The $\rho(1S,2S)$, $\psi(1S,2S)$, $\Upsilon(1S,2S)$ and $\psi_t(1S,2S)$ mesons in a double pole QCD Sum Rule

TL;DR

This paper employs a double pole QCD sum rule method to determine the masses and decay constants of various mesons, including predictions for toponium states at high energies.

Contribution

It introduces and applies a double pole QCD sum rule technique to extract meson properties and predicts toponium masses, extending the method to heavy quarkonium states.

Findings

Extracted meson masses and decay constants as functions of Borel mass.

Predicted toponium masses at 357 GeV and 374 GeV.

Demonstrated the effectiveness of the double pole sum rule approach.

Abstract

We use the method of double pole QCD sum rule which is basically a fit with two exponentials of the correlation function, where we can extract the masses and decay constants of mesons as a function of the Borel mass. We apply this method to study the mesons: $\rho(1S,2S)$, $\psi(1S,2S)$, $\Upsilon(1S,2S)$ and $\psi_t(1S,2S)$. We also present predictions for the toponiuns masses $\psi_t(1S,2S)$ of m(1S)=357 GeV and m(2S)=374 GeV.