Space-like meson electromagnetic form factor in a relativistic quark model

TL;DR

This paper presents a Lorentz covariant model for calculating the space-like electromagnetic form factors of mesons, incorporating valence quarks and an effective vacuum-like field, with numerical results matching experimental data.

Contribution

It introduces a relativistic quark model using Lorentz covariant wave functions to compute meson form factors, including the effects of an effective vacuum-like field.

Findings

Calculated meson charge radii: r_π^2=0.434 fm^2, r_{K^+}^2=0.333 fm^2, r_{K^0}^2=-0.069 fm^2.

Model normalization: form factors are normalized to unity at t=0.

Numerical results align with experimental measurements.

Abstract

The space-like electromagnetic form factor is expressed in terms of the overlap integral of the initial and final meson wave functions written as Lorentz covariant distributions of internal momenta. The meson constituents are assumed to be valence quarks and an effective vacuum-like field. The momentum of the latter represents a relativistic generalization of the potential energy of the quark system. The calculation is fully Lorentz covariant and the form factors of the charged mesons are normalized to unity at t=0. The numerical results have been obtained by freezing the transverse degrees of freedom. We found r_\pi^2=0.434 fm^2, r_{K^+}^2=0.333 fm^2, r_{K^0}^2=-0.069 fm^2 by taking m_{u,d}=430 MeV, m_s=700 MeV.