Branching Fractions of the $X(3872)$

Abstract

The recoil momentum spectrum from the decay $B^{+}\to K^{+}+\mathrm{anything}$ has recently been measured by the BaBar collaboration. The spectrum has a peak with invariant mass near the mass of the $X(3872)$ meson. The preliminary measurement by the BaBar collaboration implies that its branching fraction into $J/\psi {\pi }^{+}{\pi }^{-}$ is about 4\%. We emphasize that this is the branching fraction for the entire resonance feature from $B^{+}$-to-$K^{+}$ transitions, which includes a $D^{\ast 0}{\bar{D}}^0$ and $D^0{\bar{D}}^{\ast 0}$ threshold enhancement as well as a possible bound state below the threshold or a virtual state. If the $X$ is a bound state of charm mesons, its branching fraction into $J/\psi {\pi }^{+}{\pi }^{-}$ should be considerably larger than that of the $X$ resonance feature. We use measurements of branching ratios of the $X$ to put an upper bound on this branching fraction of 33\%. We also constrain the parameters of the simplest plausible model for the line shapes of the $X$ using the precise measurement of the resonance energy of the $X$ and an estimate of the branching fraction into $D^0{\bar{D}}^0{\pi }^0$ and $D^0{\bar{D}}^0\gamma$ from the $X$ resonance feature from $B^{+}$-to-$K^{+}$ transitions.

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Cited by in corpus (2)

• Revisiting $X(3872)\to D^0{\bar{D}}^0{\pi }^0$ in XEFT
• Possible precise measurements of the $X(3872)$ mass with the $e^{+}{e}^{-}\to {\pi }^0\gamma X(3872)$ and $p\bar{p}\to \gamma X(3872)$ reactions