Electromagnetic meson form factor from a relativistic coupled-channel approach

TL;DR

This paper derives a relativistic quantum mechanical expression for the electromagnetic form factor of pseudoscalar mesons using a point-form approach, connecting it with front-form methods and enabling extensions to complex systems.

Contribution

It introduces a coupled-channel relativistic framework for meson form factors, simplifying calculations and establishing equivalence with front-form approaches.

Findings

Derived an explicit expression for meson form factors.

Established equivalence with front-form spectator current.

Proposed extension to electroweak form factors for complex systems.

Abstract

Point-form relativistic quantum mechanics is used to derive an expression for the electromagnetic form factor of a pseudoscalar meson for space-like momentum transfers. The elastic scattering of an electron by a confined quark-antiquark pair is treated as a relativistic two-channel problem for the $q\bar{q}e$ and $q\bar{q}e\gamma$ states. With the approximation that the total velocity of the $q\bar{q}e$ system is conserved at (electromagnetic) interaction vertices this simplifies to an eigenvalue problem for a Bakamjian-Thomas type mass operator. After elimination of the $q\bar{q}e\gamma$ channel the electromagnetic meson current and form factor can be directly read off from the one-photon-exchange optical potential. By choosing the invariant mass of the electron-meson system large enough, cluster separability violations become negligible. An equivalence with the usual front-form expression, resulting from a spectator current in the $q^+=0$ reference frame, is established. The generalization of this multichannel approach to electroweak form factors for an arbitrary bound few-body system is quite obvious. By an appropriate extension of the Hilbert space this approach is also able to accommodate exchange-current effects.