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 asT₃, T_z or I₃. Weak isospin is a component of the weak hypercharge, which unifies weak interactions with electromagnetic interactions.

Fermions with negative helicity (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, "u" type quarks (u, c, t) have T₃ = +¹⁄₂ and always transform in "d" 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.

There is also a weak isospin conservation law: all weak interactions must preserve the weak isospin.

[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 T_z.

• 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] See also

• Field theoretical formulation of standard model
• Weak hypercharge