What's the limit for half-time measurement in CMS or other detectors? I've been working with data from $\mu^+ \bar{nu_\mu} $ detections. I noticed one can't determine the mass width of a particle that produces neutrinos.
Then it occurred to me how one can measure the half-life of particles that produces neutrinos and the answer, at least for $\tau$ half-life was to determine fly time before it decayed. This blowed my mind since the fly time is so short.
Then I asked if this was also possible for other particles that produce neutrinos, like the $W$ boson. But it turns out its half-life is way too small for this kind of measurement. I know that for W bosons width can be measured in other decay modes.
So the question is, where is the lower limit for particle's half-life that can be measured from flight time in the detector? Is there any other short lived particle that is measured like this (I guess $\mu$ is measured like this)?
 A: Every experiment is going to have a different capability for measuring the lifetime (see note at bottom) of a given particle via its average flight distance. A good way to estimate a given experiment's ability to measure this is to compute or look up

*

*the average flight distance of the (real or hypothetical) particle at the experiment given the center-of-mass energy of its collisions and the particle's production mechanism

*the flight distance resolution of the experiment, often published in a design paper and their updates. Note that there might be some differences in experiments' terminology or the types of resolutions they publish, depending on its characteristics.

Then a very rough estimate of the measureability of the light distance by the experiment is the ratio of these two quantities (average flight distance divided by flight distance resolution)
Note on some lingo: particle physicists almost always refer to the lifetime $\tau$ of the particle, which is longer than its half-life by a factor of $1/\ln{2}$, or about 1.44:
$$
e^{-t/\tau} = \left( \frac{1}{2} \right)^{t/t_h} = e^{-t/(t_h/\ln{2})}
$$
