Two nearby states in the $X(3872)$ region: Resolving the radiative-decay ratio tension with $\hat{I}{\cdot }_{c2}$

Abstract

Recently, LHCb reported the radiative-decay ratio ${\mathcal{R}}^{\ddot{I}ˆ{\hat{I}}^3}\equiv \mathcal{B}[X(3872)\to \ddot{I}{ˆ}^{\prime }{\hat{I}}^3]/\mathcal{B}[X(3872)\to J/\ddot{I}ˆ{\hat{I}}^3]=1.67\pm 0.25$ extracted from $B^{+}\to K^{+}(J/\ddot{I}ˆ{\hat{I}}^3,\ddot{I}{ˆ}^{\prime }{\hat{I}}^3)$. This result differs markedly ($\sim 4.6\ddot{I}ƒ$) from the BESIII value obtained from $e^{+}{e}^{-}\to {\hat{I}}^3(J/\ddot{I}ˆ{\hat{I}}^3,\ddot{I}{ˆ}^{\prime }{\hat{I}}^3)$, ${\mathcal{R}}^{\ddot{I}ˆ{\hat{I}}^3}=-0.04\pm 0.28$. Such a significant tension suggests that more than one state in the $X(3872)$ region contributes to the processes. We therefore propose a two-state scenario: a shallow $D^{\ast 0}{\bar{D}}^0$ bound state with $J^{PC}=1^{++}$ and a $2^{-+}$ charmonium candidate, $\hat{I}{\cdot }_{c2}$, slightly above the $D^{\ast 0}{\bar{D}}^0$ threshold. We show that this hypothesis consistently describes these ratios along with other branching fractions and lineshapes across multiple processes. By contrast, fits without the $\hat{I}{\cdot }_{c2}$ component fail to reproduce the radiative-ratio data. We also predict helicity-angle distributions that motivates the future experiments to test the two-state hypothesis and search for the so-far missing $\hat{I}{\cdot }_{c2}$.

15 pages, 6 figures, 8 tables, figures added, published version

References in corpus (1)

• Probing the nature of the $\ddot{I}{‡}_{c1}(3872)$ state using radiative decays