Quark Transversity Distribution in Perturbative QCD: Light-Front Hamiltonian Approach

To resolve the current ambiguity in the splitting function corresponding to the quark transversity distribution $h_1(x)$, we calculate $h_1(x)$ for a dressed quark in light-front Hamiltonian perturbation theory. Our result agrees with the expected form of the splitting function found in the literature and disagrees with the recent calculation in \cite{kuhn}. We emphasize the importance of quark mass in $h_1(x)$ in perturbative QCD and show its connection with a part of $g_T$.Comment: minor changes in the text, references adde

Off-forward Matrix Elements in Light-front Hamiltonian QCD

We investigate the off-forward matrix element of the light cone vector operator for a dressed quark state in light-front Hamiltonian perturbation theory. We obtain the corresponding splitting functions in a straightforward way. We show that the end point singularity is canceled by the contribution from the normalization of state. Considering mixing with the gluon operator, we verify the helicity sum rule in perturbation theory. We show that the quark mass effects are suppressed in the plus component of the matrix element but in the transverse component, they are not suppressed. We emphasize that this is a particularity of the off-forward matrix element and is absent in the forward case.Comment: 12 pages, revtex, 1 figur

A Field Theoretic Investigation of Spin in QCD

Utilizing the kinematical boost in light-front formalism one can address the issue of relativistic spin operators in an arbitrary reference frame. In the gauge $A^+=0$, the interaction dependent transverse spin operators can be separated into three parts. In analogy with the helicity sum rule, we propose a transverse spin sum rule. We perform a one loop renormalization of the transverse spin operator and show that the counterterm needed is the same as the linear mass counterterm in the light-front QCD Hamiltonian.Comment: 4 pages, Latex2e, contribution to the proceedings of Tenth International Light-Cone Meeting on Non-Perturbative QCD and Hadron Phenomenology, Heidelberg, June 12-17, 200

Twist Three Distribution e(x) : Sum Rules and Equation of Motion Relations

We investigate the twist three distribution function $e(x)$ in light-front Hamiltonian perturbation theory. In light-front gauge, by eliminating the constrained field, we find a mass term, an intrinsic transverse momentum dependent term and a 'genuine twist three' quark-gluon interaction term in the operator. The equation of motion relation, moment relation and the sum rules are satisfied for a quark at one loop. We compare the results with other model calculations.Comment: genuine twist three part added, conclusions on sum rules and equation of motion unchange

Nonperturbative Description of Deep Inelastic Structure Functions in Light-Front QCD

We explore the deep inelastic structure functions of hadrons nonperturbatively in an inverse power expansion of the light-front energy of the probe in the framework of light-front QCD. We arrive at the general expressions for various structure functions as the Fourier transform of matrix elements of different components of bilocal vector and axial vector currents on the light-front in a straightforward manner. The complexities of the structure functions are mainly carried by the multi-parton wave functions of the hadrons, while, the bilocal currents have a dynamically dependent yet simple structure on the light-front in this description. We also present a novel analysis of the power corrections based on light-front power counting which resolves some ambiguities of the conventional twist analysis in deep inelastic processes. Further, the factorization theorem and the scale evolution of the structure functions are presented in this formalism by using old-fashioned light-front time-ordered perturbation theory with multi-parton wave functions. Nonperturbative QCD dynamics underlying the structure functions can be explored in the same framework. Once the nonperturbative multi-parton wave functions are known from low-energy light-front QCD, a complete description of deep inelastic structure functions can be realized.Comment: Revtex, 30 pages and no figur

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

On the Matrix Element of the Transverse Component of Bilocal Vector Current and its Parton Interpretation

In this paper we study the matrix element of the transverse component of the bilocal vector current in the context of deep inelastic scattering. BJL limit of high energy amplitudes together with light-front current algebra imply the same parton interpretation for its matrix element as that of the plus component. On the other hand, the transverse component depends explicitly on the gluon field operator in QCD, appears as "twist three" and hence its matrix element has no manifest parton interpretation. In this paper we perform calculations in light-front time-ordering perturbative QCD for a dressed quark target to order $\alpha_s$ and demonstrate that the matrix element of the transverse component of the bilocal vector current has the same parton interpretation as that of the plus component.Comment: 7 pages, REVTE