Establishing the heavy quark spin and light flavor molecular multiplets of the $X(3872)$, $Z_c(3900)$ and $X(3960)$

TL;DR

This paper models the spectrum of heavy meson molecules, including the newly observed $X(3960)$, using effective field theory and symmetry considerations, predicting partner states and analyzing their properties.

Contribution

It provides a comprehensive spectrum of heavy meson molecules incorporating recent experimental data and symmetry principles, predicting partner states of known resonances.

Findings

The $X(3960)$ can be described as a bound or virtual state below threshold.

Predicted pole positions for molecular partners of $X(3872)$ and $Z_c(3900)$.

Mass of the $X(3960)$ pole is approximately 3928 MeV.

Abstract

Recently, the LHCb Collaboration reported a near-threshold enhancement, $X(3960)$, in the $D_s^+D_s^-$ invariant mass distribution. We show that the data can be well described by either a bound or a virtual state below the $D_s^+D_s^-$ threshold. The mass given by the pole position is $(3928\pm3)$ MeV. Using this mass and the existing information on the $X(3872)$ and $Z_c(3900)$ resonances, a complete spectrum of the $S$-wave hadronic molecules formed by a pair of ground state charmed and anticharmed mesons is established. Thus, pole positions of the partners of the $X(3872)$, $Z_c(3900)$ and the newly observed $D_s^+D_s^-$ state are predicted. Calculations have been carried out at the leading order of nonrelativistic effective field theory and considering both heavy quark spin and light flavor SU(3) symmetries, though conservative errors from the breaking of these symmetries are provided.