Studies on X(4260) and X(4660) particles

Abstract

Studies on the X(4260) and X(4660) resonant states in an effective lagrangian approach are reviewed. Using a Breit--Wigner propagator to describe their propagation, we find that the X(4260) has a sizable coupling to the $\omega\chi_{c0}$ channel, while other couplings are found to be negligible. Besides, it couples much stronger to $\sigma$ than to $f_0(980)$: $|g_{X\Psi \sigma}^2/g^2_{X\Psi f_0(980)}|\sim O(10) \ .$ As an approximate result for X(4660), we obtain that the ratio of $\frac{Br(X\rightarrow\Lambda_c^+\Lambda_c^-)}{Br(X\rightarrow\Psi(2s)\pi^+\pi^-)}\simeq 20$. Finally, taking X(3872) as an example, we also point out a possible way to extend the previous method to a more general one in the effective lagrangian approach.