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

TL;DR

This paper introduces a method using moments of the $D^{-} K^{+}$ mass distribution in $B^+ o D^{+} D^{-} K^{+}$ decays to identify the $2^{+}$ partner of $X_{0}(2866)$, enhancing detection of this resonance.

Contribution

A novel approach based on mass distribution moments to disentangle and identify the $2^{+}$ resonance partner in $B^+$ decay data, improving signal clarity.

Findings

Method can be implemented with current data.

Signals for the $2^{+}$ resonance are detectable with existing statistics.

Interference patterns help distinguish the $2^{+}$ state from other resonances.

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.