Pion-Mass Measurement by Crystal Diffraction of Mesonic X Rays

The energies of the $4f-3d$ atomic transitions in pionic calcium and titanium have been measured with a bent-crystal spectrometer, and were found to be 72.352±0.009 and 87.651±0.009 keV, respectively. The relationship of these transition energies to the mass of the negatively charged pion is calculated. Comparison of the measurement with the calculation yields $M_{\pi }{c}^2=139.577\mathrm{}\pm 0.013$ MeV as a new estimate of the charged-pion mass. Conservation of energy and momentum in the $\pi \to \mu +\nu$ decay process is examined, and an upper limit of 2.1 MeV (68% confidence level) is assigned to the mass of the muon neutrino. The ${\pi }^{-}$ mass measurement reported here is compared with an earlier measurement of the ${\pi }^{+}$ mass as a test of $\mathrm{CPT}$ invariance. We find $\frac{{M_{\pi }}^{+}}{{M_{\pi }}^{-}}=1.0002\mathrm{}\pm 0.0004$.