Analysis of $X(4140)$ like states and their radial excitations in QCD

Abstract

In this work, we investigated the $ X(4140) $ and like states and their radial excitations by using molecular and diquark-antidiquark currents which couple to scalar, axial vector and tensor states via QCD sum rules. In operator product expansion, we considered quark, gluon and mixed vacuum condansates up to dimension eight. For the ground states coupling to these currents, we found that masses are almost degenerate with $ X(4140) $. For the excited states, we found that scalar and tensor currents are coupling to $ D_{s}^{*}\overline{D_{s}^{*}} $ threshold. However for the axial vector currents, the mass of the first excited state is compatible with $X(4274)$. Thus we conclude that, $X(4274)$ might be the first radial excitation of $X(4140)$.