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|Flavour quantum numbers|
|Related quantum numbers|
The weak hypercharge in particle physics is a quantum number relating the electric charge and the third component of weak isospin. It is conserved (only terms that are overall weak-hypercharge neutral are allowed in the Lagrangian) and is similar to the Gell-Mann–Nishijima formula for the hypercharge of strong interactions (which is not conserved in weak interactions). It is frequently denoted YW and corresponds to the gauge symmetry U(1).
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.
Weak hypercharge, usually written as YW, satisfies the equality:
|0||+1/2||−1||Do not interact (if exist at all)|
|e−, μ−, τ−||−1||−1/2||−1||e−
|Quarks||u, c, t||+2/3||+1/2||+1/3||u
|d, s, b||−1/3||−1/2||+1/3||d
Note: sometimes weak hypercharge is scaled so that
although this is a minority usage.
Hypercharge assignments in the Standard Model are determined up to a twofold ambiguity by demanding cancellation of all anomalies.
Baryon and lepton number
Weak hypercharge is related to baryon number minus lepton number via:
where X is a GUT-associated conserved quantum number. Since weak hypercharge is always conserved this implies that baryon number minus lepton number is also always conserved, within the Standard Model and most extensions.