Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

A Deducing decay processes and Feynman diagrams using Lagrangian and conservation laws

  1. Feb 18, 2017 #1
    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.

    ---------------------------------------------------------------------------

    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?
     
  2. jcsd
  3. Feb 23, 2017 #2
    Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Deducing decay processes and Feynman diagrams using Lagrangian and conservation laws
Loading...