Dipion invariant mass spectrum in $X(3872)\to J/\psi \pi \pi$

Abstract

It is pointed out that dipion invariant mass spectrum in $X(3872)\to \pi \pi J/\psi$ is a useful probe for the $J^{PC}$ quantum number of the X(3872), complementary to the angular distributions. If X(3872) is a ${}^1{P}_1$ state, the dipion has a peak at low $m_{\pi \pi }$ region, which is not in accord with the preliminary Belle data. If X(3872) is a ${}^3{D}_2$ or ${}^3{D}_3$ state, the dipion spectrum shows a peak at high $m_{\pi \pi }$ region, which is broader than the $\rho$ resonance that might come from the decay of a molecular state: $(D\overline{D^{\ast }})(I=1)\to J/\psi \rho \to J/\psi {\pi }^{+}{\pi }^{-}$. Better measurement of $m_{\pi \pi }$ spectrum will shed light on the nature of X(3872).

Comments: More careful treatment of $X\to J/\psi \rho \to J/\psi \pi \pi$ ; The case $J^{PC}(X)=3^{--}$ is also included ; Version to appear in PRD