A Direct Algebraic Pathway to Hadronic Observables in the Contact Model

TL;DR

This paper introduces an algebraic method within the contact interaction model that simplifies the calculation of hadronic properties, such as decay constants and form factors, by avoiding complex wave function computations.

Contribution

It develops a new algebraic framework using Fierz transformations to directly compute hadron observables from minimal projected amplitudes, streamlining the process.

Findings

Successfully applied to vector mesons, extracting decay constants and form factors.

Provides a more efficient, unified approach to hadron observable calculations.

Potential for extension to baryons and complex interactions.

Abstract

We present a novel algebraic framework for computing hadron properties directly within the contact interaction model. Utilizing Fierz transformations, the method recasts the Bethe-Salpeter dynamics into equations for a minimal set of \emph{projected amplitudes} for bound-state static properties and form factors, bypassing the conventional need for the meson wave function. This approach is fully demonstrated for the vector meson, enabling the direct extraction of its decay constants and form factors. The formalism provides a more efficient and unified pathway to hadron observables, with clear potential for extension to baryons and more sophisticated interactions.