While reading about the reconstruction of high transverse momentum muons in particle detectors I came across the following statement which I do not understand:

Showers and radiative loss account mainly for the non-Gaussian tails of momentum resolution.

I know that momentum resolution is defined as $\Delta$P/P where $\Delta$P is the width of the Gaussian distribution of the deviation of the observed value from the true value. So my question is, what does non-Gaussian tails of momentum resolution mean?

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    $\begingroup$ A proper answer would be large. Particle/matter interaction have various physical mechanisms that add up to energy loss/deposition and also scattering. The sum total of the random process are sort of Gaussian--say out to $3\sigma$, and then (in my experience) there's a power law fall off. The non Gaussian nature is used cases by rare large energy (or angle) events that are too few to let the Central Limit Th'rm kick in. For energy loss (scattering) look into the Landau Distribution (non-Gaussian tails of multiple Coulomb scattering). $\endgroup$ – JEB Feb 14 '18 at 16:42

"Non Gaussian tails" means that the deviation distribution is not Gaussian. Gaussian distribution of deviations is the usual assumption in measurements. It simplifies the definition of the measurement precision. In some cases, the real distribution of the deviations is not Gaussian. In this particular case, muon momenta are measured from the path curvature in the magnetic field of the detector. The deviation distribution is Gaussian as long as the deviations are composed of small uncorrelated fluctuations, such as coming from the precision of the tracking detector. But what happens if the muon undergoes a process that significantly alters its energy during the passage through the tracking detector? This results in a large deviation of the momentum measurement, which only extremely rarely occurs in the normal distribution. For very energetic muons such processes include synchrotron radiation in the magnetic field of the detector and showering in the detector material (such as, e.g. the support structure of the tracker).

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