Weak hypercharge

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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).[1]

Definition

Weak hypercharge is the generator of the U(1) component of the electroweak gauge group, Template:Gaps and its associated quantum field B mixes with the W3 electroweak quantum field to produce the observed Template:Subatomic particle gauge boson and the photon of quantum electrodynamics.

Weak hypercharge, usually written as YW, satisfies the equality:

where Q is the electrical charge (in elementary charge units) and T3 is the third component of weak isospin. Rearranging, the weak hypercharge can be explicitly defined as:

left-handed el. charge
Q
weak isospin
T3
weak
hyper-
charge
YW
right-handed el. charge
Q
weak isospin
T3
weak
hyper-
charge
YW
Leptons Template:Subatomic particle, Template:Subatomic particle, Template:Subatomic particle 0 +1/2 −1 Do not interact (if exist at all)
Template:Subatomic particle, Template:Subatomic particle, Template:Subatomic particle −1 −1/2 −1 Template:Physics particle, Template:Physics particle, Template:Physics particle −1 0 −2
Quarks Template:Subatomic particle, Template:Subatomic particle, Template:Subatomic particle +2/3 +1/2 +1/3 Template:Physics particle, Template:Physics particle, Template:Physics particle +2/3 0 +4/3
d, s, b
−1/3 −1/2 +1/3 Template:Physics particle, Template:Physics particle, Template:Physics particle −1/3 0 −2/3

Note: sometimes weak hypercharge is scaled so that

although this is a minority usage.[2]

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 also conservedTemplate:Clarify this implies that baryon number minus lepton number is also conserved, within the Standard Model and most extensions.Template:Clarify

Neutron decay

Template:SubatomicParticleTemplate:SubatomicParticle + Template:SubatomicParticle + Template:SubatomicParticle

Hence neutron decay conserves baryon number B and lepton number L separately, so also the difference B − L is conserved.

Proton decay

Proton decay is a prediction of many grand unification theories.

Template:SubatomicParticleTemplate:SubatomicParticle + Template:SubatomicParticleTemplate:SubatomicParticle + 2Template:SubatomicParticle

Hence proton decay conserves B − L, even though it violates both lepton number and baryon number conservation.

See also

Notes

  1. {{#invoke:citation/CS1|citation |CitationClass=book }}
  2. {{#invoke:citation/CS1|citation |CitationClass=book }}