Hypercharge
From Exampleproblems
Template:Flavour quantum numbers
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:
where 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:
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 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 (baryon 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 +2/3, and an Iz of +1/2, we deduce a hypercharge of 1/3, due to its baryon number (since you need 3 quarks to make a baryon, a quark has baryon number of ±1/3).
- For a strange quark, with charge −1/3, a baryon 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.
See also
- Flavour (particle physics), baryon number and quark flavor charges: isospin, strangeness, charm, bottomness, topness
- Weak isospin, Weak hypercharge, standard modelde:Hyperladung
