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Estimating force using interaction vertices

  1. Dec 5, 2016 #1
    1. The problem statement, all variables and given/known data

    Suppose that a hypothetical fermion ##\psi## interacts with the Higgs field ##h## obey the Lagrangian

    $$\bar{\psi}(i\gamma^{\mu}{\partial_{\mu}}-y\nu)\psi-y\bar{\psi}h\psi-y_{\mu}\bar{\psi}_{\mu}h\psi_{\mu} + \frac{1}{2}(\partial_{\mu}h)(\partial^{\mu}h)-\frac{1}{2}\left(2|\kappa^{2}|\right)h^{2} - \frac{\lambda}{6}\nu h^{3} -\frac{\lambda}{24}h^{4}$$

    Use the Higgs expectation value ##\nu \approx 246\ \text{GeV}## and the interaction vertices to deduce the force between two fermions, due to the exchange of the Higgs ##h##. How strong is it compared to the electromagnetic force? (Consider both the cases of distances small or large compared to the inverse Higgs mass ##1/m_{H} \approx (125\ \text{GeV})^{-1}##.) Here a parametric answer is sufficient, ignore factors of ##2##.

    How would the same comparison go for the top quark (##m_{t} \sim 170\ \text{GeV}##), which carries the same electric charge?

    2. Relevant equations

    3. The attempt at a solution

    The interaction vertex coupling the Higgs to the fermion is ##-igy##. But the Higgs mass is independent of ##\nu##, so the Higgs Feynman propagator does not have a factor of ##\nu##. I was wondering how ##\nu## figures into the scattering amplitude for the scattering of two fermions.
     
  2. jcsd
  3. Dec 11, 2016 #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.
     
  4. Dec 11, 2016 #3

    nrqed

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    What would you take as the coupling constant between the fermion and the Higgs?
     
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