# How does one write the standard model Lagrangian in other smaller Lagrangian counterparts?

How does one write the standard model Lagrangian in other smaller Lagrangian counterparts? Before electroweak symmetry breaking by the Higgs Mechanism:

$L_{EW} = L_{g} + L_{f} + L_{h} + L_{y}$

Where

$L_{g}$ describes the interaction between the three W particles and the B particle.

$L_{g} = -W_{a}^{\muν}W_{\muν}^{a}/4 - B^{\muν}B_{\muν}/4$

$L_{f}$ is the kinetic term for the Standard Model fermions.

$L_{h}$ is the Higgs Field Lagrangian.

$L_{y}$ gives the Yukawa interaction that generates fermion masses after the Higgs acquires a vacuum expectation value.

After electroweak symmetry breaking by Higgs mechanism:

$L_{EW} = L_{K} + L_{N} + L_{C} + L_{H} + L_{HV} + L_{WWV} + L_{WWVV} + L_{Y}$

What the terms mean can be obtained by a simple Google Search, as I will not list them out here.

My question is therefore this:

$L_{SM} = \space???$

It consists of How do I express these terms in their respective shorthand form? The first term $-B^{\muν}B_{\muν}/4$ happens to be the 2nd half of $L_{g}$, so it is well understood if it was represented as $L_{U1}$?

How about the rest?

• – Qmechanic Jul 19 '16 at 11:32
• Yes, I've looked at it but it does not provide the specific terms of the Lagrangian and their association, so it was rather unsatisfactory. – Lagrangian Jul 19 '16 at 12:02

## 1 Answer

$$\mathcal{L}_{SM}=\mathcal{L}_{Dirac}+\mathcal{L}_{mass}+\mathcal{L}_{guage}+\mathcal{L}_{guage/\psi}$$

• U(1), SU(2) and SU(3) terms are probably parts of other Lagrangian terms, as they are not Lagrangians themselves. – Lagrangian Jul 21 '16 at 5:29
• @Lagrangian Refer to guage theory – Ariana Jul 21 '16 at 5:30