Light-Cone Wavefunction Representation of Deeply Virtual Compton Scattering

TL;DR

This work presents a complete light-cone Fock state representation of deeply virtual Compton scattering (γ* p → γ p) at large $Q^2$ and small $t$, expressing the amplitude as a convolution of a hard quark-level process with the target's light-cone wavefunctions. The authors derive and utilize generalized Compton form factors, $H$, $E$, and their axial counterparts, linking them through sum rules to the Dirac and Pauli form factors, $F_1$ and $F_2$, as well as to the gravitational form factors $A_q$ and $B_q$. They show that these form factors arise from both diagonal (n→n) and off-diagonal (n+1→n-1) light-cone overlaps, and that the integrated densities are frame-independent due to boost invariance of the light-cone framework. The paper validates the formalism with a one-loop QED model, demonstrating continuity across $x=ta$ and providing a practical template for embedding hadron structure in Lorentz-invariant light-cone wavefunctions.

Abstract

We give a complete representation of virtual Compton scattering $γ^* p \to γp$ at large initial photon virtuality $Q^2$ and small momentum transfer squared $t$ in terms of the light-cone wavefunctions of the target proton. We verify the identities between the skewed parton distributions $H(x,ζ,t)$ and $E(x,ζ,t)$ which appear in deeply virtual Compton scattering and the corresponding integrands of the Dirac and Pauli form factors $F_1(t)$ and $F_2(t)$ and the gravitational form factors $A_{q}(t)$ and $B_{q}(t)$ for each quark and anti-quark constituent. We illustrate the general formalism for the case of deeply virtual Compton scattering on the quantum fluctuations of a fermion in quantum electrodynamics at one loop.

Figures (8)

• Figure 1: The virtual Compton amplitude $\gamma^*(q) + p(P) \to \gamma(q') + p(P')$.
• Figure 2: One-loop covariant Feynman diagrams for virtual Compton scattering in QED.
• Figure 3: Light-cone time-ordered contributions to deeply virtual Compton scattering. Only the contributions of leading power in $1/Q$ are illustrated. These contributions illustrate the factorization property of the leading twist amplitude.
• Figure 4: Light-cone time-ordered contributions to spacelike form factors. The sum of the two contributions is $\zeta$-independent at fixed $t = \Delta^2$.
• Figure 5: Light-cone time-ordered contributions from $t$-channel exchange in the scattering process $k + (P-k) \to \Delta + (P-\Delta)$ in $\phi^3$ theory.