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Neutralino Interactions

  1. Jul 30, 2014 #1


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    Do you have any source where I can check for the neutralino (higgsino or chargino/bino -like) interaction processes?
    In general I'm trying to find the amplitudes in the Appendix A of:
    But without seeing a Lagrangian, I can't understand the possible contributing channels I think...
    Last edited: Jul 30, 2014
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  3. Aug 4, 2014 #2

    Greg Bernhardt

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    I'm sorry you are not generating any responses at the moment. Is there any additional information you can share with us? Any new findings?
  4. Aug 5, 2014 #3


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    Yes I am able to clear a lot of difficulties I've been having with it. But it's still a little bit complicated.
    For example one can have the figures I attached for [itex]χχ \rightarrow ZZ [/itex]... which are 6 in number (n=1,2,3,4 for the neutralinos), and H,h are the two neutral scalar higgs bosons.
    So in general I can write the amplitude for each one, right?
    However I am not sure how is this kind of amplitudes written... Could someone check if the formula I'm using is correct for the small higgs?

    [itex] M= [ \bar{u}_{χ} \gamma^{\mu} u_{χ}] \frac{1}{k^{2} -m_{h}^{2} +i m_{h} \Gamma_{h}} j_{\mu}^{ZZ}[/itex]

    where u's are the spinors for the χ neutralinos... k is the momentum of the scalar higgs, [itex]m_{h}[/itex] its mass, [itex]\Gamma_{h}[/itex] its width and [itex]j_{\mu}^{ZZ}[/itex] the current of ZZ bosons (I don't know its form- any help?).

    Attached Files:

  5. Aug 6, 2014 #4
    I think that the [itex]\gamma^{\mu}[/itex] in the [itex]\bar{u}_{\chi}\gamma^{\mu}{u}_{\chi}[/itex] should be removed since the neutralinos couple to a scalar, not a vector. For the coupling of the higgs to the Z see feynman rules references, peskin for example. I think it it something like [itex]\frac{m_{Z}^{2}}{v}[/itex] .
  6. Aug 6, 2014 #5


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    I think in general the [itex]M[/itex] is the coupling of the one current with the other through the propagator.
    [itex]M= j_{1}^{\mu} [prop]_{\mu \nu} j_{2}^{\nu}[/itex]
    A current then is supposed to have an index.
  7. Aug 7, 2014 #6


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    Well I tried to think of someway to do it, can someone check the amplitude please?
    it's for: [itex] χχ \rightarrow h \rightarrow W^{+} W^{-} [/itex]
    Can someone help me with how I can use the Feynman rules I've found?
    For the coupling of [itex]χχh[/itex] I have:
    [itex] -ig_{2} (c_{L} P_{L} + c_{R} P_{R} ) [/itex]
    So for this it's better to work with the left and right neutralinos separately and then add the amplitudes ([itex]M= M(χ_{L}χ_{L} \rightarrow W^{+}W^{-}) +M(χ_{R}χ_{R} \rightarrow W^{+}W^{-}) [/itex] )

    For the [itex]h W^{\pm}[/itex] vertex I found:
    [itex] ig_{2} m_{W} n^{\mu \nu} \cos(\beta-\alpha) [/itex]

    And the propagator is as given:
    [itex]\frac{i}{k^{2}-m_{h}^{2} + i m_{h} \Gamma_{h}} [/itex]

    What am I missing to get the [itex]M[/itex] is how to represent the outgoing particles....
    is it fine to write for the fermionic neutralinos the [itex] \bar{u}_{χ} \gamma^{\mu} u_{χ'}[/itex] ?
    I am not sure...
    in any case it's like:

    [itex] i M(χ_{j}χ_{j} \rightarrow W^{+}W^{-})= (-ig_{2} c_{j}) \frac{i }{k^{2}-m_{h}^{2} + i m_{h} \Gamma_{h}} ( ig_{2} m_{W} \cos(\beta-\alpha)) n^{\mu \nu} \epsilon_{\mu} \epsilon^{*}_{\nu}[/itex]

    is that right?
    Last edited: Aug 7, 2014
  8. Aug 8, 2014 #7


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    The vertex for the ##\chi\chi h## interaction is what should be within the fermion bilinear. Basically you should have (given your Feynman rules)
    -ig_{2} \bar u_\chi (c_L P_L + c_R P_R) u_{\chi'} \frac{i }{k^{2}-m_{h}^{2} + i m_{h} \Gamma_{h}} ( ig_{2} m_{W} \cos(\beta-\alpha)) n^{\mu \nu} \epsilon_{\mu} \epsilon^{*}_{\nu}.
    Since the higgs is a scalar, it cannot interact with the vector current of the form ##\bar u \gamma^\mu u##. There is simply no way to contract the free Lorentz index.
  9. Aug 8, 2014 #8


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    Aha... so it's more like I'm having a RL and LR helicities.
  10. Aug 9, 2014 #9


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    do the self couplings between gauge bosons change from SM to SUSY?
    eg the coupling of [itex]Z^0 _{\lambda} (q), W^+_{\mu}(k_+), W^-_{\nu}(k_-)[/itex] is it still
    [itex] i g \cos(\theta_{w}) [g^{\mu \nu} (k_{-}-k_{+})^{\lambda}+ g^{\nu \lambda} (-q-k_-)^{\mu} + g^{\mu \lambda} (q+k_+)^{\nu}][/itex]
    as given in Peskin Fig 21.9, or is it changed?
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