Weak Isospin - Relation With Chirality

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 way under the weak interaction. For example, up-type quarks (u, c, t) have T₃ = +1⁄₂ and always transform into down-type quarks (d, s, b), which have T₃ = −1⁄₂, and vice-versa. On the other hand, a quark never decays weakly into a quark of the same T₃. Something similar happens with left-handed leptons, which exist as doublets containing a charged lepton (e−, μ−, τ−) with T₃ = −1⁄₂ and a neutrino (ν
e, ν
μ, ν
τ) 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.

Electric charge, Q, is related to weak isospin, T₃, and weak hypercharge, Y_W, by