= Solution
The electroweak <gauge group> is $SU(2)_L\times U(1)_Y$. Left-handed <fermions> form weak-isospin doublets and right-handed charged <fermions> are singlets under $SU(2)_L$. Before <symmetry> breaking the <gauge fields> are $W^1,W^2,W^3$ and $B$, with couplings $g,g'$. A Higgs-doublet <vacuum expectation value> breaks the <symmetry> to electromagnetic $U(1)$.
In units $\hbar=c=1$, the physical combinations and tree-level relations are
$$
W^\pm=\frac{W^1\mp iW^2}{\sqrt2},\quad
A=B\cos\theta_W+W^3\sin\theta_W,\quad
Z=-B\sin\theta_W+W^3\cos\theta_W,
$$
$$
e=g\sin\theta_W=g'\cos\theta_W,\qquad
M_W=gv/2,\qquad M_Z=\frac v2\sqrt{g^2+g'^2},\qquad
\boxed{M_W=M_Z\cos\theta_W}.
$$
The <photon> remains massless. <charged currents> change members of weak doublets, whereas the $Z$ mediates <weak neutral currents> with parity-dependent couplings. At low energies $W$ exchange reduces to the Fermi contact interaction, $G_F/\sqrt2=g^2/(8M_W^2)$; the apparent weak suppression reflects the massive mediator. This unifies the gauge description, not the numerical equality of all low-energy couplings.<A Model of Leptons by Steven Weinberg>[1967, gauge structure, symmetry breaking and vector-boson mass relations]{ref}
Neutral-current <neutrino> interactions and subsequent observation of massive weak vector bosons tested this structure. In a neutral-current <neutrino> experiment, an isolated hadronic interaction without an accompanying charged <lepton> is a candidate signal; entering neutral hadrons and missed charged-current <leptons> are important backgrounds. Gargamelle's neutral-current evidence supplied a direct experimental check beyond ordinary <beta decay>.<Observation of neutrino-like interactions without muon or electron in the Gargamelle neutrino experiment by F. J. Hasert>[1973, event topology and background analysis]{ref}
Back to article page
