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Corrections to $\overline {S}_H ^{AR}$ in the amplitude ratio method

In this section, we investigate the possible corrections to the reduced muon stopping fraction in hydrogen $\overline {S}_H ^{AR}$ derived from the amplitude ratio, in an attempt to explain the observed energy dependence of $\overline {S}_H ^{AR}$, as well as to resolve the discrepancy with the absolute amplitude method (Section 6.5).