Using the TWIST spectrometer, the authors measured proton and deuteron momentum spectra from muon capture on aluminum, obtaining partial yields of 0.0322 and 0.0122 per capture above 80 and 130 MeV/c, respectively.
A practical way to regularize unfolding of sharply varying spectra with low data statistics
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abstract
Unfolding is a well-established tool in particle physics. However, a naive application of the standard regularization techniques to unfold the momentum spectrum of protons ejected in the process of negative muon nuclear capture led to a result exhibiting unphysical artifacts. A finite data sample limited the range in which unfolding can be performed, thus introducing a cutoff. A sharply falling "true" distribution led to low data statistics near the cutoff, which exacerbated the regularization bias and produced an unphysical spike in the resulting spectrum. An improved approach has been developed to address these issues and is illustrated using a toy model. The approach uses full Poisson likelihood of data, and produces a continuous, physically plausible, unfolded distribution. The new technique has a broad applicability since spectra with similar features, such as sharply falling spectra, are common.
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Charged particle spectra from $\mu^{-}$ capture on Al
Using the TWIST spectrometer, the authors measured proton and deuteron momentum spectra from muon capture on aluminum, obtaining partial yields of 0.0322 and 0.0122 per capture above 80 and 130 MeV/c, respectively.