Orbital Angular Momentum in Scalar Diquark Model and QED

We compare the orbital angular momentum of the 'quark' in the scalar diquark model as well as that of the electron in QED (to order {\alpha}) obtained from the Jaffe-Manohar de- composition to that obtained from the Ji relation. We estimate the importance of the vector potential in the definition of orbital angular momentum

Perturbative QCD and factorization of coherent pion photoproduction on the deuteron

We analyze the predictions of perturbative QCD for pion photoproduction on the deuteron, gamma D -> pi^0 D, at large momentum transfer using the reduced amplitude formalism. The cluster decomposition of the deuteron wave function at small binding only allows the nuclear coherent process to proceed if each nucleon absorbs an equal fraction of the overall momentum transfer. Furthermore, each nucleon must scatter while remaining close to its mass shell. Thus the nuclear photoproduction amplitude, M_{gamma D -> pi^0 D}(u,t), factorizes as a product of three factors: (1) the nucleon photoproduction amplitude, M_{gamma N_1 -> pi^0 N_1}(u/4,t/4), at half of the overall momentum transfer, (2) a nucleon form factor, F_{N_2}(t/4), at half the overall momentum transfer, and (3) the reduced deuteron form factor, f_d(t), which according to perturbative QCD, has the same monopole falloff as a meson form factor. A comparison with the recent JLAB data for gamma D -> pi^0 D of Meekins et al. [Phys. Rev. C 60, 052201 (1999)] and the available gamma p -> pi^0 p data shows good agreement between the perturbative QCD prediction and experiment over a large range of momentum transfers and center of mass angles. The reduced amplitude prediction is consistent with the constituent counting rule, p^11_T M_{gamma D -> pi^0 D} -> F(theta_cm), at large momentum transfer. This is found to be consistent with measurements for photon lab energies E_gamma > 3 GeV at theta_cm=90 degrees and \elab > 10 GeV at 136 degrees.Comment: RevTeX 3.1, 17 pages, 6 figures; v2: incorporates minor changes as version accepted by Phys Rev

Proton Spin Content From Lattice QCD

We calculate the form factor of the quark energy momentum tensor and thereby extract the quark orbital angular momentum of the nucleon. The calculation is done on a quenched $16^3 \times 24$ lattice at $\beta = 6.0$ and with Wilson fermions at $\kappa$ = 0.148, 0.152, 0.154 and 0.155. We calculate the disconnected insertion stochastically which employs the $Z_2$ noise with an unbiased subtraction. This proves to be an efficient method of reduce the error from the noise. We find that the total quark contribution to the proton spin is $0.29 \pm 0.07$. From this we deduce that the quark orbital angular momentum is $0.17 \pm 0.08$ and predict the gluon spin to be $0.21 \pm 0.07$, i.e. about 40% of the proton spin is due to the glue.Comment: LATTICE99(Matrix Elements), 3 pages, 3 figure

Generalized Parton Distributions at x->1

Generalized parton distributions at large $x$ are studied in perturbative QCD approach. As $x\to 1$ and at finite $t$, there is no $t$ dependence for the GPDs which means that the active quark is at the center of the transverse space. We also obtain the power behavior: $H_q^\pi(x,\xi,t)\sim (1-x)^2/(1-\xi^2)$ for pion; $H_q(x,\xi,t)\sim (1-x)^3/(1-\xi^2)^2$ and $E_q(x,\xi,t)\sim (1-x)^5/(1-\xi^2)^3f(\xi)$ for nucleon, where $f(\xi)$ represents the additional dependence on $\xi$.Comment: 7 pages, 2 figure

Nucleon Generalized Parton Distributions and Holographic Models

Using ideas from Light Front Holography, we discuss the calculation of the nucleon helicity-independent generalized parton distributions of quarks in the zero skewness case.Comment: Prepared for LIGHTCONE 2011, 23 - 27 May, 2011, Dalla

Pedagogic model for Deeply Virtual Compton Scattering with quark-hadron duality

We show how quark-hadron duality can emerge for valence spin averaged structure functions, and for the non-forward distributions of Deeply Virtual Compton Scattering. Novel factorisations of the non-forward amplitudes are proposed. Some implications for large angle scattering and deviations from the quark counting rules are illustrated.Comment: Version accepted by Phys. Rev.

Continuity of generalized parton distributions for the pion virtual Compton scattering

We discuss a consistent treatment of the light-front gauge-boson and meson wave functions in the analyses of the generalized parton distributions(GPDs) and the scattering amplitudes in deeply virtual Compton scattering(DVCS) for the pion. The continuity of the GPDs at the crossover, where the longitudinal momentum fraction of the probed quark is same with the skewedness parameter, and the finiteness of the DVCS amplitude are ensured if the same light-front radial wave function as that of the meson bound state wave function is used for the gauge boson bound state arising from the pair-creation(or nonvalence) diagram. The frame-independence of our model calculation is also guaranteed by the constraint from the sum rule between the GPDs and the form factors.Comment: 14 pages, 9 figures, we (1) changed the title, (2) added references, (3) discussed the GPD value at the crossover in Sec. III, version to appear in Phys. Rev.

Quark Imaging in the Proton Via Quantum Phase-Space Distributions

We develop the concept of quantum phase-space (Wigner) distributions for quarks and gluons in the proton. To appreciate their physical content, we analyze the contraints from special relativity on the interpretation of elastic form factors, and examine the physics of the Feynman parton distributions in the proton's rest frame. We relate the quark Wigner functions to the transverse-momentum dependent parton distributions and generalized parton distributions, emphasizing the physical role of the skewness parameter. We show that the Wigner functions allow to visualize quantum quarks and gluons using the language of the classical phase space. We present two examples of the quark Wigner distributions and point out some model-independent features.Comment: 20 pages with 3 fiture

Hadron Optics: Diffraction Patterns in Deeply Virtual Compton Scattering

We show that the Fourier transform of the Deeply Virtual Compton Scattering (DVCS) amplitude with respect to the skewness variable $\zeta$ at fixed invariant momentum transfer squared $t$ provides a unique way to visualize the structure of the target hadron in the boost-invariant longitudinal coordinate space. The results are analogous to the diffractive scattering of a wave in optics. As a specific example, we utilize the quantum fluctuations of a fermion state at one loop in QED to obtain the behavior of the DVCS amplitude for electron-photon scattering. We then simulate the wavefunctions for a hadron by differentiating the above LFWFs with respect to $M^2$ and study the corresponding DVCS amplitudes in light-front longitudinal space. In both cases we observe that the diffractive patterns in the longitudinal variable conjugate to $\zeta$ sharpen and the positions of the first minima move in with increasing momentum transfer. For fixed $t$, higher minima appear at positions which are integral multiples of the lowest minimum. Both these observations strongly support the analogy with diffraction in optics.Comment: Some plots modified, clarifications and references adde

Deeply virtual electroproduction of photons and mesons on the nucleon : leading order amplitudes and power corrections

We estimate the leading order amplitudes for exclusive photon and meson electroproduction reactions at large Q^2 in the valence region in terms of skewed quark distributions. As experimental investigations can currently only be envisaged at moderate values of Q^2, we estimate power corrections due to the intrinsic transverse momentum of the partons in the meson wavefunction and in the nucleon. To this aim the skewed parton distribution formalism is generalized so as to include the parton intrinsic transverse momentum dependence. Furthermore, for the meson electroproduction reactions, we calculate the soft overlap type contributions and compare with the leading order amplitudes. We give first estimates for these different power corrections in kinematics which are relevant for experiments in the near future.Comment: 59 pages, 21 figure