Diabatic Dynamical Diquark Bound States: Mass Corrections and Widths

TL;DR

This paper uses the diabatic formalism to calculate mass shifts and decay widths of tetraquark states, considering open meson thresholds, and compares results with a scattering approach.

Contribution

It introduces a diabatic formalism-based method to evaluate mass corrections and widths of tetraquark states, incorporating threshold effects and admixture of configurations.

Findings

Mass shifts due to open thresholds are quantified.

Decay widths to meson pairs are computed.

Results agree with previous scattering formalism studies.

Abstract

Using the diabatic formalism, which generalizes the adiabatic approximation in the Born-Oppenheimer formalism, we apply well-known Hamiltonian methods to calculate the effect of open di-meson thresholds that lie well below the mass of elementary $c\bar c q\bar q^\prime$, $c\bar c s\bar s$, and $c \bar c q \bar s$ tetraquark bound states. We compute the resulting mass shifts for these states, as well as their decay widths to the corresponding meson pairs. Each mass eigenstate, originally produced using a bound-state approximation under the diabatic formalism, consists of an admixture of a compact diquark-antidiquark configuration (an eigenstate of the original dynamical diquark model) with an extended di-meson configuration induced by the nearest threshold. We compare our results with those from our recent work that employs a scattering formalism, and find a great deal of agreement, but also comment upon interesting discrepancies between the two approaches.