# Branching ratio for a bound state

Consider the meson $\Upsilon(10860)$. It decays into $B\bar{B}$, $B\bar{B}^*+cc$ and $B^*\bar{B}^*$. The mass of $B$ is $5.28 ~\textrm{ GeV}$ and mass of $B^*$ is $5.33~\textrm{ GeV}$. The branching ratios for these decays as given in Particle data Group are $$\Gamma( B^*\bar{B}^*)> \Gamma(B\bar{B}^*+cc)\gg\Gamma(B\bar{B}).$$ I want to understand this relation between masses and the branching ratios of the decay products. Please explain.

I think, Formula of two body decays can not be used as the parent particle is a bound state of $b$ and $\bar{b}$.

• Your middle decay is supposed to be $B^* \bar{B}$ +cc., as @dmckee suggests. You misrepresented the numbers of the masses: they are 5.28 and 5.33, respectively. You omitted the $J^P$ values, $0^-$, $1^-$, respectively, and $1^-$ for the isosinglet bound state. What would you find assuming the Y to be a bound state of the decay mesons, and accounting for the angular momentum/spin values? – Cosmas Zachos Jun 21 '16 at 17:08
• @CosmasZachos The numbers are not very different. I want to imply that decay to heavier decay state has more probability. Please explain. – seeking_infinity Jun 21 '16 at 17:55
• That was my point about your unwarranted implication, too: you expect 50 MeV differences in ~200 such available energy to dominate, by dint of phase space alone, modes with very different spin signatures in a 5S decay? In any case, which part of table 1 of Simonov & Veselov do you actually disagree with? – Cosmas Zachos Jun 21 '16 at 19:00
• @CosmasZachos What does the number 200 here refer to? – seeking_infinity Jun 22 '16 at 4:43
• In MeV, the smallest available energy, 10860-2x5325~210, very crudely. See this. – Cosmas Zachos Jun 22 '16 at 10:55