Mass of Y(3940) in Bethe-Salpeter equation for quarks

TL;DR

This paper refines the Bethe-Salpeter formalism for vector bound states and applies it to calculate the mass of the Y(3940) as a D*0 anti-D*0 molecule, achieving results consistent with experiments.

Contribution

The paper corrects the general form of Bethe-Salpeter wave functions for vector bound states and applies this to compute the Y(3940) mass as a molecular state.

Findings

The calculated Y(3940) mass matches experimental data.

One-pion exchange contribution is zero in this formalism.

The formalism accounts for SU(3) symmetry breaking.

Abstract

The general form of the Bethe-Salpeter wave functions for the bound states composed of two vector fields of arbitrary spin and definite parity is corrected. Using the revised general formalism, we investigate the observed \emph{Y}(3940) state which is considered as a molecule state consisting of $D^{*0}\bar{D}^{*0}$. Though the attractive potential between $D^{*0}$ and $\bar{D}^{*0}$ including one light meson ($\sigma$, $\pi$, $\omega$, $\rho$) exchange is considered, we find that in our approach the contribution from one-$\pi$ exchange is equal to zero and consider SU(3) symmetry breaking. The obtained mass of \emph{Y}(3940) is consistent with the experimental value.