The charged and neutral pion masses revisited

Results from neutrino mass and oscillation experiments now set the mass of the muon neutrino to less than 2 eV/c(2). This fact, together with our former measurement of the muon momentum in pion decay at rest, p(mu)+ = (29.792 00 +/- 0.000 11) MeV/c, allows us to directly determine the charged pion mass with 1 ppm precision which constitutes the most precise value of the charged pion mass to date, m(pi)+ = (139.570 21 +/- 0.000 14) MeV/c(2). This value is within 1.44 sigma of the Particle Data Group's compilation of the charged pion mass value, m(pi)+ = (139.570 61 +/- 0.000 24) MeV/c(2). From p(mu)+ we derive the kinetic energy of the muon, T-mu+ = (4.119 84 +/- 0.000 03) MeV and the mass difference, m(pi)+ -m(mu)+ = (33.911 84 +/- 0.000 14) MeV/c(2). From our new m(pi)+ value, assuming CPT invariance (m(pi)- = m(pi)+) and our measured mass difference D-pi = m(pi)- -m(pi)0 = (4.593 64 +/- 0.000 48) MeV/c(2) we obtain a new value for the neutral pion mass, m(pi)0 = (134.976 57 +/- 0.000 50) MeV/c(2). One also obtains a new quantitative measure of CPT invariance in the pion sector: (m(pi)+ - m(pi)-)/m(pi)(av) = (-2.9 +/- 2.0) . 10(-6), an improvement by two orders of magnitude. (C) 2019 The Authors. Published by Elsevier B.V.