Proposed mixing between $2P$ and $1F$ wave charmonia

TL;DR

This paper studies the mixing between 2P and 1F charmonium states, revealing sizable mixing angles through unquenched calculations and proposing experimental observables for verification.

Contribution

It introduces a coupled-channel approach to quantify 2P-1F mixing in charmonium, predicting measurable decay widths and emphasizing the importance of future experimental data.

Findings

Sizable mixing angles of 7.5° and 15.4° were found.

Predicted two-photon and two-gluon decay widths for the mixed states.

Current data are insufficient to determine the mixing, requiring future measurements.

Abstract

We investigate $2P$-$1F$ mixing in charmonium, focusing on the close-in-mass $\chi_{c2}(2P)$ and $\chi_{c2}(1F)$ states. The conventional tensor force yields negligible mixing, motivating the inclusion of coupled-channel effects. Our unquenched calculation reveals sizable mixing angles of $7.5^\circ$ and $15.4^\circ$. We predict the corresponding two-photon and two-gluon decay widths as key observables for experimental verification. Additionally, we discuss the production of these two $2P$-$1F$ mixed states of charmonium via $\gamma\gamma$ fusion. Current data are insufficient to determine the mixing, highlighting the need for precise future measurements to resolve this aspect of charmonium spectroscopy.