Where is the lightest charmed scalar meson?

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 $B^-\to D^+ π^- π^-$. 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 $Dπ$ phase of the decay $B^-\to D^+ π^- π^-$ from the data in a model-independent way, and show that its difference from the $Dπ$ scattering phase shift can be traced back to an intermediate $ρ^-$ 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 $K_0^*(700)$.