hypercharge

In particle physics, the hypercharge (represented by Y) is the sum of the baryon number B and the flavor charges: strangeness S, charm C, bottomness

\tilde B

and topness T, although the last one can be omitted given the extremely short life of the top quark (it decays to other quarks before strong-interacting with other quarks).

(1) \qquad Y = B + S + C + \tilde B + T

Originally, hypercharge only included the strangeness flavor in its definition. Do not confuse hypercharge with weak hypercharge: the first one is connected to the strong interaction, while the second appears on the electroweak interaction. The Gell-Mann/Nishijima Law relates hypercharge with isospin and electric charge:

(2) \qquad Q = I_z + {1 \over 2} Y

were I_z is the third component of isospin and Q is the particle's charge. This allow us to express the hypercharge in terms of isospin and charge:

(3) \qquad Y = 2(Q - I_z)

Isospin creates multiplets of particles whose average charge is related to the hypercharge by:

(4) \qquad Y = 2 \bar Q

which is easily derived from (3), since the hypercharge is the same for all members of a multiplet, and the average of the I_z values is 0. Examples:

The nucleon group (proton plus neutron) have an average charge of 1 + 0 = +1/2, so they both have hypercharge Y = 1 (barion number B = +1, flavor charges set to 0). From Gell-Mann/Nishima Law we know that proton has isospin +1 - 1/2 = +1/2, while neutron is the 0 − 1/2 = −1/2.
This also works for quarks: for the up quark, with a charge of 3/2, and an I_z of +1/2, we deduce a hypercharge of 1/3, due to its barion number (since you need 3 quarks to make a barion, a quark has barion number of &plusminus;1/3).
For a strange quark, with charge −1/3, a barion number of 1/3 and strangeness of −1 we get an hypercharge Y = −1/3, so we deduce an I_z = 0. That means that a strange quark makes a singlet of its own (same happens with charm, bottom and top quarks), while up and down constitute a isospin doublet.

Hypercharge

See also