Abstract
Published data on the emission of charged particles following nuclear muon capture are extremely limited. In addition to its interest as a probe of the nuclear response, these data are important for the design of some current searches for lepton flavor violation. This work presents momentum spectra of protons and deuterons following $\mu^{-}$ capture in aluminum. It is the first measurement of a muon capture process performed with a tracking spectrometer. A precision of better than 10% over the momentum range of 100--190 MeV/c for protons is obtained; for deuterons of 145--250 MeV/c the precision is better than 20%. The observed partial yield of protons with emission momenta above 80 MeV/c (kinetic energy 3.4 MeV) is $0.0322\pm0.0007(\text{stat})\pm0.0022(\text{syst})$ per capture, and for deuterons above 130 MeV/c (4.5 MeV) it is $0.0122\pm0.0009(\text{stat})\pm0.0006(\text{syst})$. Extrapolating to total yields gives $0.045\pm0.001(\text{stat})\pm0.003(\text{syst}) \pm 0.001(\text{extrapolation})$ per capture for protons and $0.018\pm0.001(\text{stat})\pm0.001(\text{syst})\pm 0.002(\text{extrapolation})$ for deuterons, which are the most precise measurements of these quantities to date.
Highlights
When a negative muon loses energy by ionization and scattering in matter it encounters the field of the nucleus and at kinetic energies below the order of 10–100 eV it can undergo atomic muon capture [1,2] forming a bound muon-nucleus state, a muonic atom
The weak interaction of the bound muon with the nucleus leads to nuclear muon capture μ− + (Z, A) → νμ + X competing with muon decay
The high momentum region has small data statistics, and is more susceptible to the bias. We addressed both of those issues by utilizing a novel unfolding method [43], which tunes the existing mathematical apparatus of unfolding to our specific task
Summary
When a negative muon loses energy by ionization and scattering in matter it encounters the field of the nucleus and at kinetic energies below the order of 10–100 eV it can undergo atomic muon capture [1,2] forming a bound muon-nucleus state, a muonic atom. Muon capture and neutrino-nucleus interaction are closely related processes. The capture process probes nuclear response in the energy range below 100 MeV, providing a valuable validation of theoretical models of importance to current and future neutrino experiments [4,5]. We consider a parametric curve (log log L(α), log |S(α)|), and use the α corresponding to the point of the maximum curvature of that curve as the optimal solution. This choice of L-curve variables for the log-likelihood fit and Tikhonov regularization corresponds to the classical L curve defined for a χ 2 unfolding [50]. For the MaxEnt regularization we explored several functions of Sand chose log |S| based on the tests with Monte Carlo samples
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