Neutralino Interactions

  1. ChrisVer

    ChrisVer 2,403
    Gold Member

    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
  2. jcsd
  3. Greg Bernhardt

    Staff: Admin

    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. ChrisVer

    ChrisVer 2,403
    Gold Member

    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. 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. ChrisVer

    ChrisVer 2,403
    Gold Member

    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. ChrisVer

    ChrisVer 2,403
    Gold Member

    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. 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.
    1 person likes this.
  9. ChrisVer

    ChrisVer 2,403
    Gold Member

    Aha... so it's more like I'm having a RL and LR helicities.
  10. ChrisVer

    ChrisVer 2,403
    Gold Member

    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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