The original form of the Gell-Mann–Nishijima formula is:
This equation was originally based on empirical experiments. It is now understood as a result of the quark model. In particular, the electric charge Q of a quark or hadron particle is related to its isospin I3 and its hypercharge Y via the relation:
Since the discovery of charm, top, and bottom quark flavors, this formula has been generalized. It now takes the form:
where Q is the charge, I3 the 3rd-component of the isospin, B the baryon number, and S, C, B′, T are the strangeness, charm, bottomness and topness numbers.
Expressed in terms of quark content, these would become:
By convention, the flavor quantum numbers (strangeness, charm, bottomness, and topness) carry the same sign as the electric charge of the particle. So, since the strange and bottom quarks have a negative charge, they have flavor quantum numbers equal to −1. And since the charm and top quarks have positive electric charge, their flavor quantum numbers are +1.
From a quantum chromodynamics point of view, the Gell-Mann–Nishijima formula and its generalized version can be derived using an approximate SU(3) flavour symmetry because the charges can be defined using the corresponding conserved Noether currents.