I know that the particle $P_c(4380)^+$, has quark content $\bar{c}cuud$. Furthermore I know that the reaction $K^-+P_c(4380)^+\rightarrow K^-+J/\psi+p$, is strong and the quark content on the left hand side is $s\bar{u}+c\bar{c}+uud$.
I have two questions:
1) Intuitively one would expect that as this is a strong interaction that all the quarks on the right hand side should match up with all the quarks on the left hand side , correct ? Which makes it obvious (say we didn't know and we were trying to figure it out ) that the quark content of the $P_c(4380)^+$ particle is $\bar{c}cuud$.
2) The definition of the charm number is $C=n_c-n_{\bar{c}}$, so on the right hand side this gives zero . How can we use this number for determining how many charm quarks are involved considering , you could have zero charm, anticharm quarks or any number of them ( as long as it's the same amount for both) and it will still give C=0.