Can X(3872) be a $J^P=2^{-}$ tetraquark state?

Abstract

In this article, we test the nature of X(3872), which is assumed to be a P-wave $[cq]$-scalar-diquark $[\bar{c}\bar{q}]$-axial-vector-antidiquark tetraquark state with $J^P=2^{-}$. The interpolating current representing the $J^P=2^{-}$ state is proposed. Technically, contributions of the operators up to dimension six are included in the operator product expansion (OPE). The mass obtained for such state is $m_{2^{-}}=(4.38\pm 0.15)GeV$. We conclude that it is impossible to describe the X(3872) structure as $J^P=2^{-}$ tetraquark state.

Comments: 7 pages, 3 figures, to appear in Commun.Theor.Phys