Tetraquark resonances, flip-flop and cherry in a broken glass model

TL;DR

This paper introduces a formalism for studying tetraquark resonances using a generalized flip-flop potential, employing a simplified two-variable model to analyze decay processes and resonance behavior.

Contribution

It develops a novel approach to model tetraquark states with a simplified toy model, incorporating decay widths and resonance analysis within a complex potential framework.

Findings

Successfully modeled tetraquark decay widths.

Analyzed resonance behavior in a simplified two-variable system.

Provided insights into tetraquark stability and decay mechanisms.

Abstract

We develop a formalism to study tetraquarks using the generalized flip-flop potential, which include the tetraquark potential component. Technically this is a difficult problem, needing the solution of the Schr\"odinger equation in a multidimensional space. Since the tetraquark may at any time escape to a pair of mesons, here we study a simplified two-variable toy model and explore the analogy with a cherry in a glass, but a broken one where the cherry may escape from. We also compute the decay width in this two-variable picture, solving the Schr\"odinger equation for the outgoing spherical wave.