Off-forward matrix elements in light-front Hamiltonian QCD

Abstract

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.

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

“…The coefficient of the logarithmic term in the expression of h 1 ðxÞ gives the correct splitting function for leading order evolution of h 1 ðxÞ; the delta function from the single particle sector providing the necessary ''plus'' prescription. In the offforward case, the cancellation occurs similarly, as shown for Fðx; ; tÞ in [20]. The behavior at x ¼ 0; 1 can be improved by differentiating the LFWFs with respect to M 2 [24].…”

“…We generalize this analysis by assigning a mass M to the external electrons and a different mass m to the internal electron lines and a mass to the internal photon lines with M < m þ for stability. In effect, we shall represent a spin-1 2 system as a composite of a spin-1 2 fermion and a spin-1 vector boson [5,[17][18][19][20]. This field theory inspired model has the correct correlation between the Fock components of the state as governed by the light-front eigenvalue equation, something that is extremely difficult to achieve in phenomenological models.…”

Relations between generalized and transverse momentum dependent parton distributions

“…[87,88,89]. To our knowledge the results for the chiral-odd GPDs in (B19)-(B30) are given here for the first time.…”

Chiral odd generalized parton distributions in impact parameter space

“…In [14], a lower cutoff has been imposed on the transverse momentum, due to which the logarithms in I 1 and I 2 are of the form log 2 2 . As here we have imposed a cutoff on x at x !…”

“…In this work, we use M m and 0. In effect, we shall represent a spin-1 2 system as a composite of a spin-1 2 fermion and a spin-1 vector boson [11][12][13][14][15]. This model has the advantage that it is Lorentz invariant, and has the correct correlation between the Fock components of the state as governed by the light-front eigenvalue equation.…”