SU2doublet

SU2doublet is a term used in particle physics to denote a two-component complex field that transforms under the fundamental representation of the SU(2) gauge group, also known as weak isospin. Under SU(2) transformations, a doublet is rotated by 2×2 unitary matrices with determinant one, and its two components mix according to the generators T^a = τ^a/2, where τ^a are the Pauli matrices.

In the Standard Model, left-handed fermions come in SU(2) doublets, while right-handed fermions are SU(2) singlets. Examples include the lepton doublet L_L = (ν_e, e_L)^T and the quark doublet Q_L = (u_L, d_L)^T. Each doublet has a hypercharge Y, which fixes electric charges via Q = T3 + Y/2. The lepton doublet has Y = -1, giving charges 0 and -1; the quark doublet has Y = +1/3, giving +2/3 and -1/3.

Doublets couple to the Higgs field through Yukawa interactions, and they participate in weak interactions mediated by W± and Z bosons. After electroweak symmetry breaking, components within a doublet can acquire different masses while preserving gauge structure. The theory treats left-handed fermions as doublets under SU(2)L and right-handed fermions as singlets, reflecting observed parity violation at high energies.

Mathematically, a doublet ψ comprises two complex components, ψ = (ψ1, ψ2)^T, transforming as ψ -> U ψ under U ∈ SU(2). The SU(2) doublet and its complex conjugate define distinct representations; physical content often uses the conjugate to describe right-handed fields in certain bases.