Narrow Results

In this paper, we introduce a relative $P$-wave to construct the doubly-charm axialvector diquark operator, then take the doubly-charm axialvector (anti-)diquark operator as the basic constituent to construct the scalar and tensor tetraquark currents to study the scalar, axialvector and tensor fully-charm tetraquark states with the QCD sum rules. We observe that the ground state $ÃÃ$-type tetraquark states and the first radial excited states of the $AA$-type tetraquark states have almost degenerated masses, where the $Ã$ and $A$ stand for the diquark operators with and without the relative $P$-wave, respectively, the broad structure above the $J/\psi J/\psi$ threshold maybe consist of several diquark–antidiquark-type fully-charm tetraquark states.

In the QCD sum rules for the tetraquark (molecular) states, the higher-dimensional vacuum condensates play an important role in extracting the tetraquark masses. We carry out the operator product expansion up to the vacuum condensates of dimension-10 and observe that the vacuum condensates of dimensions 6, 8 and 10 have the same expressions but opposite signs for the $C{\gamma }_5\otimes {\gamma }_{\mu }C$-type and $C\otimes {\gamma }_{\mu }C$-type four-quark currents, which make their influences distinguishable, and they are excellent channels to examine the vacuum saturation approximation. We introduce a parameter $\kappa$ to parametrize the derivation from the vacuum saturation or factorization approximation, and choose two sets of parameters to examine the influences on the predicted tetraquark masses, which can be confronted to the experimental data in the future. In all the channels, smaller value of the $\kappa$ leads to better convergent behavior in the operator product expansion, which favors the vacuum saturation approximation.