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 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 isospin in particle physics is a quantum number relating to the weak interaction, and parallels the idea of isospin under the strong interaction. Weak isospin is usually given the symbol T or I with the third component written as T_z, T₃, I_z or I₃^[1]. Weak isospin is a component of the weak hypercharge, which unifies weak interactions with electromagnetic interactions.

The weak isospin conservation law relates the conservation of T₃; all weak interactions must preserve T₃. It is also conserved by the other interactions and is therefore a conserved quantity in general. For this reason T₃ is more important than T and often the term "weak isospin" refers to the "3rd component of weak isospin".

Contents 1 Relation with chirality 2 Weak isospin and the W bosons 3 Sources and footnotes 4 See also

[edit] Relation with chirality

Fermions with negative chirality (also called left-handed fermions) have T = ¹⁄₂ and can be grouped into doublets with T₃ = ±¹⁄₂ that behave the same under the weak interaction. For example, up-type quarks (u, c, t) have T₃ = +¹⁄₂ and always transform in down-type quarks (d, s, b) that have T₃ = −¹⁄₂ and vice versa. On the other hand, a quark never decays into a quark of the same type. Something similar happens with left-handed leptons, which exist as doublets containing a charged lepton with T₃ = −¹⁄₂ and a neutrino with T₃ = ¹⁄₂.

Fermions with positive chirality (also called right-handed fermions) have T = 0 and form singlets that do not undergo weak interactions.

[edit] Weak isospin and the W bosons

The symmetry associated with spin is SU(2). This requires gauge bosons to transform between weak isospin charges: bosons W⁺, W⁻ and W⁰. This implies that W bosons have a T = 1, with three different values of T₃.

• W⁺ (T₃ = +1) is emitted in transitions {(T₃ = +¹⁄₂) → (T₃ = −¹⁄₂)},
• W⁻ boson (T₃ = −1) is emitted in transitions {(T₃ = −¹⁄₂) → (T₃ = +¹⁄₂)}.
• W⁰ boson (T₃ = 0) would be emitted in reactions where T₃ does not change. However, under electroweak unification, the W⁰ boson mixes with the weak hypercharge gauge boson B, resulting in the observed Z⁰ boson and the photon of Quantum Electrodynamics.

[edit] Sources and footnotes

1. ^ Ambiguities: I is also used as sign for the 'normal' isospin, same for the third component I₃ aka I_z. T is also used as the sign for Topness. This articles uses T and T_3.

_{[edit] See also}

• _{Field theoretical formulation of standard model}
• _{Weak hypercharge}