BESIII $X(3790)$ enhancement as a reflection of higher charmed mesons

In this work, we show that the $X(3790)$ reported by the BESIII Collaboration is unlikely to be a genuine resonance, a conclusion that follows from the incompleteness of the BESIII experimental analysis. Although BESIII included the established charmed mesons that couple to $Dπ$, as listed by the Particle Data Group, and incorporated their reflections in the $D^0D^-$ invariant mass spectrum, this fit to the experimental data does not exhaust the charmed mesons that can contribute to the $D^0D^-$ invariant mass spectrum through reflections, as can be explicitly seen from a theoretical charmed-meson spectroscopy. We find that a predicted charmed meson, either $D(3\,{}^3S_1)$ or $D(2\,{}^3D_1)$, can play a crucial role in mimicking the $X(3790)$ structure through the corresponding reflection. This warrants caution in interpreting the $X(3790)$ as a genuine resonance. Moreover, such an interpretation is not supported by most theoretical studies of $D\bar{D}$ hadronic molecules and compact $c\bar{c}d\bar{u}$ tetraquarks currently available.