Could someone please explain what this task implies: Calculate coupling of fields: $\bar{e}_{R}e_{R}Z, HW^{+}W^{-}, W^{+}\bar{c}_{L}d_{L}$? (Exercise refers to the Standard Model Lagrangian). What do I technically have to do?


The coupling of $n$ fields refers to the constant in front of those n fields multiplied together in the Lagrangian. For example, the self coupling between two scalar fields in can be read off from the term $\mathcal{L} = \frac12 \lambda\phi^2$ as $\lambda$. In your example, you will need to expand all of the different terms in the Lagrangian as the coupling will not be as obvious.

In the standard model Lagrangian, you see only the bare fields (not physically observable), whereas you will need to expand your Lagrangian into the mixed state fields (for example $W^\pm = \frac{1}{\sqrt{2}}(W_1 \pm iW_2)$).

Then you will be able to simply read off the couplings.

  • $\begingroup$ Thanks! It's very helpful and I get it but still I don't understand something. Is it doable without getting full Lagrangian from book and reading off the couplings? How could I do it if I got such task on exam, using only basic knowledge from my mind? Could you tell me what should I know? $\endgroup$
    – Kundera
    Feb 16 '16 at 15:51
  • $\begingroup$ They would likely give you the Lagrangian in an exam, however I suppose you could be asked to construct it yourself. Typically you construct a Lagrangian by summing all terms that are allowed by all possible symmetries - so all Lorentz invariant, diffeomorphism invariant, gauge invariant or whatever terms, depending on the theory you are looking it. $\endgroup$
    – Akoben
    Feb 16 '16 at 20:40

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