Mass spectra for $qc\bar{q}\bar{c}$, $sc\bar{s}\bar{c}$, $qb\bar{q}\bar{b}$, $sb\bar{s}\bar{b}$ tetraquark states with $J^{PC}=0^{++}$ and $2^{++}$

Abstract

We have studied the mass spectra of the hidden-charm/bottom $qc\bar{q}\bar{c}$, $sc\bar{s}\bar{c}$ and $qb\bar{q}\bar{b}$, $sb\bar{s}\bar{b}$ tetraquark states with $J^{PC}=0^{++}$ and $2^{++}$ in the framework of QCD sum rules. We construct ten scalar and four tensor interpolating currents in a systematic way and calculate the mass spectra for these tetraquark states. The $X^{\ast }(3860)$ may be either an isoscalar tetraquark state or ${\chi }_{c0}(2P)$. If the $X^{\ast }(3860)$ is a tetraquark candidate, our results prefer the $0^{++}$ option over the $2^{++}$ one. The $X(4160)$ may be classified as either the scalar or tensor $qc\bar{q}\bar{c}$ tetraquark state while the $X(3915)$ favors a $0^{++}$ $qc\bar{q}\bar{c}$ or $sc\bar{s}\bar{c}$ tetraquark assignment over the tensor one. The $X(4350)$ can not be interpreted as a $sc\bar{s}\bar{c}$ tetraquark with either $J^{PC}=0^{++}$ or $2^{++}$.

Comments: 15 pages, 4 figures, 5 tables, suggestions and comments welcome