Possible signal of an exotic $I=1$, $J=2$ state in the $B \to D^{*-}D^+K^+$ reaction

TL;DR

This paper proposes that a peak observed in the extbackslash dk mass distribution in a specific decay could be linked to an exotic $I=1$, $J=2$ state, and suggests experimental angular analysis to determine its spin.

Contribution

It introduces a theoretical exotic state with specific quantum numbers and mass, and proposes a method to distinguish its spin through angular momentum analysis.

Findings

Data is compatible with the exotic state hypothesis.

Angular momentum distributions differ significantly for different spins.

Interference effects enhance signals at the resonance energy.

Abstract

We study the \proc reaction, showing that a peak in the \dk mass distribution around 2834 MeV reported by LHCb could be associated with a theoretical exotic state with that mass, a width of 19 MeV and $J^P=2^+$, stemming from the interaction of the $D^{*+}K^{*+}$ and $D^{*+}_s \rho^+$ channels, which is a partner of the $0^+$ $T_{c\bar{s}}(2900)$. We show that the data is compatible with this assumption, but also see that the mass distribution itself cannot discriminate between the spins $J=0$, $1$, $2$ of the state. Then we evaluate the momenta of the angular mass distribution and show that they are very different for each of the spin assumptions, and that the momenta coming from interference terms have larger strength at the resonant energy than the peaks seen in the angular integrated mass distribution. We make a call for the experimental determination of these magnitudes, which has already been used by the LHCb in related decay reactions.