Flavour in particle physics v • d • e

Flavour quantum numbers: Baryon number: B Lepton number: L Strangeness: S Charmness: C Bottomness: B′ Topness: T Isospin: I or I3 Weak isospin: T or T3 Electric charge: Q X-charge: X Combinations: Hypercharge: Y Y = (B + S + C + B′ + T) Y = 2 (Q − I3) Weak hypercharge: YW YW = 2 (Q − T3) X + 2YW = 5 (B − L) Flavour mixing CKM matrix PMNS matrix Flavour complementarity

The weak hypercharge in particle physics is a conserved quantum number relating the electrical charge and the third component of weak isospin, and is similar to the Gell-Mann–Nishijima formula for the hypercharge of strong interactions (which is not conserved). It is frequently denoted Y_W and corresponds to the gauge symmetry U(1).^[1]

Contents 1 Definition 2 Baryon and lepton number 2.1 Neutron decay 2.2 Proton decay 3 See also 4 Notes

[edit] Definition

It is the generator of the U(1) component of the electroweak gauge group, SU(2)xU(1) and its associated quantum field B mixes with the W³ electroweak quantum field to produce the observed Z⁰ gauge boson and the photon of quantum electrodynamics.

Weak hypercharge, usually written as Y_W, is defined as:

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 expressed as:

Note: sometimes weak hypercharge is scaled so that

although this is a minority usage.^[2]

[edit] Baryon and lepton number

Weak hypercharge is related to baryon number - lepton number via:

where X is a GUT-associated conserved quantum number. Since weak hypercharge is also conserved this implies that baryon number - lepton number is also conserved, within the Standard Model and most extensions.

[edit] Neutron decay

n → p + e⁻ + ν_e

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

[edit] Proton decay

Proton decay is a prediction of many grand unification theories.

p⁺ → e⁺ + π⁰ → e⁺ + 2γ

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

[edit] See also

• Standard Model (mathematical formulation)

[edit] Notes

1. ^ J. F. Donoghue, E. Golowich, B. R. Holstein (1994). Dynamics of the standard model. Cambridge University Press. pp. 52. ISBN 0521476526. 
2. ^ M. R. Anderson (2003). The mathematical theory of cosmic strings. CRC Press. pp. 12. ISBN 0750301600.