Hypercharge is one of two quantum numbers of the SU model of hadrons, alongside isospin I3. The isospin alone is sufficient for two quark flavours—namely, and —whereas presently six flavours of quarks are known. SU weight diagrams are 2-dimensional with the coordinates referring to two quantum numbers, I3, which is the z-component of isospin and Y, which is the hypercharge. Mathematically, hypercharge is Strong interactions conserve hypercharge, but weak interactions do not.
The Gell-Mann–Nishijima formula relates isospin and electric charge where I3 is the third component of isospin and Q is the particle's charge. Isospin creates multiplets of particles whose average charge is related to the hypercharge by: since the hypercharge is the same for all members of a multiplet, and the average of the I3 values is 0.
SU(3) model in relation to hypercharge
The SU model has multiplets characterized by a quantum number J, which is the total angular momentum. Each multiplet consists of substates with equally-spaced values of Jz, forming a symmetricarrangement seen in atomic spectra and isospin. This formalizes the observation that certain strong baryon decays were not observed, leading to the prediction of the mass, strangeness and charge of the baryon. The SU has supermultiplets containing SU multiplets. SU now needs two numbers to specify all its sub-states which are denoted by λ1 and λ2. specifies the number of points in the topmost side of the hexagon while specifies the number of points on the bottom side.
Examples
The nucleon group have an average charge of +, so they both have hypercharge Y = 1. From the Gell-Mann–Nishijima formula we know that proton has isospin I3 = +, while neutron has I3 = −.
This also works for quarks: for the up quark, with a charge of +, and an I3 of +, we deduce a hypercharge of, due to its baryon number.
For a strange quark, with charge −, a baryon number of and strangeness of −1 we get a hypercharge Y = −, so we deduce an I3 = 0. That means that a strange quark makes an isospin singlet of its own, while up and down constitute an isospin doublet.
Hypercharge was a concept developed in the 1960s, to organize groups of particles in the "particle zoo" and to develop adhocconservation laws based on their observed transformations. With the advent of the quark model, it is now obvious that hypercharge Y is the following combination of the numbers of up, down, strange, charm, top and bottom : In modern descriptions of hadroninteraction, it has become more obvious to draw Feynman diagrams that trace through individual quarks composing the interacting baryons and mesons, rather than counting hypercharge quantum numbers. Weak hypercharge, however, remains of practical use in various theories of the electroweak interaction.
