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 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).

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:

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:

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

.

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.

See also

• quark flavor charges:
  • isospin
  • strangeness
  • charm
  • bottomness
  • topness
• Weak isospin
• Weak hypercharge