Radiative decays of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>X</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>3872</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math> discriminate between the molecular and compact interpretations
Benjamı́n Grinstein, Luciano Maiani, A. D. Polosa
Abstract
Radiative decays $X\ensuremath{\rightarrow}\ensuremath{\psi}(1S)\ensuremath{\gamma}$ and $X\ensuremath{\rightarrow}{\ensuremath{\psi}}^{\ensuremath{'}}(2S)\ensuremath{\gamma}$ might be expected to have a ratio of branching fractions following the phase space volumes ratio. However data suggest the opposite, indicating a value for $\mathcal{R}=\mathcal{B}({\ensuremath{\psi}}^{\ensuremath{'}}\ensuremath{\gamma})/\mathcal{B}(\ensuremath{\psi}\ensuremath{\gamma})$ consistently larger than one. In this paper we present a calculation of $\mathcal{R}$ for both a compact diquark-antidiquark $(cq)(\overline{c}\overline{q})$ state and a $D{\overline{D}}^{*}$ molecule. In the former case $\mathcal{R}\ensuremath{\sim}1$ or larger is found. In contrast, in the molecular picture, with $D$ and ${\overline{D}}^{*}$ mesons described by the universal wave function used by Voloshin, Braaten and Kusunoki, we find $\mathcal{R}$ to be of order ${10}^{\ensuremath{-}2}$. These starkly different predictions are to be confronted with forthcoming high-statistics data analyses; a more precise experimental measure would be extremely helpful in clarifying the true nature of the $X(3872)$.