Where Is the Lightest Charmed Scalar Meson?
Meng-Lin Du, Feng-Kun Guo, Christoph Hanhart, Bastian Kubis, Ulf-G. Meißner
Abstract
The lightest charmed scalar meson is known as the ${D}_{0}^{*}(2300)$, which is one of the earliest new hadron resonances observed at modern $B$ factories. We show here that the parameters assigned to the lightest scalar $D$ meson are in conflict with the precise LHCb data of the decay ${B}^{\ensuremath{-}}\ensuremath{\rightarrow}{D}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{\ensuremath{-}}$. On the contrary, these data can be well described by an unitarized chiral amplitude containing a much lighter charmed scalar meson, the ${D}_{0}^{*}(2100)$. We also extract the low-energy $S$-wave $D\ensuremath{\pi}$ phase of the decay ${B}^{\ensuremath{-}}\ensuremath{\rightarrow}{D}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{\ensuremath{-}}$ from the data in a model-independent way, and show that its difference from the $D\ensuremath{\pi}$ scattering phase shift can be traced back to an intermediate ${\ensuremath{\rho}}^{\ensuremath{-}}$ exchange. Our work highlights that an analysis of data consistent with chiral symmetry, unitarity, and analyticity is mandatory in order to extract the properties of the ground-state scalar mesons in the singly heavy sector correctly, in analogy to the light scalar mesons ${f}_{0}(500)$ and ${K}_{0}^{*}(700)$.