Method to observe the $J^{P}=2^{+}$ partner of the $X_{0}(2866)$ in the $B^+ \to D^{+} D^{-} K^{+} $ reaction

Abstract

We propose a method based on the moments of the $D^{-} K^{+}$ mass distribution in the $B^+ \to D^{+} D^{-} K^{+} $ decay to disentangle the contribution of the $ 2^{+} $ state, partner of $X_{0}(2900)$ in the $ \bar D^{*} K^{*}$ picture for this resonance. Some of these moments show the interference patterns of the $X_{1}(2900)$ and $X_{0}(2900)$ with the $ 2^{+} $ state, which provide a clearer signal of the $ 2^{+} $ resonance than the $ 2^{+} $ signal alone. The construction of these magnitudes from present data is easy to implement, and based on these data we show that clear signals for that resonance should be seen even with the present statistics.