Decays of the X(3872) and ${\chi }_{c1}(2P)$ charmonium

Abstract

We re-examine the re-scattering mechanism for the X(3872), as a candidate for the 2P charmonium state ${\chi }_{c1}(2P)$, decaying to $J/\psi \rho (\omega )$ through exchanging $D^{(\ast )}$ mesons between intermediate states $D(\bar{D})$ and ${\bar{D}}^{\ast }(D^{\ast })$. We evaluate the dispersive part, as well as the absorptive one, of the re-scattering amplitude and find that the contribution from the dispersive part is dominant even when X(3872) lies above the threshold of the neutral channel $t{h}_n=m_{D^0}+m_{D^{\ast 0}}$. We predict $R_{\rho /\omega }\simeq 1$ for the $m_X$ region scanned by experiments. Meanwhile, we also estimate the rate of $X\to D^0{\bar{D}}^0{\pi }^0$. Our results favor a charmonium interpretation of X(3872) when it lies slightly below the threshold of $D^0{\bar{D}}^{\ast 0}$. Furthermore, we evaluated the width of $X\to J/\psi \rho$ with the help of a phenomenological effective coupling constant $g_X$, and find the total width of X(3872) to be in the range of 1-2 MeV.

arXiv commentVersion submitted and accepted for publication in PRD; more discussions and references added

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