Off-shell pion properties: electromagnetic form factors and light-front wave functions

TL;DR

This paper investigates off-shell pion electromagnetic form factors and light-front wave functions using a constituent quark model, comparing theoretical calculations with experimental data and previous models to understand off-shell properties.

Contribution

It introduces a microscopic approach to compute off-shell pion form factors and validates the model against experimental data and previous theoretical results.

Findings

The constituent quark model reproduces experimental off-shell form factors within a few percent.

The model's results are consistent with previous covariant model simulations, with about 10% variation.

Off-shell properties of pion PDFs and TMDs are analyzed through light-front wave functions.

Abstract

The off-shell pion electromagnetic form factors are explored with corresponding off-shell light-front wave functions modeled by constituent quark and anti-quark. We apply the Mandelstam approach for the microscopic computation of the form factors relating the model parameters with the pion decay constant and charge radius. Analyzing the existing data on the cross-sections for the Sullivan process, H(e,e',pi)n, we extract the off-shell pion form factor using the relation derived from the generalized Ward-Takahashi identity for the pion electromagnetic current. They are compared with our previous results from exactly solvable manifestly covariant model of a (3+1)-dimensional fermion field theory. We find that the adopted constituent quark model reproduces the extracted off-shell form factor $F_1(Q^2,t)$ from the experimental data within a few percent difference and matches well with our previous theoretical simulation which exhibits a variation of about 10\% for the extracted off-shell pion form factor $g(Q^2,t)$. We also identify the pion valence parton distribution function (PDF) and transverse momentum distribution (TMD) in terms of the light-front wave function and discuss their off-shell properties.