Weak isospin

In particle physics, weak isospin is a quantum number relating to the electrically charged part of the weak interaction: Particles with half-integer weak isospin can interact with the
W^±
bosons; particles with zero weak isospin do not. Weak isospin is a construct parallel to the idea of isospin under the strong interaction. Weak isospin is usually given the symbol T or I, with the third component written as T₃ or I₃. It can be understood as the eigenvalue of a charge operator.

T₃ is more important than T; typically "weak isospin" is used as short form of the proper term "3rd component of weak isospin".

The weak isospin conservation law relates to the conservation of ${\displaystyle \ T_{3}\$ ;} weak interactions conserve T₃. It is also conserved by the electromagnetic and strong interactions. However, interaction with the Higgs field does not conserve T₃, as directly seen by propagation of fermions, mixing chiralities by dint of their mass terms resulting from their Higgs couplings. Since the Higgs field vacuum expectation value is nonzero, particles interact with this field all the time even in vacuum. Interaction with the Higgs field changes particles' weak isospin (and weak hypercharge). Only a specific combination of them, ${\displaystyle \ Q=T_{3}+{\tfrac {1}{2}}Y_{\mathrm {W} }\ }$ (electric charge), is conserved.