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Higgs decay

  1. Jun 19, 2012 #1
    1. The problem statement, all variables and given/known data
    I have decay of Higgs to fermion and antifermion and I need to find out the invariant, averaged amplitude.

    And I wrote down the Feynman diagram, and calculated everything and I came to this part:

    [itex]\langle|M|^2\rangle=\frac{g_w^2}{4}\frac{m_f^2}{m_w^2}(4p_1\cdot p_2-4m_f^2)[/itex]

    Now to calculate [itex]p_1\cdot p_2[/itex] I sit in Higgs rest frame, so that the impulses of the fermions are the same (magnitude), but have different sign: [itex]\vec{p}_1=-\vec{p}_2[/itex].

    So what I need to end up with is:

    [itex]\langle|M|^2\rangle=\frac{g_w^2}{4}\frac{m_f^2}{m_w^2}(2m_h^2-8m_f^2)[/itex]

    But I just cannot get the right result!

    [itex]p_1\cdot p_2=(E_1+E_2)^2-(\vec{p}_1+\vec{p}_2)^2=(E_1+E_2)^2[/itex]

    If the magnitude of the impulses of the two fermions are the same, and if the masses are the same the energies should also be the same, right? That is, [itex]E_1=E_2=E[/itex], then the scalar product of two 4-vectors is:

    [itex]p_1\cdot p_2=4E^2[/itex], where E is the energy of the fermion. Since the energy is conserved: [itex]E_H=E_1+E_2\Rightarrow E=\frac{E_H}{2}[/itex], but since the Higgs is at rest it's mass is equal to it's energy so [itex]E=\frac{m_H}{2}[/itex], but if I put that back into the scalar product I have:
    [itex]p_1\cdot p_2=m_H[/itex], but that doesn't give me the right answer :\

    Where is my mistake?!
     
  2. jcsd
  3. Jun 19, 2012 #2
    Ok I think I solved it, I was messing up the kinematics. I feel like an idiot -.-"
     
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