- #1
spaghetti3451
- 1,344
- 33
The decay processes of the ##W## bosons are completely governed by the charged current interaction terms of the Standard model:
$$\mathcal{L}_{cc}
= ie_{W}\big[W_{\mu}^{+}(\bar{\nu}_{m}\gamma^{\mu}(1-\gamma_{5})e_{m} + V_{mn}\bar{u}_{m}\gamma^{\mu}(1-\gamma_{5})d_{n})\\
+ W_{\mu}^{-}(\bar{e}_{m}\gamma^{\mu}(1-\gamma_{5})\nu_{m} + (V^{\dagger})_{mn}\bar{d}_{m}\gamma^{\mu}(1-\gamma_{5})u_{n})\big].$$
I would like to find the possible decay processes of the ##W^{-}## boson.
I would like to find the Feynman diagrams for each of these processes.
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I find that I have to use electric charge conservation and lepton charge conservation to deduce that the possible decay processes are
$$W^{-} \to e^{-} \bar{\nu}_{e}$$
$$W^{-} \to \mu^{-}\bar{\nu}_{\mu}$$
$$W^{-} \to \tau^{-}\bar{\nu}_{\tau}$$
$$W^{-} \to d\bar{u}$$
$$W^{-} \to s\bar{c}$$
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As the fermion is outgoing, the arrow on its external line in the Feynman diagram must point outwards.
As the anti-fermion is outgoing, the arrow on its external line in the Feynman diagram must point inwards.
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1. Is there a way to obtain these possible decay processes without using conservation laws and by simply inspecting the Lagrangian?
2. Is there a way to determine if the arrows on the external fermion and anti-fermion lines must point inwards and outwards without knowing using their particle/anti-particle property and by simply inspecting the Lagrangian?
$$\mathcal{L}_{cc}
= ie_{W}\big[W_{\mu}^{+}(\bar{\nu}_{m}\gamma^{\mu}(1-\gamma_{5})e_{m} + V_{mn}\bar{u}_{m}\gamma^{\mu}(1-\gamma_{5})d_{n})\\
+ W_{\mu}^{-}(\bar{e}_{m}\gamma^{\mu}(1-\gamma_{5})\nu_{m} + (V^{\dagger})_{mn}\bar{d}_{m}\gamma^{\mu}(1-\gamma_{5})u_{n})\big].$$
I would like to find the possible decay processes of the ##W^{-}## boson.
I would like to find the Feynman diagrams for each of these processes.
---------------------------------------------------------------------------
I find that I have to use electric charge conservation and lepton charge conservation to deduce that the possible decay processes are
$$W^{-} \to e^{-} \bar{\nu}_{e}$$
$$W^{-} \to \mu^{-}\bar{\nu}_{\mu}$$
$$W^{-} \to \tau^{-}\bar{\nu}_{\tau}$$
$$W^{-} \to d\bar{u}$$
$$W^{-} \to s\bar{c}$$
---------------------------------------------------------------------------
As the fermion is outgoing, the arrow on its external line in the Feynman diagram must point outwards.
As the anti-fermion is outgoing, the arrow on its external line in the Feynman diagram must point inwards.
---------------------------------------------------------------------------
1. Is there a way to obtain these possible decay processes without using conservation laws and by simply inspecting the Lagrangian?
2. Is there a way to determine if the arrows on the external fermion and anti-fermion lines must point inwards and outwards without knowing using their particle/anti-particle property and by simply inspecting the Lagrangian?