Isospin-violating strong decays of scalar single-heavy tetraquarks

Abstract

We present a study of the isospin-violating one-pion strong decays of single heavy tetraquarks $X_Q=X(sq\bar{q}\bar{Q})$, $Q=c,b$, 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 $X(su\bar{u}\bar{Q})$ and $X(sd\bar{d}\bar{Q})$ 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.

Comments: 13 pages