# Deriving hadrons by their quantum numbers

While preparing for an exam I found a problem where one has to find the composition of hadrons given their quantum numbers.

$$\text{ (Charge, Baryon number, Strangeness, Charm, Bottomness)=(Q,B,s,c,b)}$$

We know that (source: hyperphysics):
$$Q_s=-\frac{1}{3}$$, $$S =-1$$, $$Q_b=-\frac{1}{3}$$, $$B=-1$$, $$Q_c=+\frac{2}{3}$$, baryon number = $$\frac{1}{3}(n_q-\overline{n}_q)$$,
$$n_q$$ and $$\overline{n}_q$$ being respectively the number of quarks and anti-quarks.

However there is one particle that shouldn't exist which is: $$\text{(2,1,0,1,0)}$$ This Hadron has to consist of $$ccc$$, since it's the only possible way to achieve a charge of $$2$$ given our three quarks.
However, I'm confused why it isn't $$(2,1,0,3,0)$$, since there are three charm quarks with $$c=1$$ for each one, mounting to $$3$$.
Any help is appreciated.

• – anna v Sep 18 '19 at 13:51