Editing Standard Model (section)

==== Electroweak sector ====
{{Main|Electroweak interaction}}
The electroweak sector is a [[Yang–Mills theory|Yang–Mills gauge theory]] with the symmetry group {{nowrap|U(1) × SU(2)<sub>L</sub>}},
<math display="block">\mathcal{L}_\text{EW} = \overline{Q}_{\text{L}j} i\gamma^\mu D_{\mu} Q_{\text{L}j} + \overline{u}_{\text{R}j} i\gamma^\mu D_{\mu} u_{\text{R}j} + \overline{d}_{\text{R}j} i\gamma^\mu D_{\mu} d_{\text{R}j} + \overline{\ell}_{\text{L}j} i\gamma^\mu D_{\mu} \ell_{\text{L}j} + \overline{e}_{\text{R}j} i\gamma^\mu D_{\mu} e_{\text{R}j} - \tfrac{1}{4} W_a^{\mu\nu} W_{\mu\nu}^a - \tfrac{1}{4} B^{\mu\nu} B_{\mu\nu}, </math>
where the subscript <math>j</math> sums over the three generations of fermions; <math>Q_\text{L}, u_\text{R}</math>, and <math>d_\text{R}</math> are the left-handed doublet, right-handed singlet up type, and right handed singlet down type quark fields; and <math>\ell_\text{L}</math> and <math>e_\text{R}</math> are the left-handed doublet and right-handed singlet lepton fields. 

The electroweak [[gauge covariant derivative]] is defined as <math>D_\mu \equiv \partial_\mu - ig' \tfrac12 Y_\text{W} B_\mu - ig \tfrac{1}{2} \vec\tau_\text{L} \vec W_\mu</math>, where 
* {{mvar|B<sub>μ</sub>}} is the U(1) gauge field,
* {{math|''Y''<sub>W</sub>}} is the [[weak hypercharge]] – the generator of the U(1) group,
* {{math|{{vec|''W''}}<sub>''μ''</sub>}} is the 3-component SU(2) gauge field,
* {{math|{{overset|lh=0.5|→|''τ''}}<sub>L</sub>}} are the [[Pauli matrices]] – infinitesimal generators of the SU(2) group – with subscript L to indicate that they only act on ''left''-chiral fermions,
* {{mvar|g'}} and {{mvar|g}} are the U(1) and SU(2) coupling constants respectively,
* <math>W^{a\mu\nu}</math> (<math>a = 1, 2, 3</math>) and <math>B^{\mu\nu}</math> are the [[field strength tensor]]s for the weak isospin and weak hypercharge fields.

Notice that the addition of fermion mass terms into the electroweak Lagrangian is forbidden, since terms of the form <math>m\overline\psi\psi</math> do not respect {{nowrap|U(1) × SU(2)<sub>L</sub>}} gauge invariance. Neither is it possible to add explicit mass terms for the U(1) and SU(2) gauge fields. The Higgs mechanism is responsible for the generation of the gauge boson masses, and the fermion masses result from Yukawa-type interactions with the Higgs field.