Exploring Neutralino Interactions: Amplitude Analysis and Source Check

In summary, the author is trying to find the amplitudes for the neutralino (higgsino or chargino/bino -like) interaction processes. However, without seeing a Lagrangian, he can't understand the possible contributing channels. He is able to clear some difficulties he's been having, but it is still a little bit complicated. For example, he can have the figures I attached for χχ \rightarrow ZZ ... 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, he can write the amplitude for each one, right? However, he isn
  • #1
ChrisVer
Gold Member
3,378
464
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:
http://journals.aps.org/prd/abstract/10.1103/PhysRevD.47.376
But without seeing a Lagrangian, I can't understand the possible contributing channels I think...
 
Last edited:
Physics news on Phys.org
  • #2
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?
 
  • #3
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?).
Thanks
 

Attachments

  • neutralinos.jpg
    neutralinos.jpg
    5.4 KB · Views: 319
  • #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] .
 
  • #5
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]
No?
A current then is supposed to have an index.
 
  • #6
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:
  • #7
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.
 
  • Like
Likes 1 person
  • #8
Aha... so it's more like I'm having a RL and LR helicities.
 
  • #9
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?
 

1. What is a neutralino?

A neutralino is a hypothetical particle that is predicted by some theories of particle physics, such as supersymmetry. It is thought to be a neutral and stable particle that could potentially be a candidate for dark matter.

2. What is amplitude analysis?

Amplitude analysis is a technique used in particle physics to study the properties of subatomic particles. It involves analyzing the strength and phase of the waves that are produced when particles interact with each other.

3. How is source check used in exploring neutralino interactions?

Source check is a method used to verify the source of signals in particle detectors. In exploring neutralino interactions, it is used to ensure that the signals observed are indeed coming from neutralino interactions and not from other sources of background noise.

4. What are the potential implications of studying neutralino interactions?

If neutralinos are found to exist and their interactions can be understood, it could provide valuable insights into the nature of dark matter and potentially lead to the discovery of new physics beyond the Standard Model.

5. How is data collected and analyzed in exploring neutralino interactions?

Data on neutralino interactions is collected through particle detectors, which record the signals produced when particles interact. This data is then analyzed using advanced statistical methods to search for patterns and anomalies that could indicate the presence of neutralino interactions.

Similar threads

  • Special and General Relativity
2
Replies
49
Views
3K
Replies
1
Views
1K
  • Beyond the Standard Models
Replies
2
Views
2K
Replies
15
Views
1K
  • Quantum Interpretations and Foundations
Replies
1
Views
398
  • High Energy, Nuclear, Particle Physics
Replies
4
Views
1K
Replies
6
Views
696
  • Advanced Physics Homework Help
Replies
2
Views
2K
  • High Energy, Nuclear, Particle Physics
Replies
2
Views
1K
  • High Energy, Nuclear, Particle Physics
Replies
11
Views
1K
Back
Top