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# 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 Iz 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 Iz 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 Iz 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 Iz = 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.