QCD Sum Rules for the production of the X(3872) as a mixed molecule-charmonium state in B meson decay

TL;DR

This paper uses QCD sum rules to estimate the production rate of the X(3872) meson in B meson decay, considering it as a mixture of charmonium and molecular states, and finds results consistent with experimental limits.

Contribution

It introduces a QCD sum rule calculation for the X(3872) production in B decay, considering a mixed molecular-charmonium structure, and determines the branching ratio within a specific mixing angle range.

Findings

Branching ratio matches experimental upper limit.

Compatible with mass and decay width analyses.

Supports mixed state interpretation of X(3872).

Abstract

We use QCD sum rules to calculate the branching ratio for the production of the meson X(3872) in the decay $B\to X(3872)K$, assumed to be a mixture between charmonium and exotic molecular $[c\bar{q}][q\bar{c}]$ states with $J^{PC}=1^{++}$. We find that in a small range for the values of the mixing angle, $5^\circ\leq\theta\leq13^\circ$, we get the branching ratio ${\mathcal{B}}(B\to XK)=(1.00\pm0.68)\times10^{-5}$, which is in agreement with the experimental upper limit. This result is compatible with the analysis of the mass and decay width of the mode $J/\psi(n\pi)$ and the radiative decay mode $J/\psi\gamma$ performed in the same approach.