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unscientific
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Homework Statement
[/B]
(a) Explain lepton universality.
(b) Explain why decay mode is forbidden and find hadronic branching ratios.
(c) Find the lifetime of tau lepton.
(d) What tau decay mode would be suitable?
(e) Find the precision.
(f) How do you improve the results?
(g) Why is it much harder to measure lifetime of muon?
Homework Equations
The Attempt at a Solution
Part(a)[/B]
For weak interactions, the coupling of leptons to gauge bosons are the same for all leptons. Thus different decay modes have the same vertex factor.
Part(b)
It is forbidden because for weak charged interactions, a tau neutrino must be produced? By universality, branching ratio to electronic decay is 18%. Thus branching ratio to hadronic decay is 64%.
Part(c)
Given that ##\Gamma \propto G_F^2 m_\tau ^5##, let us consider
[tex]\frac{\Gamma_{\left( \tau^- \rightarrow e^- + \bar {\nu_e} + \nu_\tau \right)}}{\Gamma_{\left( \mu^- \rightarrow e^- \bar{\nu_e} + \nu_\mu \right)}} = \left(\frac{m_\tau}{m_\mu}\right)^5 [/tex]
[tex]\frac{t_\mu}{t_\tau} = \left(\frac{m_\tau}{m_\mu}\right)^5[/tex]
[tex]t_\tau \approx 2 \times 10^{-12} s [/tex]
For lepton decay of tau lepton, only ##18%## decays to electronic mode.
For lepton decay of muon, it only electronic mode is possible.
Factoring in branching ratio, ##t_\tau \approx 3 \times 10^{-13} s##.
I have a feeling that this is a roundabout way to calculate the tau lepton's lifetime. Is there a more straightforward way to calculate this?
Part(d)
To achieve better tracks in a cloud chamber, the muonic decay is preferred over the electronic decay, since mass of the electron is much smaller than that of a muon. Is this right?
Part(e)
Not sure how to find the uncertainty, as we are not given the speed. Can we assume a speed of like ##\approx 100m s^{-1}##? Then the uncertainty would simply be ##10^{-8}s##.
I'm not sure on the last 2 parts..