Meaning of hypercharge in electroweak theory?

[Mr. Apple]

Anybody knows what is the physical meaning of hypercharge in electroweak theory?

 

[Ben Niehoff]

Electroweak theory uses an SU(2) x U(1) gauge group. However, the U(1) subgroup in this combination is NOT the U(1) of electric charge. It is a U(1) of hypercharge.

This SU(2) x U(1) gauge symmetry is broken via the Higgs mechanism, resulting in three massive gauge fields (W and Z bosons), one massless U(1) gauge field (photon), and one massive scalar (the Higgs particle). The trick is that the leftover U(1) after symmetry breaking is not the same as the U(1) before; instead, it is some linear combination of things. So in effect, the electric charge (and electrodynamics) we see in everyday life is not the "natural" U(1) charge of electroweak theory; it is some linear combination of things in SU(2) x U(1) that happen to have the symmetry U(1).

So basically, electric charge is some linear combination of hypercharge and isospin that has a remaining U(1) symmetry after symmetry breaking by the Higgs mechanism.

 

[sir-pinski]

Hypercharge is a fundamental property of particles in the electroweak theory, which describes the unification of the electromagnetic and weak nuclear forces. It is a conserved quantum number that determines the strength of a particle's interaction with the Higgs field, which gives particles their mass. In the electroweak theory, hypercharge is related to the electric charge and weak isospin of a particle through a mathematical relationship known as the Gell-Mann–Nishijima formula. This formula allows for the prediction of the electric charge of a particle based on its hypercharge and weak isospin, providing a deeper understanding of the underlying structure of matter. In summary, hypercharge plays a crucial role in the electroweak theory by connecting the fundamental forces and providing insight into the properties of particles.