Analysis of virtual meson production in solvable (1+1) dimensional scalar field theory

TL;DR

This paper investigates virtual scalar meson production in a solvable (1+1) dimensional scalar field theory, analyzing light-front amplitudes, form factors, and generalized parton distributions to understand gauge invariance and partonic structure.

Contribution

It provides a detailed analysis of light-front time-ordered amplitudes and derives GPDs in a solvable (1+1)D model, clarifying their relation to form factors and parton distributions.

Findings

Computed real and imaginary parts of the Compton form factor across all kinematic regions.

Analyzed the significance of 'cat's ears' contributions for gauge invariance.

Derived GPDs from light-front amplitudes and connected them to form factors and PDFs.

Abstract

Light-front time-ordered amplitudes are investigated in the virtual scalar meson production process in (1+1) dimensions using the solvable scalar field theory extended from the conventional Wick-Cutkosky model. There is only one Compton form factor (CFF) in the (1+1) dimensional computation of the virtual meson production process, and we compute both the real and imaginary parts of the CFF for the entire kinematic regions of $Q^2>0$ and $t<0$. We then analyze the contribution of each and every light-front time-ordered amplitude to the CFF as a function of $Q^2$ and $t$. In particular, we discuss the significance of the "cat's ears" contributions for gauge invariance and the validity of the "handbag dominance" in the formulation of the generalized parton distribution (GPD) function used typically in the analysis of deeply virtual meson production processes. We explicitly derive the GPD from the "handbag" light-front time-ordered amplitudes in the $-t/Q^2<<1$ limit and verify that the integrations of the GPD over the light-front longitudinal momentum fraction for the DGLAP and ERBL regions correspond to the valence and nonvalence contributions of the electromagnetic form factor that we have recently reported [Phys. Rev. D $\textbf{103}$, 076002 (2021)]. We also discuss the correspondence of the GPD to the parton distribution function for the analysis of the deep inelastic lepton-hadron scattering process and the utility of the new light-front longitudinal spatial variable $\tilde{z}$.