Dynamical transition between two mesons and a tetraquark

TL;DR

This study uses Monte Carlo simulations to analyze the transition between meson pairs and tetraquark states in a four-quark system, revealing how the configuration depends on particle density and highlighting the role of tetraquarks in the system's dynamics.

Contribution

It introduces a detailed 3-D Monte Carlo approach to investigate the dynamical transition between meson pairs and tetraquarks, incorporating quantum correlations and effective potentials.

Findings

Transition from meson pairs to tetraquark states with increasing density

Linear behavior of the four-body potential preserved across configurations

Recombination probabilities highlight the importance of tetraquark states

Abstract

We consider a system composed of two identical light quarks ($qq$) and two identical antiquarks ($\bar Q\bar Q$) that can be linked either as two mesons or as a tetraquark, incorporating quantum correlations between identical particles and an effective many-body potential between particles. We perform a 3-D Monte Carlo simulation of the system, considering the configurations allowed to form: i) Only two mesons, ii) Only tetraquark and iii) two mesons and tetraquark . We characterize each case and determine whether it is energetically more favorable to form a tetraquark or two mesons, as a function of the interparticle separation distance which, for a fixed number of particles, can be identified as a particle density. We determine how the two mesons, which dominate the low density regime, mixes with a tetraquark state as the density increases. Properties like the mean square radius and the two-particle correlation function are found to reflect such transition, and we provide a parameterization of the diquark correlation function in the isolated case. We track the dynamical flipping among configurations to determine the recombination probability, exhibiting the importance of the tetraquark state. We analize the four-body potential evolution and show that its linear behavior is preserved, although the slope can reflect the presence of a mixed state. Results are shown for several light-quarks to heavy-antiquarks mass ratios whenever they are found to be relevant.