The laws governing the strong force are somewhat well-known at this point, but calculations involving them are difficult and in many cases beyond our reach. Furthermore the fundamental constants are not known to a very high precision. Both of these problems can be addressed by collecting experimental data about how these particles behave in real life, both to pin down the constants, and to accept or reject calculation techniques.

It won't improve our understanding of quantum numbers in general (a quantum number is just a discrete conserved quantity). The final paragraph mentions measuring the quantum numbers of this particular particle, namely its angular momentum and parity.