Editing Standard Model (section)

==== Higgs sector ====
{{Main|Higgs mechanism}}
In the Standard Model, the [[Higgs field]] is an SU(2){{sub|L}} doublet of complex [[Scalar (physics)|scalar]] fields with four degrees of freedom:
<math display="block"> 
\varphi = \begin{pmatrix} \varphi^+ \\ \varphi^0 \end{pmatrix}
= \frac{1}{\sqrt{2}} \begin{pmatrix} \varphi_1 + i\varphi_2 \\ \varphi_3 + i\varphi_4 \end{pmatrix},
</math>
where the superscripts + and 0 indicate the electric charge <math>Q</math> of the components. The weak hypercharge <math>Y_\text{W}</math> of both components is 1. Before symmetry breaking, the Higgs Lagrangian is
<math display="block"> \mathcal{L}_\text{H} = \left(D_{\mu}\varphi\right)^{\dagger} \left(D^{\mu}\varphi \right) - V(\varphi),</math>
where <math>D_{\mu}</math> is the electroweak gauge covariant derivative defined above and <math>V(\varphi)</math> is the potential of the Higgs field. The square of the covariant derivative leads to three and four point interactions between the electroweak gauge fields <math>W^{a}_{\mu}</math> and <math>B_{\mu}</math> and the scalar field <math>\varphi</math>. The scalar potential is given by
<math display="block"> V(\varphi) = -\mu^2\varphi^{\dagger}\varphi + \lambda \left( \varphi^{\dagger}\varphi \right)^2, </math>
where <math>\mu^2>0</math>, so that <math>\varphi</math> acquires a non-zero [[Vacuum expectation value]], which generates masses for the Electroweak gauge fields (the Higgs mechanism), and <math>\lambda>0</math>, so that the potential is bounded from below. The quartic term describes self-interactions of the scalar field <math>\varphi</math>.

The minimum of the potential is degenerate with an infinite number of equivalent [[ground state]] solutions, which occurs when <math>\varphi^{\dagger}\varphi = \tfrac{\mu^2}{2\lambda}</math>. It is possible to perform a [[Unitary gauge|gauge transformation]] on <math>\varphi</math> such that the ground state is transformed to a basis where <math>\varphi_1 = \varphi_2 = \varphi_4 = 0</math> and <math>\varphi_3 = \tfrac{\mu}{\sqrt{\lambda}} \equiv v </math>. This breaks the symmetry of the ground state. The expectation value of <math>\varphi</math> now becomes 
<math display="block"> \langle \varphi \rangle = \frac{1}{\sqrt{2}} \begin{pmatrix} 0 \\ v \end{pmatrix},</math>
where <math>v</math> has units of mass and sets the scale of electroweak physics. This is the only dimensional parameter of the Standard Model and has a measured value of ~{{val|246|u=GeV/c2}}. 

After symmetry breaking, the masses of the W and Z are given by <math>m_\text{W}=\frac{1}{2}gv</math> and <math> m_\text{Z}=\frac{1}{2}\sqrt{g^2+g'^2}v</math>, which can be viewed as predictions of the theory. The photon remains massless. The mass of the [[Higgs boson]] is <math>m_\text{H}=\sqrt{2\mu^2}=\sqrt{2\lambda}v</math>. Since <math>\mu</math> and <math>\lambda</math> are free parameters, the Higgs's mass could not be predicted beforehand and had to be determined experimentally.