Transversity 2008

The following secions are included:

• PREFACE

• ORGANIZING COMMITTEES

• ACKNOWLEDGMENT

• CONTENTS

No abstract received.

Ways to access transversity through asymmetry measurements are reviewed. The recent first extraction and possible near future extractions are discussed.

We explain the origin of the controversy about the existence of a transverse angular momentum sum rule, and show that it stems from utilizing an incorrect result in the literature, concerning the expression for the expectation values of the angular momentum operators. We demonstrate a new, short and direct way of obtaining correct expressions for these expectation values, from which a perfectly good transverse angular momentum sum rule can be deduced. We also introduce a new classification of sum rules into primary and secondary types. In the former all terms occurring in the sum rule can be measured experimentally; in the latter some terms cannot be measured experimentally.

Preliminary results on azimuthal single-spin asymmetries in semi-inclusive electro-production of pions and charged kaons at the HERMES experiment are presented. Significant amplitudes for both the Collins and the Sivers mechanisms are extracted from the full data set collected with a transversely polarized target. A new method for the evaluation of the acceptance effects, developed in view of a future extraction of the P_h⊥-weighted moments, is also discussed.

The measuring of transverse single spin asymmetries (SSA) is part of the physics program at COMPASS, a fixed target experiment at CERN SPS. In 2002-04 the COMPASS experiment has collected data with a transversely polarised ⁶LiD target using a 160 GeV/c polarised µ⁺ beam. By measuring transverse SSA one has access to the transversity distribution function Δ_Tq(x). This is one of the three quark distribution functions, which are needed to fully describe the spin structure of the nucleon at leading twist. At COMPASS three different quark polarimeters have been used to access transversity: the Collins effect, which produces an azimuthal asymmetry in the single hadron distribution, the azimuthal target spin asymmetries of charged hadron pairs and the transverse polarisation of Λ hyperons.

In addition the SSA arising from the correlation between the transverse nucleon spin and the quark intrinsic transverse momentum (Sivers effect), was measured, together with six more transverse target spin asymmetries.

All the asymmetries measured on the deuteron target are small and compatible with zero.

COMPASS is a running fixed-target experiment at the CERN SPS with a rich physics program focused on nucleon spin structure and on hadron spectroscopy. One of the main goals of the spin program is the measurement of the transverse spin effects in semi-inclusive DIS off transversely polarised nucleons. In the years 2002, 2003 and 2004 data have been taken using a 160 GeV/c naturally polarised µ⁺ beam and a deuterium target (⁶LiD) transversely polarised respect to the beam direction. In 2007 the run year has been devoted to collect data with a proton (NH₃) target. The preliminary results for the Collins and Sivers asymmetries, extracted from the 2007 data with transverse target polarisation, are presented here. Results are also compared with existing model predictions.

First results from a new global analysis of the experimental data on azimuthal asymmetries in SIDIS, from HERMES and COMPASS collaborations, and in e⁺e^- → h₁h₂X processes, from the Belle collaboration, are presented. 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 at JLab and COMPASS, operating on a transversely polarized proton target, are given.

We study the Sivers effect in transverse single spin asymmetries (SSA) for pion and kaon production in Semi-Inclusive Deep Inelastic Scattering (SIDIS) processes. We perform a fit of data from HERMES and COMPASS Collaborations, which allow a new determination of the Sivers distribution functions for quark and anti-quark with u, d and also s flavours.

We summarize the intuitive connection between deformations of parton distributions in impact parameter space and single-spin asymmetries. Lattice results for the x²-moment of the twist-3 polarized parton distribution g₂(x) are used to estimate the average transverse force acting on the active quark in SIDIS in the instant after being struck by the virtual photon.

Possible relations between two a priori different classes of parton distributions, the Generalized Parton Distributions (GPDs) and the Transverse Momentum Dependent parton distributions (TMDs), are discussed in this note. Although these relations were proven to hold exactly only in simple models they imply an appealingly simple and intuitive explanation for single-spin asymmetries in semi-inclusive deep-inelastic scattering. In this context we perform a first classification of common mother functions of GPDs and TMDs, so-called Generalized Transverse Momentum Dependent parton distributions (GTMDs), investigate their GPD- and TMD-limits, and gain new insight into the nature of these relations.

Exclusive π⁰ 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 Q² 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 transversity.

Here an estimate for the Sivers asymmetry in semi-inclusive proton-proton scattering in intermediate energy regime (fixed target, 10-50 GeV beam energy) is presented, by a model where initial state interactions are extracted from the phenomenology of elastic proton-proton scattering.

Generalized parton distributions (GPDs) provide a new and powerful framework for a complete description of the nucleon structure. They can provide a three-dimensional picture of how the quarks and gluons form a nucleon. GPDs can be probed experimentally in hard exclusive meson production or deeply virtual Compton scattering (DVCS). The COMPASS experiment at CERN is a unique place to study these reactions. At COMPASS, a high energy polarized positive or negative muon beam is scattered off a polarized or unpolarized fixed target. First results for exclusive ρ⁰ meson production are shown. The transverse target spin asymmetry for exclusively produced ρ⁰ on a transversely polarized deuteron target has been measured. Prospects for future measurements of DVCS and exclusive meson production at COMPASS will be shown. The experiment will use the existing COMPASS spectrometer with a new target, a new recoil detector and extended calorimetry. Simulations for different models and a test of the recoil detector have been performed.

A variety of measurements performed utilizing transversely polarized proton-proton collisions at the Relativistic Heavy Ion Collider (RHIC) are now available. Recent results from the PHENIX and BRAHMS experiments are presented and discussed.

We summarize the present phenomenology of Sivers and Collins effects for transverse single spin asymmetries in polarized proton–proton collisions within the framework of the generalized parton model (GPM). We will discuss a reassessment of the Collins effect and some preliminary predictions for SSA's in p^↑p → π, K + X processes at RHIC obtained using updated information from SIDIS data and a new set of meson fragmentation functions.

A formalism to evaluate the Sivers function, developed for calculations in constituent quark models, is applied to the Isgur-Karl model. A non-vanishing Sivers asymmetry, with opposite signs for the u and d flavor, is found; the Burkardt sum rule is fulfilled up to 2%. Nuclear effects in the extraction of neutron single spin asymmetries in semi-inclusive deep inelastic scattering off ³He are also evaluated. In the kinematics of JLab, it is found that the nuclear effects described by an Impulse Approximation approach are under control.

Polarized and unpolarized Drell-Yan processes are crucial to investigate transverse momentum dependent distribution functions. Some of them are directly accessible even when integrating on the leptonic degree of freedom, others require the study of the angular decay distribution of the virtual photon. Exploiting our recent fit of SIDIS data on the Sivers functions we present predictions for Sivers effect at COMPASS-DY.

The roles of the Drell-Yan experiments in studying the Transverse-Momentum-Dependent (TMD) parton distributions are discussed. Recent results from the Fermilab E866 experiment on the angular distributions of Drell-Yan dimuons in p + p and p + d at 800 GeV/c are presented. These data are compared with the pion-induced Drell-Yan data, and with models which attribute the cos2ɸ azimuthal distribution to the presence of the transverse-momentum-dependent Boer-Mulders structure function . Constraints on the magnitude of the sea-quark structure functions are obtained. Future prospects for studying the TMDs with Drell-Yan experiments at Fermilab and J-PARC are also discussed.

A polarised antiproton beam at the Facility for Antiproton and Ion Research, proposed by the PAX collaboration, will provide new physics possibilities, uniquely accessible at the planned High Energy Storage Ring at FAIR. Our proposal to realise an asymmetric collider, in which polarised antiprotons with momenta of about 3.5 GeV/c collide with polarised protons with momenta up to 15 GeV/c, is well suited to perform a direct measurement of the transversity distribution function h₁.

The COMPASS experiment is investigating possible physics aspects connect with the use of the polarized target (PT) together with the secondary (CERN–SPS) hadron beams. The main purpose of this project is to study the Drell–Yan reactions as a clear tool to measure the parton distribution functions, in particular the Boer-Mulders, the Sivers and the transversity functions.

Azimuthal Asymmetries in unpolarized SIDIS can be used to probe the transverse momentum of quarks inside the nucleon. Furthermore, they give access to the so-far unmeasured Boer-Mulders function. We report on the first measurement of azimuthal asymmetries of the SIDIS cross section from scattering of muons off a deuteron target.

In unpolarized Semi-Inclusive Deep Inelastic Scattering the cos ɸ_h and cos 2ɸ_h azimuthal asymmetries originate due to quark intrinsic transverse momentum K_T and transverse spin s_T. The complicated issue of disentangling the physical azimuthal dependence of the cross-section from the acceptance and instrumental effects is discussed and preliminary Monte Carlo studies on a fully differential analysis corrected for instrumental and radiative effects are presented.

A single-spin asymmetry has been measured in the azimuthal distribution of π⁺π^- pairs produced in semi-inclusive deep-inelastic scattering on a transversely polarized hydrogen target. For the first time, evidence is found for a correlation between the transverse target polarization and the azimuthal orientation of the plane containing the two pions. The corresponding single-spin asymmetry is expected to be related to the product of the poorly known quark transversity distribution function and an unknown naive T-odd chiral-odd dihadron fragmentation function.

Various methods of relating (naively) twist-2 Sivers function and twist-3 quark–gluon correlators are reviewed. The applications of Sivers function at large transverse momenta provides a justification (up to colour factors) of practical methods of calculations used earlier by Torino group. These factors correspond to colour correlations between partons inside hadrons and the ones participating in hard processes. The particular case of such correlations is represented by sign change between SIDIS and Drell–Yan processes.

This talk reports on recent work where we studied the connection between the description of semi-inclusive DIS at high transverse momentum (based on collinear factorization) and low transverse momentum (based on transverse-momentum-dependent factorization). We used power counting to determine the leading behavior of the structure functions at intermediate transverse momentum in the two descriptions. When the power behaviors are different, two distinct mechanisms are present and there can be no matching between them. When the power behavior is the same, the two descriptions must match. An explicit calculation however shows that for some observables this is not the case, suggesting that the transverse-momentum-dependent-factorization description beyond leading twist is incomplete.

The 'pretzelosity' distribution is discussed. Theoretical properties, model results, and perspectives to access experimental information on this leading twist, transverse momentum dependent parton distribution function are reviewed. Its relation to helicity and transversity distributions is highlighted.

The flavor dependence of the naive time reversal odd ("T-odd") Boer-Mulders and Sivers parton distribution functions as well as the "T-even" but chiral odd function are explored in the spectator framework. These transverse momentum dependent parton distribution functions are of significance for the analysis of azimuthal asymmetries in semi-inclusive deep inelastic scattering. In this context we also consider the Collins fragmentation function . With this input, we calculate the leading twist unpolarized cos(2ɸ) asymmetry, and sin(2ɸ) single spin asymmetry for a longitudinally polarized target in semi-inclusive deep inelastic scattering.

A confining gauge theory violates the completeness of asymptotic states held as foundation points of the S-matrix. Spin-dependent experiments can yield results that appear to violate quantum mechanics. The point is illustrated by violation of the Soffer bound in QCD. Experimental confirmation that the bound is violated would be a discovery of immense importance, sweeping away fundamental assumptions of strong interaction physics held for the past 50 years.

Some properties of intrinsic transverse momentum dependent nucleon distribution functions are considered in the simple quark-diquark model. The transverse target polarization dependent asymmetries for SIDIS are calculated and compared with recent results of COMPASS. The model describes well the measured asymmetries. Generalization of quark-diquark model for Sivers function is discussed.

We use a spectator model of the nucleon, including scalar and axial-vector diquarks, to investigate all its leading-twist spin structures. We interpret the results in terms of overlaps of light-cone wave functions, and we identify the non-trivial role of the quark-diquark relative orbital angular momentum. The model parameters are fixed by reproducing the phenomenological parametrization of unpolarized and helicity parton distributions at the lowest available scale. Predictions for the other parton densities, and for some of the related spin asymmetries, are given and, whenever possible, compared with available phenomenological parametrizations.

We investigate the gluonic pole matrix element contributing to the first p_T moment of the distribution and fragmentation functions in a spectator model. By performing a spectral analysis, we find that for a large class of spectator models, the contribution of gluonic pole matrix elements is non-zero for the distribution correlators, whereas in fragmentation correlators they vanish. This outcome is important in the study of universality for fragmentation functions.

We present recent results on studies of spin orbit correlations using the Jefferson Lab CLAS detector and discuss both near term and long-term future plans with CLAS, including measurements with longitudinally and transversely polarized targets. Single Spin Asymmetries (SSAs) were measured with CLAS for unpolarized and longitudinally polarized targets using a longitudinally polarized beam. Measurements of SSA for charged and neutral pions indicate that there are significant spin and azimuthal asymmetries, which can be interpreted in terms of transverse momentum dependent (TMD) distributions.

We present a general representation for the nucleon distribution amplitudes and for the nucleon to pion transition distribution amplitudes in terms of light-cone wave functions. We apply our formalism to a light-cone constituent quark model giving some numerical results for both the classes of observables.

A brief report of the ongoing experimental efforts to produce a beam of polarized antiprotons, which may be used in a second stage of the FAIR/HESR-facility currently under construction in Darmstadt (Germany), is given.

No abstract received.

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