Abstract
We have studied the mass spectra of the hidden-charm/bottom $qcqc$,
$scsc$ and $qbqb$, $sbsb$ 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 $qcqc$ tetraquark state while the $X(3915)$ favors a
$0^++$ $qcqc$ or $scsc$ tetraquark assignment over the
tensor one. The $X(4350)$ can not be interpreted as a $scsc$
tetraquark with either $J^PC=0^++$ or $2^++$.
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