Vector mesons from a holographic QCD model in $f(R)$-dilaton gravity

TL;DR

This study explores the spectrum and decay constants of vector mesons within an $f(R)$-dilaton gravity framework, focusing on the Starobinsky model and its deviations from Einstein-dilaton gravity, with results aligning with experimental data.

Contribution

It introduces a holographic QCD model using $f(R)$-dilaton gravity, specifically analyzing the Starobinsky model and its impact on vector meson properties.

Findings

Results for rho meson masses agree with experimental data at $ ext{alpha}=10^{-8}$.

The model generalizes previous holographic QCD studies and reduces to standard results when $ ext{alpha}=0$.

The spectral decomposition is obtained via a Sturm-Liouville problem in AdS$_5$ spacetime.

Abstract

In this paper we investigate the spectrum and decay constants of vector mesons based on $f(R)$-dilaton gravity. We focus particularly on the well-known Starobinsky model, given by the function $f(R)= R+ \alpha R^2$ in the metric formalism, and we examine the deviations from the pure Einstein-dilaton case. We thus provide the field equations for Starobinsky-dilaton gravity in $\rm AdS_{5}$ spacetime and calculate the spectral decomposition of the vector mesons by means of a Sturm-Liouville problem. Remarkably, for the rho mesons $m_{\rho^2}$ and $m_{\rho^3}$, our results are in good agreement with the experimental data when $\alpha= 10^{-8}$. Our work also generalizes previous studies and recovers standard results when $\alpha= 0$.