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

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 $\alpha= 0$.