Estimate top quark branching ratios without calculating

AI Thread Summary
Estimating the branching ratios for the decays t → b + W → b + c anti-s and t → b + W → b + anti-tau nu(tau) requires understanding the W boson's decay modes, both leptonic and hadronic. The CKM matrix plays a crucial role, as it relates flavor eigenstates to mass eigenstates, affecting the decay probabilities. While the probability of W decaying into c anti-s is influenced by the CKM element V_cs, which is approximately 0.974, this does not imply a 95% decay probability due to other possible decay channels. The discussion highlights that the absolute probabilities are not simply derived from the CKM matrix elements, as they must account for other competing processes. Overall, a qualitative estimation must consider both the CKM matrix and the contributions from various decay modes.
ClaraBS
Messages
3
Reaction score
0

Homework Statement



Hi, I need to get an estimate of the branching ratios of the processes [/B]

t ---> b + W ---> b + c anti-s

t ---> b + W ---> b + anti-tau nu(tau)


without doing the calculations, just a qualitative estimation.
I know I have to take into account the way W decays leptonically or hadronically, but I cannot arrive to an answer.
Thanks a lot for any help.


Homework Equations

The Attempt at a Solution

 
Last edited:
Physics news on Phys.org
ClaraBS said:
I know I have to take into account the way W decays leptonically or hadronically
Well that is obvious from the problem statement.
What could lead to a deviation from a ratio of 1?
Is "c quark" a full and precise description of a quark, especially in QCD?
 
mfb said:
Is "c quark" a full and precise description of a quark, especially in QCD?

No, it is just a flavour eigenstate. I have to consider the CKM matrix relating flavour to mass eigenstates... So, given the CKM element ## V_{cs} = 0.974 ##, the probability for W to decay into c anti-s should be its square, ## 0.974^2 \approx 0.95 ## ?
But what about the leptonic channel?
 
Well, that is a contribution, but that effect is small.
What about colors?

The decay probability W->c ##\bar s## is certainly not 95%. That is just a relative value (relative to a diagonal CKM matrix).
 
It seemed to me really strange to get 95%, in fact, but I am definitely not getting the point :frown:
 
Concerning the CKM matrix: if the matrix would be diagonal (no transitions between generations), then the matrix element would be 1 for ##u \bar d##, ##c \bar s## and even for ##t \bar b##. The last one is impossible due to energy/momentum conservation of course. The "1" would just tell you that the two former decays have approximately the same probability. It does not tell you the absolute probability of any decay.
Now the matrix element does not give exactly 1. So ##c \bar s## is a bit less likely, because ##c \bar d## and ##u \bar s## can also happen.
This is a tiny effect, however - 5% difference.

What about colors? Quarks can have three different colors. For ##W \to c \bar s##, do you know which color the c quark gets? If not, do you care about it? If not, you should consider all possible cases as decay modes, and add their individual probabilities.
 
Thread 'Help with Time-Independent Perturbation Theory "Good" States Proof'
(Disclaimer: this is not a HW question. I am self-studying, and this felt like the type of question I've seen in this forum. If there is somewhere better for me to share this doubt, please let me know and I'll transfer it right away.) I am currently reviewing Chapter 7 of Introduction to QM by Griffiths. I have been stuck for an hour or so trying to understand the last paragraph of this proof (pls check the attached file). It claims that we can express Ψ_{γ}(0) as a linear combination of...
Back
Top