Weak hypercharge

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Flavour in particle physics

Flavour quantum numbers Lepton number: L Baryon number: B Electric charge: Q Weak hypercharge: YW Weak isospin: Tz Isospin: I, Iz Hypercharge: Y Strangeness: S Charm: C Bottomness: B' Topness: T Y=B+S+C+B'+T Q=Iz+Y/2 Q=Tz+YW/2 B-L conserved in the standard model Related topics: CPT symmetry CKM matrix CP symmetry Chirality

Weak hypercharge is twice the difference between the electrical charge and the weak isospin. It is the generator of the center of the electroweak gauge group.

In a relation that parallels the Gell-Mann/Nishima Law (see hypercharge) we have

<math>Q = I^W_z + {1 \over 2} Y^W</math>

where Q is the electrical charge (in elementary charge units), <math>I^W_z</math> is the third component of the weak isospin, and <math>Y^W</math> is the weak hypercharge. From here we can define the weak hypercharge in terms of particle electrical charge and weak isospin.

Given that weak isospin is 1/2 for all fermions, all weak isospin doublets will have an average charge

<math>\bar Q = {Y^W \over 2}</math>

with

• Y = −1 for leptons (+1 for antileptons)
• Y = +1/3 for quarks (−1/3 for antiquarks)

See also

• Field theoretical formulation of the standard model
• Weak isospin