Definitions

# Weak hypercharge

The weak hypercharge in particle physics is a quantum number relating the electrical charge and the third component of weak isospin, and is similar to the Gell-Mann–Nishijima formula of strong interactions. It is the generator of the U(1) component of the electroweak gauge group, SU(2)xU(1) and its associated quantum field B mixes with the W3 electroweak quantum field to produce the observed Z0 gauge boson and the photon of quantum electrodynamics.

Weak hypercharge, usually written as YW, is defined as:

$qquad Q = T_z + \left\{Y_W over 2\right\}$
where Q is the electrical charge (in elementary charge units) and Tz is the third component of weak isospin. Rearranging, the weak hypercharge can be expressed as:
$qquad Y_W = 2\left(Q - T_z\right)$