Isospin-violating strong decays of scalar single-heavy tetraquarks

TL;DR

This paper investigates the isospin-violating strong decays of scalar heavy tetraquarks, analyzing different mechanisms contributing to decay rates and emphasizing the impact of the tetraquark's size parameter on decay predictions.

Contribution

It introduces a detailed analysis of isospin violation mechanisms in heavy tetraquark decays, highlighting the dominant role of tetraquark mixing and the importance of size parameters.

Findings

Tetraquark states are likely isosinglets with minor isotriplet admixture.

The mixing mechanism significantly influences decay rates.

Decay rates are highly sensitive to the size parameter $\\Lambda_{X_Q}$.

Abstract

We present a study of the isospin-violating one-pion strong decays of single heavy tetraquarks $X_Q = X(s q \bar q \bar Q)$, $Q=c, b$, and $q=u, d$ with spin-parity $J^P = 0^+$. We assume that the tetraquarks have the configuration of a color diquark and a antidiquark. Three mechanisms of isospin violation can contribute to the decay rate: (1) mixing of the $X(s u \bar u \bar Q)$ and $X(s d \bar d \bar Q)$ tetraquark currents, (2) an explicit $m_d-m_u$ quark mass difference in the quark diagrams describing the corresponding decay transitions and (3) $\pi^0-\eta$ mixing in the final state. Our main results are: (1) It is quite likely that the investigated tetraquark states are isosinglet states with a small admixture of an isotriplet component; (2) The first isospin-breaking mechanism affects the decay rater more significantly than the others; (3) Our calculations contain a size parameter $\Lambda_{X_Q}$, characterizing the distribution of the quarks in the tetraquark state $X_Q$. Absolute decay rates depend very much on the choice of $\Lambda_{X_Q}$, varied from 1 to 2 GeV, reflecting the compactness of the multiquark system.