Where Is the Lightest Charmed Scalar Meson?

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

Figure 1

Comparison of the predictions of Eq. (5) from UChPT (blue) and a Breit-Wigner parametrization (green) for ${\delta }_0$ with the phase extracted in Ref. [25] (red) and that using Eq. (3) (black). The bands correspond to errors propagated from the input UChPT scattering amplitudes and from the Breit-Wigner resonance parameters.

Figure 2

The decay $B^{-}\to D^{+}{\pi }^{-}{\pi }^{-}$ via the coupled channel $B^{-}\to D^0{\pi }^0{\pi }^{-}$. The filled square denotes the $D^0{\pi }^0\to D^{+}{\pi }^{-}T$-matrix element.

Figure 3

Results of UChPT (blue) and the BW description (green), with the best fits ${\chi }^2/\mathrm{d}.\mathrm{o}.\mathrm{f}.=1.2$ and 2.0, respectively.

Figure 4

Phases obtained from Eq. (14) with scattering phase shifts from UChPT (blue) and BW (green).