Hi all,(adsbygoogle = window.adsbygoogle || []).push({});

I'm trying to calculate the Feynman Rules for the effective electroweak chiral Lagrangian. For example, this is the first term in the Lagrangian:

\begin{eqnarray}

\mathcal{L}=\frac{v^2}{4}\text{Tr}(D_{\mu}U D^{\mu}U^{\dagger})

\end{eqnarray}

where

\begin{eqnarray}

U=\text{exp}(\frac{i\pi \cdot \tau}{v})

\end{eqnarray}

where $\tau$ are the Pauli matrices and $\pi$ are the Goldstone bosons. See,for example equations 1 and 2 in:

http://arxiv.org/PS_cache/hep-ph/pdf/0201/0201098v1.pdf" [Broken]

My questions are:

1. Does anyone know of a reference in which the Feynman rules for the electroweak Lagrangian are given?

2. Does anyone know how to get the Feynman Rules out of this Lagrangian? It seems that this is a little complicated because of the presence of the trace.

3. Also, do I have to know explicitly what the $\pi$ matrix is? I would assume so, as I seem to be struggling otherwise. I don't know what it is though. For example for chiral perturbation thoery in QCD Wikipedia has the following article:

http://en.wikipedia.org/wiki/Chiral_perturbation_theory

in which it gives an explicit representation for the matrix U. But what is the equivalent in the electroweak theory?

Hope I've explained myself clearly. I'm not quite sure if these are the right questions to ask...

Anyhow, any advice or help would be very much appreciated! If anyone knows of any good online resources e.g. papers/lecture notes which might help that would be great too!

Thank you very much.

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# Feynman Rules for Electroweak Effective Chiral Lagrangian - How to calculate them?

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