# The flavor dependence of $m_\varrho / f_\pi$

## TL;DR

This study computes the ratio of vector meson mass to pion decay constant in SU(3) gauge theory with varying fermion flavors, finding it remains constant across different flavor numbers, suggesting robustness of vector meson properties in composite Higgs models.

## Contribution

The paper provides the first systematic lattice calculation of the $m_\varrho / f_\pi$ ratio across multiple fermion flavors in SU(3), demonstrating flavor independence within errors.

## Key findings

- $m_\varrho / f_\pi$ ratio is approximately 7.95(15) across $N_f=2$ to 6.
- Other low energy quantities related to the vector meson are also flavor-independent.
- Results support the robustness of vector meson properties in composite Higgs models regardless of fermion content.

## Abstract

We calculate the $m_\varrho / f_\pi$ ratio in the chiral and continuum limit for $SU(3)$ gauge theory coupled to $N_f = 2,3,4,5,6$ fermions in the fundamental representation. Keeping all systematic effects under full control we find no statistically significant $N_f$-dependence; $m_\varrho / f_\pi = 7.95(15)$. Assuming the KSRF-relations we conclude that 3 other low energy quantities related to the vector meson are also $N_f$-independent within errors including the $\varrho\pi\pi$ coupling $g_{\varrho\pi\pi}$. If the model is thought of as a strong dynamics inspired composite Higgs model our results indicate that the experimentally most easily accessible new composite particle, the vector meson, and its properties may be robust and independent of the fermion content of the model as long as the gauge group is $SU(3)$, provided $N_f$-independence extends all the way to the conformal window.