Can momentum be calculated to achieve a 2mm decay length for a tau particle?

Context: Graduate
Thread starter ChrisVer
Start date Jun 1, 2015
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Decay Length Momentum

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SUMMARY

The discussion centers on calculating the momentum required for a tau particle to achieve a decay length of 2mm, given its mean lifetime of 2.9 x 10^-13s. The formula presented, l_lab = t_lab u = γu t_lft, indicates that momentum (pc) can be expressed as mγu = m(l_lab/t_lft). This formula is confirmed as reasonable for the context of particle physics and tau decay calculations.

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Understanding of special relativity and Lorentz factor (γ)
Familiarity with particle decay concepts and mean lifetime
Knowledge of momentum in the context of particle physics
Basic proficiency in algebra for manipulating equations

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Jun 1, 2015

ChrisVer

Science Advisor

Hi,
I'm looking for the momentum so that the decay length of a tau (mean lifetime ##t_{lft}=2.9 \times 10^{-13}s##) can be ##2mm##.
I was wondering whether someone can use the formula I got:

[itex]l_{lab}= t_{lab} u = \gamma u t_{lft} \Rightarrow pc= m \gamma u = m \frac{l_{lab}}{t_{lft}}[/itex]?

(Looking just for a confirmation)