# Mass spectrum and decay constants of radially excited vector mesons

## TL;DR

This paper computes the masses and decay constants of ground and excited vector mesons using a covariant Bethe-Salpeter framework, highlighting the limitations of current models in reproducing the full spectrum.

## Contribution

It provides a detailed calculation of vector meson properties within a symmetry-preserving truncation, revealing the need for improved interaction models beyond rainbow-ladder.

## Key findings

- Numerical results agree well with experimental data where available.
- No single interaction parametrization reproduces both ground and excited states accurately.
- Identifies qualitative features to guide future model improvements.

## Abstract

We calculate the masses and weak decay constants of flavorless ground and radially excited $J^P=1^-$ mesons and the corresponding quantities for the K^*, within a Poincar\'e covariant continuum framework based on the Bethe-Salpeter equation. We use in both, the quark's gap equation and the meson bound-state equation, an infrared massive and finite interaction in the leading symmetry-preserving truncation. While our numerical results are in rather good agreement with experimental values where they are available, no single parametrization of the QCD inspired interaction reproduces simultaneously the ground and excited mass spectrum, which confirms earlier work on pseudoscalar mesons. This feature being a consequence of the lowest truncation, we pin down the range and strength of the interaction in both cases to identify common qualitative features that may help to tune future interaction models beyond the rainbow-ladder approximation.