3.1 Quark Mixing & Cabibbo theory Flashcards
What three problems were observed wrt the standard model?
- Strangeness. ΔS = 1 transitions were surpressed relative to ΔS = 0
- Coupling factor in the beta decay was different to the muon decay
- No FCNC
What was Cabibbo’s proposal?
He suggested that the state observed by the W was not equivalent to the state of definite flavour
What did Cabibbo suggest the W coupled with the same strength to?
The electron, muon and d’
d’ = dcos(theta) + s sin(theta)
theta = cabibbo angle
What is the d’?
A mix of the d and the s quark = quark mixing
d’ = dcos(theta) + s sin(theta)
theta = cabibbo angle = mixing angle
How does the Cabibbo d’ solve the problem of the different strangeness transitions probability?
The quark mixing weighs the vertices differently
- ΔS = 1 you have a sin(theta)
- ΔS = 0 you have a cos(theta)
What is the cabibbo angle equal to?
13 degrees - true for any ΔS = 1 transition
What other problem did the Cabibbo theory solve apart from the strangeness one?
Predicted the change in probability in the coupling factor for the beta decay and muon decay
In which two places did Cabibbo theory fail?
It says the rate of the Z0 decaying into u u bar, d dbar, s s bar is now different
- Also says that FCNC can exist
How was the Cabibbo problem of the FCNC and the Z0 decay fixed?
A solution was proposed that the weak interaction sees a new state, s’ that is orthogonal to d’
How is the weak space related to flavour space?
d’ = cos(Θ) sin(Θ) d
s’ = -sin(Θ) cos(Θ) s
Weak space = 2D rotation matrix and flavour space
What did the amendment to Cabibbo theory predict?
The charm quark
- An extra quark with weak isospin of 1/2 to couple to the s’
How did the charm quark solve the FCNC problem?
There was no probability for a cross generation transition
- Probability for all the decays was now equal from the Z0
How does the W couple to quarks within the weak basis?
It couples WITHIN the generation
- All with the same strength
