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Cross section for scattering of gauge bosons and Majorana neutrinos

  1. Jan 4, 2007 #1
    For my diploma thesis I must provide a calculation that reproduces the
    results given on page 46 of the paper hep-ph/0309342 . For those who do
    not want to look it up, I briefly explain what it is about: It concerns
    the two-body scattering processes

    (1) N + V => L + H,
    (2) N + L => V + H,
    (3) N + H => V + L

    where N denotes a right-handed Majorana neutrino, L and H are the SM
    lepton and Higgs doublet and V represents either a SU(2) or U(1) gauge
    boson. The processes are considered in the early universe, where
    SU(2)xU(1) is unbroken and L and V are massless (but N is not). The
    Higgs mass is also neglected since m_H << m_N, but this is of minor
    importance here. The Majorana neutrino has a Yukawa coupling to the
    lepton and Higgs doublet but does not couple to the gauge bosons. (See
    Feynman diagrams in the paper.)
    The problem is, that not only am I unable to reproduce the result given
    for (2) and (3), but the result I get makes no sense. When I calculate
    just the s-channel contribution |M_s|^2, then the result is negative!
    With process (1), which occurs only in the t-channel and u-channel,
    there is no problem, but for both (2) and (3) which have an s-channel
    contribution I get a negative amplitude squared. To make it even
    stranger-if I start from (1) and use crossing to obtain the result for
    (3), I get the same as the author of the paper does. But still, there
    must be something wrong since the direct calculation fails.

    My question is now: Is there anything special about these diagrams,
    some peculiarity that I most likely have not taken into account? My
    supervisor told me some stories that the diagrams might violate the
    Ward identity and I should try to add something which he called
    "contact terms", but he was unable to explain me properly, what this
    means. In the literature, I have not found any example where anything
    like that happens. I rather assume it could be connected to the
    polarization sums for the gauge bosons which maybe contain something
    special here. I used the same formula as for the photons (remember that
    the SU(2) gauge bosons are also massless in this case!), maybe this is
    wrong? But it works for process (1), this really confuses me...

    I hope someone can give me a hint what could be going on here, since it
    would be a pity to leave this part out. Few people have considered
    these processes and I would like to include their effect in my thesis.

    Thanks in advance,
    Denis Besak
  2. jcsd
  3. Jan 13, 2007 #2
    Is there really no one who could give me a hint? :-(
  4. Jan 22, 2007 #3
    denis.besak@gmx.de wrote:
    > When I calculate just the s-channel contribution |M_s|^2, then the
    > result is negative!

    Can you explain in more detail how do you calculate it?

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