction of the transversity ratio, …
Using the recent experimental data on the left right asymmetry in fragmentation of transversely polarized quarks and the theoretical calculation of the proton transversity distribution in the effective chiral quark soliton model we explain the azimuthal asymmetries in semi-inclusive hadron production on longitudinal (HERMES) and transversely (SMC) polarized targets with no free parameters. On this basis we state that the proton transversity distribution could be successfully measured in future DIS experiments with longitudinally polarized target.
I review the present state of knowledge concerning transversity distributions and related observables. In particular, I discuss the phenomenology of transverse asymmetries in e p\uparrow, p p\uparrow, p\uparrow p\uparrow and pbar \uparrow p\uparrow scattering, and the perspectives of ongoing and future research.
A review is presented of some aspects of semi-inclusive deeply inelastic scattering and transversity. In particular, the role of $k_T$-dependent and higher-twist (or multi-parton) distributions in generating single-spin asymmetries is discussed.
We study inclusive Lambda hyperon production in pp collisions at BNL RHIC, with just one transversely polarized proton. We show that the measurement of the spin transfer between the initial proton and the produced Lambda is sensitive to the proton transversity distributions and to the corresponding Lambda transversity fragmentation functions. In view of our present ignorance of these distributions and fragmentation functions, we resort to positivity bounds for making some predictions for the corresponding spin transfer asymmetry.
We study the kaon leptoproduction on the basis of the handbag approach. We consider the leading-twist contribution together with the transversity twist-3 effects which were found to be important in the description of pseudo-scalar meson production. We present our predictions for the cross section and spin asymmetries in the kaon leptoproduction.
The observation of the quark transversity distribution requires another soft object sensitive to the quark's transverse spin. Dihadron fragmentation functions represent a convenient tool to analyze partonic spin, which can influence the angular distribution of the two hadrons. In particular, the so-called interference fragmentation functions can be used to probe transversity both in semi-inclusive deep inelastic scattering as well as proton-proton collisions. We discuss two single-spin asymmetries sensitive to transversity in the these two processes, at leading twist and leading order in alpha…
A quantitative estimate is presented for the double transverse spin asymmetries at measured q_T in both the Drell-Yan process and W-boson production due to Transverse Momentum Dependent (TMD) effects. These spin asymmetries are calculated as a function of the lepton azimuthal angle as measured in the laboratory frame. In this frame, in contrast to the Collins-Soper frame, the TMD effects contribute to the spin asymmetry A_{TT}(q_T) in the same way as transversity does, which makes them a background for transversity measurements in the Drell-Yan process and new physics studies in W-boson produc…
A major experimental program is presently underway worldwide to determine the fundamental non-perturbative functions, the Sivers, Boer-Mulders and transversity distributions, which are vital for an understanding of the internal structure of the nucleon. However, at present, many simplifying assumptions are used in extracting these functions from the data. We demonstrate that if the binning of the data in Q^2 is small enough so that Q^2-evolution can be neglected inside a bin, then one can obtain stringent tests of these assumptions. Failure to satisfy these tests implies that the presently ext…
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 distribution can be measured at leading-twist in single-particle inclusive DIS, where it appears in connection with chiral-odd fragmentation functions. Among these functions, we focus on the time-reversal odd ones. They occur in fragmentation to unpolarized hadrons or polarized spin-one hadrons. Using a simple model, we show how these functions can be non-vanishing and we discuss the asymmetries where they can be measured together with the transversity distribution.
A new method is suggested for the extraction of $u$-quark and $d$-quark transversity distributions, using single spin asymmetry (SSA) data in semi-inclusive deep inelastic scattering (SIDIS) processes, where they couple to the Collins or the di-hadron fragmentation functions. We discuss a recent suggestion to extract the transversity distribution using the concept of difference asymmetries and their ratios, which avoids the requirement of Collins function. We suggest new measurements, involving ratios of polarized cross-sections, that would directly probe the ratio $h_1^{d_v}/h_1^{u_v}$. We al…
We present [1] the first simultaneous extraction of the transversity distribution and the Collins fragmentation function, obtained through a combined analysis of experimental data on azimuthal asymmetries in semi-inclusive deep inelastic scattering (SIDIS), from the HERMES and COMPASS Collaborations, and in e+ e- --> h1 h2 X processes, from the Belle Collaboration.
A calculation of nuclear effects in the extraction of neutron single spin asymmetries in semi-inclusive deep inelastic scattering off 3He is described. In the kinematics of forth-coming experiments at JLab, it is found that the nuclear effects arising within an Impulse Approximation approach are under control.
The T-odd distribution functions contributing to transversity properties of the nucleon and their role in fueling nontrivial contributions to azimuthal asymmetries in semi-inclusive deep inelastic scattering are investigated. We use a dynamical model to evaluate these quantities in terms of HERMES kinematics. We point out how the measurements of cos(2phi) asymmetry may indicate the presence of T-odd structures in unpolarized ep scattering.
The Drell-Yan $K$-factors for transversely polarised hadrons are examined. Since transverse spin is peculiar in having no DIS reference point, the effects of higher-order corrections on DY asymmetries are examined via a DIS definition for transversity devised using a hypothetical scalar vertex. The results suggest that some care may be required when interpreting experimentally extracted partonic transversity, particularly when comparing with model calculations or predictions.
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…
A pedagogical presentation of single-spin asymmetries and transversity is offered. Detailed discussion is given of various aspects of single-spin asymmetries in lepton-nucleon and in hadron-hadron scattering and of the role of perturbative QCD and evolution in the context of transversity.
We discuss transversity distributions and Drell-Yan transverse double spin asymmetries. First, the antiquark flavor asymmetry $Δ_{_T} \bar u/Δ_{_T} \bar d$ is discussed by using two different descriptions, a meson-cloud model and a Pauli exclusion model. We find that both calculations produce a significant $Δ_{_T} \bar d$ excess over $Δ_{_T} \bar u$. Next, we study its effects on the transverse spin asymmetry $A_{_{TT}}$ and on the Drell-Yan proton-deuteron asymmetry $Δ_{_T}σ^{pd}/2 Δ_{_T}σ^{pp}$. We find that the ratio $Δ_{_T}σ^{pd}/2 Δ_{_T}σ^{pp}$ is very useful for investigating the flavor …
The question of the K factor in transversely polarised Drell-Yan (DY) processes is examined. The transverse-spin case is peculiar for the absence of a reference point in deeply inelastic scattering (DIS). Therefore, in order to study more fully the possible effects of higher-order corrections on DY asymmetries, a DIS definition for transversity is devised using a hypothetical scalar (Higgs-like) vertex. The results show that some care may be required in interpreting experimentally extracted partonic transversity, in particular when comparing with model calculations or predictions.
The unpolarized, helicity and transversity distributions of quarks in the proton are calculated in the overlap representation of light-cone wavefunctions truncated to the lowest order Fock-space components with three valence quarks. The three distributions at the hadronic scale satisfy an interesting relation consistent with the Soffer inequality. Results are derived in a relativistic quark model including radiative corrections up to the next-to-leading order. Predictions for the double transverse-spin asymmetry in Drell-Yan dilepton production initiated by proton-antiproton collisions are pre…
Nucleon transversity and single transverse spin asymmetries have been the recent focus of large efforts by both theorists and experimentalists. On-going and planned experiments from HERMES, COMPASS and RHIC are mostly on the proton or the deuteron. Presented here is a planned measurement of the neutron transversity and single target spin asymmetries at Jefferson Lab in Hall A using a transversely polarized $^3$He target. Also presented are the results and plans of other neutron transverse spin experiments at Jefferson Lab. Finally, the factorization for semi-inclusive DIS studies at Jefferson …
Some general remarks on parton transverse spin distributions and transverse motions are presented. The issue of accessing experimental information on the transversity distributions h_1^q is discussed. In particular direct information could be obtained from Drell-Yan processes with polarized protons and antiprotons (planned at GSI), while indirect information, coupling h_1^q to the Collins fragmentation function, is being gathered by HERMES and COMPASS collaborations. The related issue of transverse Single Spin Asymmetries (SSA) measured in several processes and the role of the Sivers distribut…
We discuss transversity distributions and transverse spin asymmetries. First, $Q^2$ evolution results are shown for transversity and longitudinally polarized distributions. Second, the antiquark flavor asymmetry $Δ_{_T} \bar u/Δ_{_T} \bar d$ is discussed in two different descriptions, a meson-cloud model and an exclusion model. Both calculations produce a significant $Δ_T \bar d$ excess over $Δ_{_T} \bar u$. Third, we explain general formalism of the polarized proton-deuteron Drell-Yan processes. This study is partly intended to find the asymmetry $Δ_{_T} \bar u/Δ_{_T} \bar d$ by the p-d asymm…
We present an update of a previous global analysis of the experimental data on azimuthal asymmetries in semi-inclusive deep inelastic scattering (SIDIS), from the HERMES and COMPASS Collaborations, and in e+ e- -> h1 h2 X processes, from the Belle Collaboration. Compared to the first extraction, a more precise determination of the Collins fragmentation function and the transversity distribution function for u and d quarks is obtained.
We study the time-reversal odd quark fragmentation function and its consequences on the hard processes. T-odd quark fragmentation function may arise, although QCD is T-invariant, from the non-perturbative dynamics in the fragmentation process. Assuming the factorization, we extract the T-odd fragmentation function from the inclusive pion production in the transversely polarized proton-proton collision. We then estimate the single spin asymmetry $A_{OT}$ of the semi-inclusive deep inelastic scattering with unpolarized lepton and the transversely polarized proton. We also discuss the meson cloud…
We show that measurements of single-spin asymmetries (SSAs) in charged current weak interaction processes such as deep inelastic neutrino scattering on a polarized target and inclusive $W$ production in polarized hadron-hadron collisions discriminate between the two fundamental QCD mechanisms (the Sivers and Collins effects) which have been proposed to explain such time-reversal-odd asymmetries. It has recently been shown that QCD final-state interactions due to gluon exchange between the struck quark and the proton spectators in semi-inclusive deep inelastic lepton scattering will produce non…
Based on a simple quark-diquark model, we propose a set of unpolarized, longitudinally polarized and transversely polarized fragmentation functions for the $Λ$ by fitting the unpolarized $Λ$ production data in $e^+ e ^- $ annihilation. It is found that the helicity structure of the obtained $Λ$ fragmentation functions is supported by the all available experimental data on the longitudinal $Λ$ polarization. Within the same framework of the diquark model, the nucleon transversity distributions are presented and consistent descriptions of the available HERMES data on the azimuthal spin asymmetrie…
In a perturbative QCD approach, with inclusion of spin and transverse momentum effects, experimental data on azimuthal asymmetries observed in polarized semi-inclusive deeply inelastic scattering and e+ e- annihilations can be used to determine the Sivers, transversity and Collins soft functions. By using these functions, within the same scheme, we predict p(transv. polarized) p -> h + X single spin asymmetries in remarkable agreement with RHIC experimental data.
A new, preliminary global analysis of the experimental data on azimuthal asymmetries in SIDIS from HERMES and COMPASS collaborations, and in e+e- --> h_1 h_2 X processes from the BELLE collaboration, is performed. The new data allow for a more precise determination of the Collins fragmentation function and of the transversity distribution function for $u$ and $d$ quarks, in comparison with the results of our previous analysis. Estimates for the single spin asymmetry A_UT^{\sin(ϕ_h + ϕ_S)} at JLab and COMPASS, operating on a transversely polarized proton target, are presented.
A global analysis of the experimental data on azimuthal asymmetries in semi-inclusive deep inelastic scattering (SIDIS), from the HERMES and COMPASS Collaborations, and in e+e- --> h1 h2 X processes, from the BELLE Collaboration, is performed. It results in the extraction of the Collins fragmentation function and, for the first time, of the transversity distribution function for u and d quarks. These turn out to have opposite signs and to be sizably smaller than their positivity bounds. Predictions for the azimuthal asymmetry A_{UT}^{sin(phi_h + phi_S)}, as will soon be measured at JLab and CO…
The $T$-odd distribution functions contributing to transversity properties of the nucleon and their role in fueling nontrivial contributions to azimuthal asymmetries in semi-inclusive deep inelastic scattering are investigated. We use a dynamical model to evaluate these quantities in terms of HERMES kinematics.
After reviewing the most important COMPASS results on transverse spin effects in SIDIS, I will present the recent work we have done on weighted Sivers asymmetries and "transversity induced" $Λ$ polarisation. Using the high statistics data collected in 2010 on a transversely polarised proton target COMPASS has evaluated the transverse momentum weighted Sivers asymmetries both in $x$- and in $z$-bins. The results are also compared with the standard unweighted asymmetries. Using the whole data sample collected over the years on transversely polarised deuteron and proton targets COMPASS has measur…
Using a generalized parton model approach including spin and intrinsic parton motion effects, and assuming the validity of factorization for large-pT jet production in hadronic collisions, we study the azimuthal distribution around the jet axis of leading unpolarized or (pseudo)scalar hadrons, namely pions, produced in the jet fragmentation process. We identify the observable leading-twist azimuthal asymmetries for the unpolarized and single-polarized case related to quark and gluon-originated jets. We account for all physically allowed combinations of the transverse momentum dependent (TMD) p…
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 …
Contents : 1. Pre-history 2. Transversity versus helicity 3. The massless limit. "Cardan" and "see-saw" transformations 4. Transversity distribution delta q(x). The diquark spectator model 5. Soffer inequality 6. Tensor charge sum rule 7. t-channel analysis 8. Selection rules for delta q(x) measurements 9. Evolution with Q squared 10. Quark polarimetry. The sheared-jet (Collins) effect 11. Single-spin asymmetries in inclusive experiments 12. Quark distribution dependent on both spin and transverse momentum 13. First evidence of quark transversity
Both meson photoproduction and semi-inclusive deep inelastic scattering can potentially probe transversity properties of the nucleon. We explore how that potential can be realized dynamically. The role of rescattering in both exclusive and inclusive meson production as a source for single spin asymmetries is examined. Using a dynamical model, we evaluate the spin independent $\cos 2ϕ$ asymmetry associated with transversity of quarks inside unpolarized hadrons, at HERMES kinematics. We also explore the effects of rescattering on the transversity distribution of the nucleon.
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…
We present a global re-analysis of the most recent experimental data on azimuthal asymmetries in semi-inclusive deep inelastic scattering, from the HERMES and COMPASS Collaborations, and in e+e- --> h_1 h_2 X processes, from the Belle Collaboration. The transversity and the Collins functions are extracted simultaneously, in the framework of a revised analysis in which a new parameterisation of the Collins functions is also tested.
We compute the quark and antiquark transversity distributions in the nucleon at a low normalization point of 600 MeV in the large-$N_c$ limit, where the nucleon can be described as a soliton of an effective chiral theory (chiral quark-soliton model). The flavor-nonsinglet distributions, $δu(x) - δd(x)$ and $δ\bar u(x) - δ\bar d(x)$, appear in leading order of the $1/N_c$-expansion, while the flavor-singlet distributions, $δu(x) + δd(x)$ and $δ\bar u(x) + δ\bar d(x)$, are non-zero only in next-to-leading order. The transversity quark and antiquark distributions are found to be significantly dif…
Predictions are made for azimuthal asymmetries in pion and kaon production from SIDIS off a longitudinally polarized deuterium target for HERMES kinematics, based on information on the 'Collins fragmentation function' from DELPHI data and on predictions for the transversity distribution function from non-perturbative calculations in the chiral quark-soliton model. There are no free parameters in the approach, which has been already successfully applied to explain the azimuthal asymmetries from SIDIS off polarized proton targets observed by HERMES and SMC.
In semi-inclusive deep inelastic scattering of polarized leptons on a transversely polarized target eight target transverse spin-dependent azimuthal modulations are allowed. In the QCD parton model half of these asymmetries can be interpreted within the leading order approach and the other four are twist-three contributions. The first two leading twist asymmetries extracted by HERMES and COMPASS experiments are related: one to the transversity distribution and the Collins effect, the other to the Sivers distribution function. These results triggered a lot of interest in the past few years and …
Azimuthal spin asymmetries, both for charged and neutral pion production in semi-inclusive deep inelastic scattering of unpolarized charged lepton beams on longitudinally and transversely polarized nucleon targets, are analyzed and calculated. Various assumptions and approximations in the quark distributions and fragmentation functions often used in these calculations are studied in detail. It is found that different approaches to the distribution and fragmentation functions may lead to quite different predictions on the azimuthal asymmetries measured in the HERMES experiments, thus their effe…
