electroweakmodel

The electroweak model, a central component of the Standard Model of particle physics, is the gauge theory that unifies the electromagnetic and weak nuclear forces. It is based on the gauge group SU(2)_L x U(1)_Y and uses spontaneous symmetry breaking via the Higgs mechanism to give mass to the W and Z bosons while leaving the photon massless.

Fermions are arranged in left-handed SU(2)_L doublets and right-handed singlets, with gauge bosons arising from the SU(2)_L and U(1)_Y gauge fields. The interactions are governed by two gauge couplings, g and g', and electromagnetism emerges through mixing of the neutral gauge fields, described by the weak mixing angle theta_W. The photon and the Z boson are linear combinations of the underlying gauge fields, and the charged W bosons W± arise from the SU(2)_L sector.

Symmetry breaking occurs when the Higgs field acquires a vacuum expectation value v ≈ 246 GeV, breaking SU(2)_L x U(1)_Y to U(1)_em. This yields masses for the W and Z bosons: M_W = (1/2) g v and M_Z = (1/2) sqrt(g^2 + g'^2) v, while the photon remains massless. The weak mixing angle relates the couplings through tan theta_W = g'/g and the electric charge e = g sin theta_W = g' cos theta_W, with cos theta_W = M_W / M_Z.

Phenomenologically, the model predicts charged-current interactions mediated by W and neutral-current interactions mediated by Z and the photon. Radiative corrections enable precision tests, and data from LEP, SLC, the Tevatron, and the LHC have largely confirmed its predictions. The discovery of the Higgs boson in 2012 with a mass near 125 GeV provides crucial support for the mechanism of electroweak symmetry breaking. The electroweak model remains a foundational framework for understanding particle interactions and a focus of ongoing searches for new physics.