Editing Electroweak interaction (section)

=== Before electroweak symmetry breaking ===
The [[Lagrangian (field theory)|Lagrangian]] for the electroweak interactions is divided into four parts before [[electroweak symmetry breaking]] manifests,
: <math>\mathcal{L}_{\mathrm{EW}} = \mathcal{L}_g + \mathcal{L}_f + \mathcal{L}_h + \mathcal{L}_y~.</math>

The <math>\mathcal{L}_g</math> term describes the interaction between the three {{mvar|W}}  vector bosons and the {{mvar|B}} [[vector boson]], 
: <math>\mathcal{L}_g = -\tfrac{1}{4} W_{a}^{\mu\nu}W_{\mu\nu}^a - \tfrac{1}{4} B^{\mu\nu}B_{\mu\nu},</math>
where <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 gauge fields.

<math>\mathcal{L}_f</math> is the [[kinetic term]] for the Standard Model fermions. The interaction of the gauge bosons and the fermions are through the [[gauge covariant derivative]],
: <math>\mathcal{L}_f = \overline{Q}_j iD\!\!\!\!/\; Q_j+ \overline{u}_j iD\!\!\!\!/\; u_j+ \overline{d}_j iD\!\!\!\!/\; d_j + \overline{L}_j iD\!\!\!\!/\; L_j + \overline{e}_j iD\!\!\!\!/\; e_j,</math>
where the subscript {{mvar|j}} sums over the three generations of fermions; {{mvar|Q}}, {{mvar|u}}, and {{mvar|d}} are the left-handed doublet, right-handed singlet up, and right handed singlet down quark fields; and {{mvar|L}} and {{mvar|e}} are the left-handed doublet and right-handed singlet electron fields.
The [[Feynman slash notation|Feynman slash]] <math>D\!\!\!\!/</math> means the contraction of the 4-gradient with the [[Dirac matrices]], defined as
: <math>D\!\!\!\!/ \equiv \gamma^\mu\ D_\mu,</math>
and the covariant derivative (excluding the [[gluon]] gauge field for the [[strong interaction]]) is defined as
: <math>\ D_\mu \equiv \partial_\mu - i\ \frac{g'}{2}\ Y\ B_\mu - i\ \frac{g}{2}\ T_j\ W_\mu^j.</math>
Here <math>\ Y\ </math> is the weak hypercharge and the <math>\ T_j\ </math> are the components of the weak isospin.

The <math>\mathcal{L}_h</math> term describes the [[Higgs field]] <math>h</math> and its interactions with itself and the gauge bosons,
: <math>\mathcal{L}_h = |D_\mu h|^2 - \lambda \left(|h|^2 - \frac{v^2}{2}\right)^2\ ,</math>
where <math>v</math> is the [[vacuum expectation value]].

The <math>\ \mathcal{L}_y\ </math> term describes the [[Yukawa interaction]] with the fermions, 
: <math>\mathcal{L}_y = - y_{u}^{ij}\epsilon^{ab}\ h_b^\dagger\ \overline{Q}_{ia} u_j^c - y_{d}^{ij}\ h\ \overline{Q}_i d^c_j - y_{e}^{ij}\ h\ \overline{L}_i e^c_j + \mathrm{h.c.} ~,</math>
and generates their masses,  manifest when the Higgs field acquires a nonzero vacuum expectation value, discussed next. The <math>\ y_k^{ij}\ ,</math> for <math>\ k \in \{ \mathrm{u, d, e} \}\ ,</math> are matrices of Yukawa couplings.