The mass spectra and decay properties of dimesonic states, using the Hellmann potential

TL;DR

This paper computes the mass spectra and decay properties of dimesonic states using the Hellmann potential with relativistic corrections, comparing results with experimental meson states to identify possible molecular configurations.

Contribution

It introduces a variational approach with the Hellmann potential and relativistic corrections to study dimesonic states, incorporating OPEP and decay calculations, providing theoretical predictions aligned with experimental data.

Findings

Mass spectra match several experimental meson states.

Decay widths are consistent with observed values.

The model successfully predicts molecular nature of certain states.

Abstract

Mass spectra of the dimesonic (meson-antimeson) molecular states are computed using the Hellmann potential in variational approach, which consists of relativistic correction to kinetic energy term as well as to the potential energy term. For the study of molecular bound state system, the Hellmann potential of the form $V(r)=-\frac{\alpha_{s}}{r} + \frac{B e^{-Cr}}{r}$ is being used. The one pion exchange potential (OPEP) is also incorporated in the mass calculation. The digamma decay width and decay width of the dimesonic system are evaluated using the wave function. The experimental states such as $f_{0}(980)$, $b_{1}(1235)$, $h_{1}(1380)$, $a_{0}(1450)$, $f_{0}(1500)$, $f_{2}'(1525)$,$f_{2}(1565)$, $h_{1}(1595)$, $a_{2}(1700)$, $f_{0}(1710)$, $f_{2}(1810)$ are compared with dimesonic states. Many of these states (masses and their decay properties) are close to our theoretical predictions.