$D^*\pi$ interaction from the lineshape of $D_1(2420)$ in $B$-decays

TL;DR

This paper models the $D^* o ext{pi}$ interaction in $B$-decays to reproduce the $D_1(2420)$ lineshape observed by LHCb, using coupled channel meson-meson interactions and hadronization formalism.

Contribution

First model calculation reproducing the $D_1(2420)$ lineshape in $B$-decays using coupled channel interactions and hadronization formalism.

Findings

Successfully reproduces the $D_1(2420)$ lineshape from experimental data.

Provides estimates for the $D^* o ext{pi}$ scattering length.

Offers insights into the properties of $D_1(2420)$.

Abstract

We present a model calculation to reproduce the differential mass distribution for the $D^*\pi$ system in the reactions $B^- \to D^{*+} \pi^- \pi^-$ and $B^{+}\to D_s^+D^{*-}\pi^{+}$ analyzed by the LHCb Collaboration, which shows a dominant signal for $D_1(2420)$. %\textbf{We} (The idea is to) We consider a model based on coupled channel meson-meson interactions that can describe the properties of $D_1(2420)$ in terms of the underlying dynamics, use it to determine the invariant mass distribution of the $D^*\pi$ system, and compare the results with the experimental data. We also determine the $D^*\pi$ scattering length, for which different values are available from different sources, leading to a controversy. To our knowledge, this is the first attempt to reproduce the mentioned data using model calculations. Our formalism relies on the hadronization of different mesons through a weak decay, allowing for the final-state (strong) interactions among the relevant constituents. We benefit from our previous work when obtaining the amplitudes corresponding to the strong interactions. We hope that our findings can be useful in further investigations of the properties of $D_1(2420)$.