I would like to consider the interaction terms in the Standard Model which allow the following decay process:(adsbygoogle = window.adsbygoogle || []).push({});

The only interaction terms in the Standard Model which allow this decay process are contained in the charged current interactions:

$$\mathcal{L}_{cc}

= ie_{W}\big[W_{\mu}^{+}(\bar{\nu}'_{m}\gamma^{\mu}(1+\gamma_{5})e'_{m} + V_{mn}\bar{u}'_{m}\gamma^{\mu}(1+\gamma_{5})d'_{n})

+ W_{\mu}^{-}(\bar{e}'_{m}\gamma^{\mu}(1+\gamma_{5})\nu'_{m} + (V^{\dagger})_{mn}\bar{d}'_{m}\gamma^{\mu}(1+\gamma_{5})u'_{n})\big].$$

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1. Is the vertex between the quarks only allowed by the term ##ie_{W}W_{\mu}^{+} V_{mn}\bar{u}'_{m}\gamma^{\mu}(1+\gamma_{5})d'_{n}##?

2. Is this because the down quark enters the vertex and therefore must not have a bar on top of it?

3. Simialrly, is the vertex between the leptons only allowed by the term ##ie_{W}W_{\mu}^{-} (V^{\dagger})_{mn}\bar{d}'_{m}\gamma^{\mu}(1+\gamma_{5})u'_{n}##?

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# A Matching interaction terms and decay processes in standard model

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