The original form of the Gell-Mann–Nishijima formula is: :Q = I_3 + \frac{1}{2} (B+S)\ 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: :Q = I_3 + \frac{1}{2} Y\ :Y = 2(Q - I_3) Since the discovery of charm, top, and bottom quark flavors, this formula has been generalized. It now takes the form: :Q = I_3 + \frac{1}{2} (B+S+C+B^\prime+T) 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: :\begin{align} Q &= \frac{2}{3}\left[\left(n_\text{u} - n_\bar{\text{u}}\right) + \left(n_\text{c} - n_\bar{\text{c}}\right) + \left(n_\text{t} - n_\bar{\text{t}}\right)\right] - \frac{1}{3}\left[\left(n_\text{d} - n_\bar{\text{d}}\right) + \left(n_\text{s} - n_\bar{\text{s}}\right) + \left(n_\text{b} - n_\bar{\text{b}}\right)\right] \\ B &= \frac{1}{3}\left[\left(n_\text{u} - n_\bar{\text{u}}\right) + \left(n_\text{c} - n_\bar{\text{c}}\right) + \left(n_\text{t} - n_\bar{\text{t}}\right) + \left(n_\text{d} - n_\bar{\text{d}}\right) + \left(n_\text{s} - n_\bar{\text{s}}\right) + \left(n_\text{b} - n_\bar{\text{b}}\right)\right] \\ I_3 &= \frac{1}{2}[(n_\text{u}-n_\bar{\text{u}})-(n_\text{d}-n_\bar{\text{d}})] \\ S &= -\left(n_\text{s} - n_\bar{\text{s}}\right);\quad C = +\left(n_\text{c} - n_\bar{\text{c}}\right);\quad B^\prime = -\left(n_\text{b} - n_\bar{\text{b}}\right);\quad T = +\left(n_\text{t} - n_\bar{\text{t}}\right) \end{align} 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. == Weak interaction analog==