Chiral-odd Generalized Parton Distributions Research Articles

Beam spin asymmetry in the electroproduction of a pseudoscalar meson or a scalar meson off the scalar target

We discuss the electroproduction of pseudoscalar ($0^{-+}$) or scalar ($0^{++}$) meson production off the scalar target. The most general formulation of the differential cross section for the $0^{-+}$ or $0^{++}$ meson production process involves only one or two hadronic form factors, respectively, on a scalar target. The Rosenbluth-type separation of the differential cross section provides the explicit relation between the hadronic form factors and the different parts of the differential cross section in a completely model-independent manner. The absence of the beam spin asymmetry for the pseudoscalar meson production provides a benchmark for the experimental data analysis. The measurement of the beam spin asymmetry for the scalar meson production may also provide a unique opportunity not only to explore the imaginary part of the hadronic amplitude in the general formulation but also to examine the significance of the chiral-odd generalized parton distribution (GPD) contribution in the leading-twist GPD formulation.

Measurement of the beam spin asymmetry of [formula omitted] in the deep-inelastic regime with CLAS

The beam spin asymmetry of the exclusive pseudoscalar channel e→p→e′p′η was measured for the first time in the deep-inelastic regime (W>2 GeV/c2 and Q2>1 GeV2/c2) using a longitudinally polarized 5.78 GeV electron beam at Jefferson Lab with the CEBAF Large Acceptance Spectrometer. The data were accumulated in 144 four-dimensional bins of Q2, xB, −t and ϕ over a wide kinematic range, where ϕ is the azimuthal angle between the lepton and hadron scattering planes, The measured azimuthal dependence with large amplitudes of the sin⁡ϕ moments is a clear indication of a substantial contribution to the polarized cross-section from transversely polarized virtual photons. In the framework of generalized parton distributions (GPDs) this contribution is expressed via longitudinal-transverse interference between chiral-even and chiral-odd GPDs. The experimental results are compared to the existing theoretical models demonstrating the sensitivity to the product of chiral-odd and chiral-even GPDs and provide new constraints to the existing GPD parameterizations.

Spin-flavor structure of chiral-odd generalized parton distributions in the large-Nclimit

We study the spin-flavor structure of the nucleon's chiral-odd generalized parton distributions (transversity GPDs) in the large-N_c limit of QCD. In contrast to the chiral-even case, only three combinations of the four chiral-odd GPDs are non-zero in the leading order of the 1/N_c expansion: E_T-bar = E_T + 2 H_T-tilde, H_T and E_T-tilde. The degeneracy is explained by the absence of spin-orbit interactions correlating the transverse momentum transfer with the transverse quark spin. It can also be deduced from the natural N_c-scaling of the quark-nucleon helicity amplitudes associated with the GPDs. In the GPD E_T-bar the flavor-singlet component u + d is leading in the 1/N_c expansion, while in H_T and E_T-tilde it is the flavor-nonsinglet components u - d. The large-N_c relations are consistent with the spin-flavor structure extracted from hard exclusive pi0 and eta electroproduction data, if it is assumed that the processes are mediated by twist-3 amplitudes involving the chiral-odd GPDs and the chiral-odd pseudoscalar meson distribution amplitudes.

Hard Exclusive Meson Production at COMPASS

The concept of Generalized Parton Distributions (GPDs) combines two-dimensional spatial information given by form factors, with longitudinal momentum information from Parton Distribution Functions. GPDs provide comprehensive description of the nucleon structure involving a wealth of new information. For instance, according to Ji’s sum rule, the GPDs [Formula: see text] and [Formula: see text] enable access to the total angular momenta of quarks, antiquarks and gluons. While [Formula: see text] can be approached using measurements of electroproduction cross sections, asymmetry measurements in hard exclusive meson production off transversely polarized targets can help to constrain the GPD [Formula: see text] and chiral-odd GPDs. In 2007 and 2010 the COMPASS experiment at CERN collected data by scattering a [Formula: see text] muon beam off a transversely polarized NH3 target. Exclusive vector-meson production [Formula: see text] with a [Formula: see text] or [Formula: see text] meson in the final state is studied and five single-spin and three double-spin azimuthal asymmetries are measured.

Beyond-Standard-Model Tensor Interaction and Hadron Phenomenology.

We evaluate the impact of recent developments in hadron phenomenology on extracting possible fundamental tensor interactions beyond the standard model. We show that a novel class of observables, including the chiral-odd generalized parton distributions, and the transversity parton distribution function can contribute to the constraints on this quantity. Experimental extractions of the tensor hadronic matrix elements, if sufficiently precise, will provide a, so far, absent testing ground for lattice QCD calculations.

Chiral-odd generalized parton distributions for proton in a light-front quark-diquark model

We present a study of the chiral-odd generalized parton distributions for $u$ and $d$ quarks in a proton using the light front wave functions of the scalar quark-diquark model for nucleon constructed from the soft-wall AdS/QCD correspondence. We obtain the GPDs in terms of overlaps of the LFWFs. Numerical results for chiral-odd GPDs in momentum as well as transverse position spaces considering both zero and nonzero skewness($\zeta$) are presented. For nonzero skewness, the GPDs are also evaluated in longitudinal position space.

Chiral odd generalized parton distributions and spin densities in the impact parameter space

In the present work we have studied the chiral odd generalized parton distributions in the impact parameter space by assuming a flexible parametrization in a quark-diquark model. In order to obtain the explicit contributions from the up and down quarks, we have considered both the scalar (spin-0) and the axial-vector (spin-1) configurations for the diquark. We have also studied the spin densities for the up and down quarks in this model for monopole, dipole and quadrupole contributions for unpolarized and polarized quarks in unpolarized and polarized protons.

Flexible parametrization of generalized parton distributions: The chiral-odd sector

We present a physically motivated parameterization of the chiral-odd generalized parton distributions. The parametrization is an extension of our previous one in the chiral-even sector which was based on the reggeized diquark model. While for chiral even generalized distributions a quantitative fit with uncertainty estimation can be performed using deep inelastic scattering data, nucleon electromagnetic, axial and pseudoscalar form factors measurements, and all available deeply virtual Compton scattering data, the chiral-odd sector is far less constrained. While awaiting the analysis of measurements on pseudoscalar mesons exclusive electroproduction which are key for the extraction of chiral odd GPDs, we worked out a connection between the chiral-even and chiral-odd reduced helicity amplitudes using Parity transformations. The connection works for a class of models including two-components models. This relation allows us to estimate the size of the various chiral odd contributions and it opens the way for future quantitative fits.

Accessing Transversity GPDs in Neutrino Production of a Charmed Meson

We demonstrate that the transversity chiral odd generalized parton distributions can be accessed through the azimuthal dependence of the nu N -> l D N' or nubar N -> l D N' differential cross sections, in the framework of the colinear QCD approach, where GPDs factorize from perturbatively calculable coefficient functions calculated up to order mc/Q.

Exclusive processes at JLab at 6 GeV

Deeply virtual exclusive reactions provide a unique opportunity to probe the complex internal structure of the nucleon. They allow to access information about the correlations between parton transverse spatial and longitudinal momentum distributions from experimental observables. Dedicated experiments to study Deeply Virtual Compton Scattering (DVCS) and Deeply Virtual Meson Production (DVMP) have been carried out at Jefferson Lab using continuous electron beam with energies up to 6 GeV. Unpolarized cross sections, beam, target and double spin asymmetries have been measured for DVCS as well as for π 0 exclusive electroproduction. The data from Hall B provide a wide kinematic coverage with Q 2 =1-4.5 GeV 2 , xB=0.1-0.5, and −t up to 2 GeV 2 . Hall A data have limited kinematic range partially overlapping with Hall B kinematics but provide a high accuracy measurements. Scaling tests of the DVCS cross sections provide solid evidence of twist-2 dominance, which makes chiral-even GPDs accessible even at modest Q 2 . We will discuss the interpretation of these data in terms of Generalized Parton Distributions (GPDs) model. Successful description of the recent CLAS π 0 exclusive production data within the framework of the GPD-based model provides a unique opportunity to access the chiral-odd GPDs.

OBSERVATIONS OF CHIRAL ODD GPDs AND THEIR IMPLICATIONS

Our original suggestion to investigate exclusive π0 electroproduction as a method for extracting the tensor charge, transversity, and other quantities related to chiral odd generalized parton distributions from cross section and asymmetry data is reviewed. We explain some of the details of the process: i) the connection between the helicity description and the cartesian basis; ii) the dependence on the momentum transfer squared, Q2, and iii) the angular momentum, parity, and charge conjugation constraints (JPC quantum numbers).

Easy as πo: on the interpretation of recent electroproduction results

Our original suggestion to investigate exclusive πo electroproduction as a method for extracting from data the tensor charge, transversity and other quantities related to chiral odd generalized parton distributions is further examined. We now explain the details of the process: (i) the connection between the helicity description and the Cartesian basis; (ii) the dependence on the momentum transfer squared Q2 and (iii) the angular momentum, parity and charge conjugation constraints (JPC quantum numbers).

GENERALIZED PARTON DISTRIBUTIONS IN THE CHIRAL ODD SECTOR AND THEIR ROLE IN NEUTRAL MESON ELECTROPRODUCTION

Our original suggestion to investigate exclusive π0 electroproduction as a method for extracting from data the tensor charge, transversity, and other quantities related to chiral odd generalized parton distributions is further examined. We now explain the details of the process: i) the connection between the helicity description and the cartesian basis; ii) the dependence on the momentum transfer squared, Q2, and iii) the angular momentum, parity, and charge conjugation constraints (JPC quantum numbers).

Nucleon tensor charge from exclusiveπ0electroproduction

Exclusive ${\ensuremath{\pi}}^{o}$ 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. This differs markedly from deeply virtual Compton scattering, and both vector meson and charged $\ensuremath{\pi}$ electroproduction, where the axial charge can enter the amplitudes. Contrarily, the tensor charge enters the ${\ensuremath{\pi}}^{o}$ process. The connection through the helicity description of the process to both the partonic and hadronic perspectives is studied and exploited in model calculations to indicate how the tensor charge and other transversity parameters can be related to cross section and spin asymmetry measurements over a broad range of kinematics.

Chiral-odd generalized parton distributions in transverse and longitudinal impact parameter spaces

We investigate the chiral odd generalized parton distributions (GPDs) for non-zero skewnessin transverse and longitudinal position spaces by taking Fourier transform with respect to the transverse and longitudinal momentum transfer respectively. We present overlap formulas for the chiral-odd GPDs in terms of light-front wave functions (LFWFs) of the proton both in the ERBL and DGLAP regions. We calculate them in a field theory inspired model of a relativistic spin 1/2 composite state with the correct correlation between the different LFWFs in Fock space, namely that of the quantum fluctuations of an electron in a generalized form of QED. We show the spin-orbit correlation effect of the two-particle LFWF as well as the correlation between the constituent spin and the transverse spin of the target.

Chiral-odd generalized parton distributions, transversity decomposition of angular momentum, and tensor charges of the nucleon

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 on 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 in the derived second moment sum rule within the CQSM, thereby providing an additional support to the qualitative connection between chiral-odd GPDs and Boer-Mulders effects. We further confirm isoscalar dominance of the corresponding first moment sum rule, which indicates that the Boer-Mulders functions for the $u$ and $d$ quarks have roughly equal magnitude with the same sign. Also made are some comments on the recent empirical extraction of the tensor charges of the nucleon by Anselmino et al. We demonstrate that a comparison of their result with any theoretical predictions must be done with great care, in consideration of fairly strong scale dependence of tensor charges, especially at the lower renormalization scale.

Chiral odd generalized parton distributions in impact parameter space

We investigate the chiral odd generalized parton distributions (GPDs) for the quantum fluctuations of an electron in QED. This provides a field theory inspired model of a relativistic spin-(1/2) composite state with the correct correlation between the different light-front wave functions (LFWFs) in Fock space. We express the GPDs in terms of overlaps of LFWFs and obtain their representation in impact parameter space when the momentum transfer is purely transverse. We show the spin-orbit correlation effect of the two-particle LFWF as well as the correlation between the constituent spin and the transverse spin of the target.

Generalized parton distributions for the nucleon in chiral perturbation theory

We complete the analysis of twist-two generalized parton distributions of the nucleon in one-loop order of heavy-baryon chiral perturbation theory. Extending our previous study of the chiral-even isosinglet sector, we give results for chiral-even isotriplet distributions and for the chiral-odd sector. We also calculate the one-loop corrections for the chiral-odd generalized parton distributions of the pion.

Transversity GPD in photoproduction and electroproduction of two vector mesons

The chiral-odd generalized parton distribution (GPD), or transversity GPD, of the nucleon can be accessed experimentally through the photo- or electroproduction of two vector mesons on a polarized nucleon target, \gamma^(*) N --> \rho_1 \rho_2 N', where \rho_1 is produced at large transverse momentum, \rho_2 is transversely polarized, and the mesons are separated by a large rapidity gap. We predict the cross section for this process for both transverse and longitudinal \rho_{2} production. To this end we propose a model for the transversity GPD H_T(x,\xi,t), and give an estimate of the relative sizes of the transverse and longitudinal \rho_{2} cross sections. We show that a dedicated experiment at high energy should be able to measure the transversity content of the proton.

Chiral-odd generalized parton distributions in constituent quark models

We derive the overlap representation of chiral-odd generalized parton distributions using the Fock-state decomposition in the transverse-spin basis. This formalism is applied to the case of light-cone wave functions in a constituent quark model. Numerical results for the four chiral-odd generalized parton distributions at the hadronic scale are shown in different kinematics. 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.