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

TL;DR

This paper addresses the D^*π interaction by modeling the D_1(2420) as a resonance generated dynamically from coupled-channel S-wave vector–pseudoscalar interactions, and tests the model against LHCb data for B^−→D^{*+}π^−π^− and B^+→D_s^+D^{*-}π^+ decays. The authors build a weak- decay plus hadronization framework, incorporating final-state interactions via a Bethe–Salpeter unitarization, and compute the D^{*+}π^− invariant mass distribution with a minimal set of parameters, dropping the bare quark-model pole to focus on two-meson dynamics. They obtain a reasonable description of the D^{*+}π^− lineshapes, extract a D^*π isospin-1/2 scattering length a_{D^*π} = −0.45 fm (in agreement with chiral-unitary expectations), and show that S-wave vector–pseudoscalar rescattering can substantially contribute to the observed signals, providing an alternative interpretation to LHCb’s D-wave–based analyses. The results underscore the importance of two-meson dynamics in heavy-flavor decays and offer a method to constrain light–heavy meson interactions from heavy-meson decay data.

Abstract

We present a model calculation to reproduce the differential mass distribution for the $D^*π$ system in the reactions $B^- \to D^{*+} π^- π^-$ and $B^{+}\to D_s^+D^{*-}π^{+}$ 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 $D^*π$ system, and compare the results with the experimental data. We also determine the $D^*π$ 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 $D_1(2420)$.

Figures (4)

• Figure 1: Quark-level diagrams with an external emission of a $W^{-}$ boson which contribute to the processes: (a) $B^- \to D^{*+}\pi^{-}\pi^{-}$ and (b) $B^{-}\to D_s^-D^{*+}\pi^{-}$. Here $q$ denotes a light quark, $q=\{u,d,s\}$. The quark pair generated from the vacuum, together with $c$ and $\bar{u}$, hadronize as a vector and a pseudoscalar meson which can interact to produce $D^{*+}\pi^-$ eventually.
• Figure 2: Tree-level mechanism for $B^-\to P_E D^{*+}\pi^-$, with $P_E=\pi^-$, $D^-_s$.
• Figure 3: Rescattering contribution to the $B^- \to D^{*+}\pi^{-}\pi^{-}$ and $B^{-}\to D_s^-D^{*+}\pi^{-}$ reactions, associated with the dynamical generation of $D_{1}(2420)$ through the vector-pseudoscalar interaction, indicated by a blob in the figure. Here, $P_{E}$ represents either $\pi^-$ or $D_s^-$ and, in the case of being $\pi^-$, the amplitude needs to be symmetrized to account for the generation of $D_1(2420)$ in any of the $D^{*+}\pi^-$ pair present in the final state.
• Figure 4: Invariant mass distribution for $D^{*+}\pi^-$ in the process $B^-\to D^-_s D^{*+}\pi^-$ (left) and $B^-\to D^{*+}\pi^-\pi^-$ (right). The experimental data are taken from Refs. LHCb:2024vhs (left panel) and LHCb:2019juy (right panel). The bands shown represent the uncertainties related to the theoretical model considering different form factors to regularize the integrals appearing in the calculation of the amplitude $t$ involved in Eq. (\ref{['Smassdistri']}) (we refer the reader to the Appendix \ref{['app:amplbroad']} for more details). The same form factors have been used in both figures. The meaning of $m_{D^{*+}\pi^-(\text{low})}$ can be found in the main text in the discussions related to this figure.