Production of the $ X(3872)$ state via the $B^0 \to K^{\ast 0} X(3872)$ decay

TL;DR

This work analyzes X(3872) production in B^0 -> K^{*0} X(3872) using a triangle-diagram mechanism under a D D^* - c.c. molecular interpretation. An effective Lagrangian framework is employed to model B^0 -> D_s^{(*)+} D^{(*)-} production, subsequent D_s^{(*)+} decays to K^{*0} plus a D^{(*)}, and final-state D^{(*)+} D^{(*)-} rescattering into X(3872); the analysis explicitly includes charged components (D^{+} D^{*-} - c.c.) and uses a Gaussian regulator with cutoff Λ to control ultraviolet behavior. The X-D^{*} ar{D} coupling g_{X D^{*} ar{D}} is varied within ranges reported in the literature (roughly 1.8–3.6 GeV and related estimates), and the resulting BR(B^0 -> K^{*0} X(3872)) and the ratio R to B^0 -> K^{*0} ψ(2S) are found to be consistent with experimental data for g_{X D^{*} ar{D}} in the ~2.4–6.7 GeV range; the results reinforce the importance of charged components in short-range production and support a predominantly molecular description of X(3872). The study also highlights a ~40% theoretical uncertainty, mainly from input couplings and the regulator Λ, and notes that a fuller picture may require incorporating additional X(3872) components beyond DD^* - c.c.

Abstract

In this work the production of the state $X(3872)$ is estimated via the reaction $B^0 \to K^{\ast 0} X(3872)$ through triangle mechanisms described by the sequence $B^0 \to D_s^{(*)+} (\to K^{\ast 0} D^{(*)+} ) \ D^{(*)-} \to K^{\ast 0} \ ( D^{(*)+} D^{(*)-} ) \to K^{\ast 0} X(3872) $. The molecular configuration $(D\bar D^* - c.c. )$ of the $X(3872)$ is considered. By means of the effective Lagrangian approach, the branching ratio $\mathcal{B}(B^0 \to K^{\ast 0} X(3872))$ is calculated as a function of the strength of the coupling of the charged components $(D^+\bar D^{*-} - c.c. )$ to the $X(3872)$ and compared with experimental data. Besides, employing the decay $B^0 \to K^{\ast 0} ψ(2S)$ as a normalization channel, the ratio of branching fractions $R = \frac{\mathcal{B}( B^0 \to K^{\ast 0} X(3872) )}{\mathcal{B}( B^0 \to K^{\ast 0} ψ(2S) )}\times \frac{\mathcal{B}( X(3872) \to J/ψπ^{+} π^{-} )}{\mathcal{B}( ψ(2S) \to J/ψπ^{+} π^{-} )} $ is also estimated. The findings provide another concrete example for the vital role of charged components in achieving a quantitatively correct description of the $X(3872)$.

Figures (4)

• Figure 1: The weak decay relevant for the reaction to be evaluated. The $\bar{b}$ quark decays into a $\bar{c}$ quark by an external emission of a $W^{+}$ boson which decays into a $c\bar{s}$ pair to form a $D_s^{(\ast)+}$ meson. The $d$ quark is a spectator of the reaction and together with the $\bar{c}$ produces the $D^{(*)-}$.
• Figure 2: Triangle Feynman diagrams for the decay $B^0 \to K^{\ast 0} X(3872)$ via the following charmed meson loops: (a) $B^0 \to D_s^{+} (\to K^{\ast 0} D^{+} ) D^{*-} \to K^{\ast 0} ( D^+ D^{*-} ) \to K^{\ast 0} X(3872)$; (b) $B^0 \to D_s^{\ast +} (\to K^{\ast 0} D^{\ast +} ) D^{-} \to K^{\ast 0} ( D^{\ast +} D^{-} ) \to K^{\ast 0} X(3872)$; (c) $B^0 \to D_s^{\ast +} (\to K^{\ast 0} D^{+} ) D^{*-} \to K^{\ast 0} ( D^+ D^{*-} ) \to K^{\ast 0} X(3872)$; (d) $B^0 \to D_s^{ +} (\to K^{\ast 0} D^{\ast +} ) D^{-} \to K^{\ast 0} ( D^{* +} D^{-} ) \to K^{\ast 0} X(3872)$. The respective momenta of the particles are in parentheses.
• Figure 3: Branching ratio of the decay $(B^0 \to K^{\ast 0} X(3872))$ as a function coupling constant $g_{X D^{*} \bar{D}}$. The gray band denotes the uncertainties coming from the values of the size parameter $\Lambda$ in the range $0.9\Lambda - 1.1 \Lambda$. The lighter blue band denotes the available experimental data from Ref. ParticleDataGroup:2024cfk, also reproduced in Table \ref{['tableBR']}.
• Figure 4: Ratio $R$ defined in Eq. (\ref{['ratio']}) as a function of $g_{X D^{*} \bar{D}}$ as a function coupling constant $g_{X D^{*} \bar{D}}$. The gray band denotes the uncertainties coming from the values of the size parameter $\Lambda$ in the range $0.9\Lambda - 1.1 \Lambda$. The lighter blue band denotes the available experimental data from Ref. LHCb:2025vjj.