Relative $P$-wave excitations of $D^{(*)}\bar D^{(*)}$ configurations in QCD sum rules

Abstract

We investigate the relative $P$-wave excitations of the $D^{(*)}\bar D^{(*)}$ systems using the QCD sum rule method. By introducing a covariant derivative between two ground-state charmed meson fields, we construct color-singlet interpolating currents to describe the relative orbital excitation between the two meson clusters. The $P$-wave $D\bar D$, $D\bar D^*/D^*\bar D$, and $D^*\bar D^*$ configurations with $J^{P}=1^{-}$ are systematically studied. Their masses are predicted to be around $3.8$, $3.9$, and $4.0$-$4.1$GeV, respectively. These values are close to the corresponding thresholds and are compatible with the structures around $X(3790)$ and $G(3900)$, supporting their possible interpretations as $P$-wave $D\bar D$ and $D\bar D^*/D^*\bar D$ configurations, respectively. In addition, we find that the $J^{PC}=1^{-+}$ and $1^{--}$ combinations in the $D\bar D^*/D^*\bar D$ sector possess identical correlation functions in the present QCD sum rule framework, leading to degenerate mass predictions for these two channels. These results indicate that relative $P$-wave excitations of heavy meson pairs may constitute another interesting class of near-threshold hadronic configurations worthy of further experimental investigation.