section_path: Properties/Weak isospin and weak hypercharge
section_name: Weak isospin and weak hypercharge
paragraph_text: Weak isospin and weak hypercharge
  
  All particles have a property called weak isospin (symbol T), which serves as an additive quantum number that restricts how the particle can interact with the W of the weak force. Weak isospin plays the same role in the weak interaction with W as electric charge does in electromagnetism, and color charge in the strong interaction; a different number with a similar name, weak charge, discussed below, is used for interactions with the Z. All left-handed fermions have a weak isospin value of either + + 1 / 2 or − + 1 / 2; all right-handed fermions have 0 isospin. For example, the up quark has T = + + 1 / 2 and the down quark has T = − + 1 / 2. A quark never decays through the weak interaction into a quark of the same T: Quarks with a T of + + 1 / 2 only decay into quarks with a T of − + 1 / 2 and conversely.
  
  In any given strong, electromagnetic, or weak interaction, weak isospin is conserved: The sum of the weak isospin numbers of the particles entering the interaction equals the sum of the weak isospin numbers of the particles exiting that interaction. For example, a (left-handed) π, with a weak isospin of +1 normally decays into a ν (with T = + + 1 / 2) and a μ (as a right-handed antiparticle, + + 1 / 2).
  
  For the development of the electroweak theory, another property, weak hypercharge, was invented, defined as
  
  where Y is the weak hypercharge of a particle with electrical charge Q (in elementary charge units) and weak isospin T. Weak hypercharge is the generator of the U(1) component of the electroweak gauge group; whereas some particles have a weak isospin of zero, all known spin- 1 / 2 particles have a non-zero weak hypercharge.