The $\bar{B}^0 \to D^{*+} \bar{D}^{*0} K^- $ reaction to detect the $I=0, J^P=1^+$ partner of the $X_0(2866)$

TL;DR

This paper proposes using the $ar{B}^0 o D^{*+} ar{D}^{*0} K^-$ decay to detect a predicted $I=0, J^P=1^+$ partner of the $X_0(2866)$, showing it as a strong peak and estimating its production rate.

Contribution

It introduces a new reaction channel to observe the $R_1$ partner state of $X_0(2866)$ and estimates its production rate, aligning with experimental data.

Findings

Strong peak observed in $D^{*+} K^-$ spectrum indicating $R_1$ state.

Estimated branching ratio for $R_1$ production is about $4 imes 10^{-3}$.

Method reproduces the signal-to-background ratio seen in LHCb data.

Abstract

We have chosen the $\bar{B}^0 \to D^{*+} \bar{D}^{*0} K^-$ reaction in order to observe the $I=0, J^P=1^+$ ($R_1$) partner state of the $X_0(2866)$ stemming from the $D^*\bar{K}^*$ molecular picture. The reaction proceeds via external emission in the most favored Cabibbo decay mode and one observes the $R_1$ state as a very strong peak versus the background in the $D^{*+} K^-$ spectrum. The branching ratio for $R_1$ production in this reaction is estimated of the order of $4\times 10^{-3}$. The method used, applied to the $B^+ \to D^- D^+ K^+$ reaction, produces a ratio of signal to background in the $D^- K^+$ spectrum in very good agreement with the LHCb experiment that observed the $X_0(2866)$.