More about on the mass of the new charmonium states

TL;DR

This paper uses QCD sum rules to predict the existence and mass splitting of orthogonal partner states of known charmonium-like particles, suggesting new states that could clarify their nature.

Contribution

It introduces the estimation of masses and residues of orthogonal charmonium states, extending the understanding of their possible mixtures and mass spectrum.

Findings

Mass splitting among X, Y, and their orthogonal states is at most 200 MeV.

Orthogonal states are predicted to exist based on mixing models.

Experimental detection of these states could clarify the nature of charmonium-like particles.

Abstract

If the $X(3872)$ is described by the picture as a mixture of the charmonium and molecular $D^{\ast} D$ states; $Y(3940)$ as a mixture of the $\chi_{c0}$ and $D^\ast D^\ast$ states; and $X(4260)$ as a mixture of the tetra-quark and charmonium sates, their orthogonal combinations should also exist. We estimate the mass and residues of the states within the QCD sum rules method. We find that the mass splitting among $X$, $Y$ and their orthogonal states is at most $200MeV$. Experimental search of these new states can play critical role for establishing the nature of the new charmonium states.