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Electroweak Lagrangian

The electroweak Lagrangian is a mathematical expression describing the interactions between the electromagnetic and weak forces, expressed in terms of fields and their derivatives.
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The statement of the theorem

The full electroweak Lagrangian density LEW\mathcal{L}_{EW} is constructed from the gauge fields WμaW_{\mu}^a and BμB_{\mu}, the Higgs doublet ϕ\phi, and the matter fields ψ\psi: \nLEW=−14WμaWμa−14BμBμ+(Dμϕ)∗(Dμϕ)−V(ϕ)+ψˉiγμDμψ\mathcal{L}_{EW} = -\frac{1}{4} W_{\mu}^a W^{\mu a} - \frac{1}{4} B_{\mu} B^{\mu} + (D_{\mu} \phi)^* (D^{\mu} \phi) - V(\phi) + \bar{\psi} i \gamma^{\mu} D_{\mu} \psi \nWhere Dμ=∂μ−igτ⃗2⋅W⃗μ−ig′Y2BμD_{\mu} = \partial_{\mu} - i g \frac{\vec{\tau}}{2} \cdot \vec{W}_{\mu} - i g' \frac{Y}{2} B_{\mu}. This expression is invariant under the local gauge transformations of U(1)Y×SU(2)LU(1)_Y \times SU(2)_L.
Source: Wikipedia