Rho-meson, Bethe-Salpeter equation, and the far infrared

TL;DR

This paper investigates how different gauge-dependent inputs in the Bethe-Salpeter equation affect the rho meson properties, finding that these properties are mainly sensitive to high-energy scales above a few hundred MeV.

Contribution

It demonstrates that variations in gauge-dependent inputs at low energies do not significantly alter rho meson mass and decay constant predictions when the quark-gluon vertex is also varied.

Findings

Rho meson properties are insensitive to gauge-dependent input variations below the hadronic scale.

Adjusting the quark-gluon vertex allows consistent predictions across different input forms.

Sensitivity to input functions is primarily at scales above a few hundred MeV.

Abstract

The Bethe-Salpeter equation in QCD connects the gauge-dependent gluon and quark degrees of freedom with the gauge-invariant properties of mesons. We study the rho meson mass and decay constant for various versions of the gauge-dependent input functions discussed in the literature, which start to differ generically below the hadronic scale, and show qualitative different infrared behavior. We find that, once the gauge-dependent quark-gluon vertex is permitted to vary as well, the rho mass and decay constant is reproduced equally well for all forms investigated. A possible conclusion from this is that these $\rho$-meson properties are only sensitive to changes in the input at scales above a few hundred MeV.