Isospin-violating strong decays of scalar single-heavy tetraquarks

We present a study of the isospin-violating one-pion strong decays of single heavy tetraquarks XQ=X(sqqQ), Q=c, b, and q=u, d with spin-parity JP=0+. We assume that the tetraquarks have the configuration of a color diquark and an antidiquark. Three mechanisms of isospin violation can contribute to the decay rate: (1) mixing of the X(suūQ) and X(sddQ) tetraquark currents, (2) an explicit md-mu quark mass difference in the quark diagrams describing the corresponding decay transitions, and (3) π0-η mixing in the final state. Our main results are as follows: (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 rather more significantly than the others; (3) Our calculations contain a size parameter ΛXQ, characterizing the distribution of the quarks in the tetraquark state XQ. Absolute decay rates depend very much on the choice of ΛXQ, varied from 1 to 2 GeV, reflecting the compactness of the multiquark system.