Relative sign in diagrams for ##Z##-boson exchange for ##WW## scattering

In summary, the scattering process ##W^{+}W^{-} \to W^{+}W^{-}## in the Standard Model is mediated by a four-##W## scattering, ##Z##-boson exchange, and Higgs exchange. The relative minus sign between the matrix elements for the two diagrams in ##Z##-boson exchange is dictated by Fermi-Dirac statistics and is possibly due to a closed loop. However, there is no u channel process involved in the Z mediator case.
  • #1
spaghetti3451
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Consider the scattering process ##W^{+}W^{-} \to W^{+}W^{-}##. This process is mediated in the Standard Model by

1. a four-##W## scattering,
2. ##Z##-boson exchange,
3. Higgs exchange.

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Let us consider the diagrams for ##Z##-boson exchange:

82a12c3798.png
Why is there a relative minus sign between the matrix elements for the two diagrams?
 
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  • #2
Newbie here...have you considered that the relative minus sign btwn two terms is dictated by the Fermi-Dirac stats? something about a possible closed loop - which carries the extra minus sign.

I hope this helps.

Deneen
 
  • #3
Could you be more specific?
 
  • #4
]
rel min sign.jpg
 
  • #5
how can you use Fermi-Dirac statistics for W/Z bosons?
Also I think that that minus sign mentioned in your reference appears between t- and u- channels...
 
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  • #6
@spaghetti3451 Could you explain why you think there should be a relative minus in the first place for this process? There is no u channel process here in the case of a Z mediator.
 

Related to Relative sign in diagrams for ##Z##-boson exchange for ##WW## scattering

1. What is a relative sign in diagram for Z-boson exchange?

A relative sign in diagram for Z-boson exchange is a graphical representation of the interaction between two W-bosons (representing the weak force) via the exchange of a Z-boson. This diagram shows the relative sign of the interaction, which is determined by the coupling constants associated with the Z-boson and the W-bosons.

2. How is this diagram used in the study of WW scattering?

The relative sign in diagram for Z-boson exchange is used in the study of WW scattering because it helps to calculate the probability of this interaction occurring. By understanding the relative sign and the coupling constants involved, physicists can make predictions about the likelihood of WW scattering happening in different scenarios.

3. What information can be obtained from these diagrams?

Relative sign in diagrams for Z-boson exchange provide information about the strength and sign of the interaction between particles. They also show the spin and charge of the particles involved, which is important for understanding the behavior of the weak force.

4. How does the relative sign affect the outcome of WW scattering?

The relative sign in the diagram for Z-boson exchange plays a crucial role in the outcome of WW scattering. It determines whether the interaction is attractive or repulsive, and this affects the overall probability of the scattering event occurring. A positive relative sign between the Z-boson and W-bosons indicates an attractive interaction, while a negative sign indicates a repulsive interaction.

5. Are there any other applications of these diagrams besides WW scattering?

Yes, relative sign in diagrams for Z-boson exchange are also used in other areas of particle physics, such as in the study of weak interactions in other particle collisions. They can also be used to understand the behavior of other bosons, such as the Higgs boson. Additionally, these diagrams are important for testing the predictions of the Standard Model of particle physics.

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