Weak hypercharge

In the Standard Model of electroweak interactions of particle physics, the weak hypercharge is a quantum number relating the electric charge and the third component of weak isospin. It is frequently denoted Y_W and corresponds to the gauge symmetry U(1).

It is conserved (only terms that are overall weak-hypercharge neutral are allowed in the Lagrangian). However, one of the interactions is with Higgs field. Since Higgs field vacuum expectation value is nonzero, particles interact with this field all the time even in vacuum. This changes their weak hypercharge (and weak isospin). Only a specific combination of them, ${\displaystyle Q=T_{3}+{\frac {Y_{\rm {W}}}{2}}}$ (electric charge), is conserved.

Mathematically, weak hypercharge is similar to the Gell-Mann–Nishijima formula for the hypercharge of strong interactions (which is not conserved in weak interactions).

Weak hypercharge is the generator of the U(1) component of the electroweak gauge group, SU(2)×U(1) and its associated quantum field B mixes with the W³ electroweak quantum field to produce the observed
Z
gauge boson and the photon of quantum electrodynamics.

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