On unique predictions for single spin azimuthal asymmetry

Theoretically there are two approaches to predict single spin azimuthal asymmetries. One is to take transverse momenta of the partons into account by using transverse momentum dependent parton distributions, while another is to take asymmetries as twist-3 effects. The non-perturbative effects in these approaches are parameterized with different matrix elements, and predictions can be different. Recently, gauge invariant definitions of transverse momentum dependent parton distributions were derived. With these definitions it can be shown that there are relations between non-perturbative matrix elements in these two approaches. These relations may enable us to unify two approaches and to have unique predictions for single spin azimuthal asymmetries. In this letter we derive these relations by using time-reversal symmetry and show that even with these relations the single spin azimuthal asymmetry in a Drell-Yan process is predicted differently in different approaches.Received: 2 July 2004, Published online: 24 September 2004     

Space- and time-like electromagnetic pion form factors in light-cone pQCD

We present a combined analysis of the space- and time-like electromagnetic pion form factors in light-cone perturbative QCD with transverse momentum dependence and Sudakov suppression. Including the genuine non-perturbative “soft” QCD and the power suppressed twist-3 corrections to the standard twist-2 perturbative QCD result, the experimental form factor data available at moderate energies/momentum transfers can be explained reasonably well. To this end, the bulk of the existing discrepancy between the space- and time-like experimental data is ostensibly reconciled.     

Understanding higher twist: operator approach to power corrections

A thorough discussion of perturbative QCD for twist-4 is presented from a practical point of view. Misleading uses of intrinsic transverse momentum and mass terms are criticized and corrected in the complete expressions relevant for a model-independent experimental test of power corrections which is proposed. Upper and lower bounds for the twist-4 scale are deduced from a theoretically-consistent analysis of present DIS data with a simplified assumption on twist-4, from which a power-dominatedR=σ _L /R=σ _T is predicted.     

On path-dependence of the QCD correlation functions

Gauge-invariant hadronic and vacuum correlation functions in QCD contain the systems of Wilson lines and loops having complicated geometrical structure. Path-dependence propagates, therefore, into such important properties of the quantum correlators as the renormalization-group behaviour, light-cone peculiarities, evolution, etc. In the present paper, I briefly overview several instructive examples of the manifestations of the structure of paths in the hadronic and vacuum correlation functions with explicit transverse momentum/distance dependence. In particular, the transverse-momentum dependent (TMD) parton densities and the skewed jet quenching parameter in Euclidean and Minkowski space-time are addressed.     

Transverse spin structure of the nucleon from lattice-QCD simulations

We present the first calculation in lattice QCD of the lowest two moments of transverse spin densities of quarks in the nucleon. They encode correlations between quark spin and orbital angular momentum. Our dynamical simulations are based on two flavors of clover-improved Wilson fermions and Wilson gluons. We find significant contributions from certain quark helicity flip generalized parton distributions, leading to strongly distorted densities of transversely polarized quarks in the nucleon. In particular, based on our results and recent arguments by Burkardt [Phys. Rev. D 72, 094020 (2005)], we predict that the Boer-Mulders function h(1/1), describing correlations of transverse quark spin and intrinsic transverse momentum of quarks, is large and negative for both up and down quarks.     

Transverse spin asymmetries for W-production in proton–proton collisions

We study parity-even and parity-odd polarization observables for the process pp→l^±X$pp\to l^{\pm }X$, where the lepton comes from the decay of a W-boson. By using the collinear twist-3 factorization approach, we consider the case when one proton is transversely polarized, while the other is either unpolarized or longitudinally polarized. These observables give access to two particular quark–gluon–quark correlation functions, which have a direct relation to transverse momentum dependent parton distributions. We present numerical estimates for RHIC kinematics. Measuring, for instance, the parity-even transverse single spin correlation would provide a crucial test of our current understanding of single spin asymmetries in the framework of QCD.     

Twist-3 contribution to the pion electromagnetic form factor

Non-leading contribution to the pion electromagnetic form factor which comes from the pion twist-3 wave function is analyzed in the modified hard scattering approach (MHSA) proposed by Li and Sterman. This contribution is enhanced significantly due to bound state effect (the twist-3 wave function is independent of the fractional momentum carried by the parton and has a large factor with being the pion meson mass and being the mean u- and d-quark masses). Consequently, although it is suppressed by the factor , the twist-3 contribution is comparable with and even larger than the leading twist (twist-2) contribution at intermediate energy region of being . Received: 23 March 1998 / Published online: 3 November 1999     

Wigner Distributions in Light-Front Quark Models

We discuss the quark Wigner distributions which represent the quantum-mechanical analogues of the classical phase-space distributions. These functions can be obtained through a Fourier transform in the transverse space of the generalized transverse momentum dependent parton distributions, which encode the most general one-body information of partons in momentum space. In particular, we present a study within light-front quark models. The quark orbital angular momentum is also obtained from the phase-space average of the orbital angular momentum operator weighted with the Wigner distribution of unpolarized quark in a longitudinally polarized nucleon. The corresponding results calculated within different light-front quark models are compared with alternative definitions of the quark orbital angular momentum as given in terms of generalized parton distributions and transverse momentum dependent parton distributions.     

Studying the Sivers and Boer-Mulders Function with Lattice QCD

Transverse momentum dependent parton distribution functions (TMDs) characterize the intrinsic momentum distribution of quarks inside the nucleon. However, they also encode final or initial state interactions of the processes in which they are measured, such as semi-inclusive deep inelastic scattering (SIDIS) or the Drell–Yan process (DY). Consequently certain TMDs are process-dependent and predicted to be equal but opposite in sign for SIDIS and DY. Extending our method on the lattice to non-local operators with U-shaped Wilson lines, we can study these naively time-reversal odd TMDs, in particular the Sivers- and the Boer-Mulders function. We express our results in terms of Fourier-transformed TMDs that appear naturally in the Fourier transformed cross section of, e.g., SIDIS, and in Bessel-weighted asymmetries. We discuss the method, its limitations and preliminary results from an exploratory calculation using lattices generated by the MILC and LHP collaborations.     

Collins effect in single spin asymmetries of the $p^{\uparrow}p \to \pi X$ process

We investigate the Collins effect in single spin asymmetries (SSAs) of the process by taking into account the transverse momentum dependence of the microscopic sub-process cross sections, with the transverse momentum in the Collins function integrated over. We find that the asymmetries due to the Collins effect can only explain the available data at best qualitatively, by using our choices of quark distributions in the quark-diquark model and a pQCD-based analysis, together with several options of the Collins function. Our results indicate the necessity to take into account contributions from other effects such as the Sivers effect or twist-3 contributions.Received: 21 June 2004, Revised: 26 November 2004, Published online: 15 February 2005PACS: 13.75.Cs, 13.85.Ni, 13.87.Fh, 13.88. + eJian-Jun Yang: Deceased on June 11, 2004.     

Observation of beta-delayed protons in the decay of Cl

The QCD operator product expansion analysis of twist-4 effects in leptoproduction is recast as a parton model. All twist-4 corrections are expressed in terms of a limited number of multiparton (quark and gluon) longitudinal distribution functions in an infinite momentum frame.     

Four loop anomalous dimension of the second moment of the non-singlet twist-2 operator in QCD

We present the result of a calculation for the first even moment of the non-singlet four-loop anomalous dimension of Wilson twist-2 operators in QCD with full color and flavor structures.     

Twist-3 single-spin asymmetries in semi-inclusive deep-inelastic scattering

The single-spin asymmetries for a longitudinally polarized lepton beam or a longitudinally polarized nucleon target in semi-inclusive deep-inelastic scattering are twist-3 observables. We study these asymmetries in a simple diquark spectator model of the nucleon. Analogous to the case of transverse target polarization, non-vanishing asymmetries are generated by gluon exchange between the struck quark and the target system. It is pointed out that the coupling of the virtual photon to the diquark is needed in order to preserve electromagnetic gauge invariance at the twist-3 level. The calculation indicates that previous analyses of these observables are incomplete.     

Exploring light-cone sum rules for pion and kaon form factors

We analyze the higher-twist effects and the SU(3)-flavor symmetry breaking in the correlation functions used to calculate form factors of pseudoscalar mesons in the QCD light-cone sum rule approach. It is shown that the Ward identities for these correlation functions yield relations between twist-4 two- and three-particle distribution amplitudes. In addition to the relations already obtained from the QCD equations of motions, we have found a new one. With the help of these relations, the twist-4 contribution to the light-cone sum rule for the pion electromagnetic form factor is reduced to a very simple form. Simultaneously, we correct a sign error in an earlier calculation. The updated light-cone sum rule prediction for the pion form factor at intermediate momentum transfers is compared with the recent Jefferson Lab data. Furthermore, from the correlation functions with strange-quark currents the kaon electromagnetic form factor and the weak transition form factors are predicted with accuracy. Received: 30 June 2002 / Published online: 7 October 2002 RID="a"     

Collins and sivers effects in p↑p → jet πX: Universality and process dependence

In this paper we briefly review the transverse momentum dependent generalized parton model and its application to the study of azimuthal asymmetries in the distribution of leading hadrons (mainly pions) inside large transverse momentum jets inclusively produced in polarized proton-proton collisions. We put particular emphasis on the phenomenological interest of these observables, in combination with similar asymmetries measured in semi-inclusive deeply inelastic scattering, Drell-Yan processes and e ⁺ e ^? collisions, for the study of the universality properties of the transverse momentum dependent parton distribution and fragmentation functions. We present results for RHIC kinematics at center-of-mass energies √s = 200 and 500 GeV, for central and mainly forward jet rapidities, in particular for the Sivers distribution and the Collins fragmentation function, that are believed to be responsible for many of the largest asymmetries measured in the last years. We also briefly discuss the case of inclusive jet production and recent phenomenological applications of other theoretical approaches, like the colour gauge invariant generalized parton model and the collinear twist-three approach, aiming at clarifying the issues of the universality and process dependence of transverse momentum dependent functions.     

Transverse momentum in semi-inclusive deep inelastic scattering

Within the framework of perturbative quantum chromodynamics we derive the evolution equations for transverse momentum dependent distributions and apply them to the case of semi-inclusive deep inelastic scattering. The evolution equations encode the perturbative component of transverse momentum generated by collinear parton branchings. The current fragmentation is described via transverse momentum dependent parton densities and fragmentation functions. Target fragmentation instead is described via fracture functions. We present, to leading logarithmic accuracy, the corresponding semi-inclusive deep inelastic scattering cross-section, which applies to the entire phase space of the detected hadron. Some phenomenological implications and further developments are briefly outlined.     

Twist-4 photon helicity-flip amplitude in DVCS on a nucleon in the Wandzura-Wilczek approximation

We computed the twist-4 part of the photon spin-flip amplitude in deeply virtual Compton scattering on a nucleon in the Wandzura–Wilczek approximation. We found a factorizable contribution, which arises from photon scattering on quarks with non-zero angular momentum along the collision axis. As the genuine twist-2 amplitude arises at the NLO, for moderate virtualities of the hard photon, GeV, a kinematical twist-4 correction can give a numerically important contribution to the photon helicity-flip amplitude. Received: 2 July 2001 / Revised version: 17 July 2001 / Published online: 31 August 2001     

The property of maximal transcendentality for the universal anomalous dimension in the N = 4 SYM

We show the results for the universal anomalous dimension γ _uni(j) of Wilson twist-2 operators in the N = 4 Supersymmetric Yang-Mills theory.     

Extracting TMDs from CLAS12 data

We present studies of double longitudinal spin asymmetries in semi-inclusive deep inelastic scattering using a new dedicated Monte Carlo generator, which includes quark intrinsic transverse momentum within the generalized parton model based on the fully differential cross section for the process. Additionally we employ Bessel-weighting to the MC events to extract transverse momentum dependent parton distribution functions and also discuss possible uncertainties due to kinematic correlation effects.     

The pretzelosity TMD and quark orbital angular momentum

We study the connection between the quark orbital angular momentum and the pretzelosity transverse-momentum dependent parton distribution function. We discuss the origin of this relation in quark models, identifying as key ingredient for its validity the assumption of spherical symmetry for the nucleon in its rest frame. Finally we show that the individual quark contributions to the orbital angular momentum obtained from this relation cannot be interpreted as the intrinsic contributions, but include the contribution from the transverse centre of momentum which cancels out only in the total orbital angular momentum.