Measurement of the Rate of Muon Capture in Hydrogen Gas and Determination of the Protons Pseudoscalar Coupling $g_P$

The rate of nuclear muon capture by the proton has been measured using a new experimental technique based on a time projection chamber operating in ultra-clean, deuterium-depleted hydrogen gas at 1 MPa pressure. The capture rate was obtained from the difference between the measured $mu^-$ disappearance rate in hydrogen and the world average for the $mu^+$ decay rate. The targets low gas density of 1% compared to liquid hydrogen is key to avoiding uncertainties that arise from the formation of muonic molecules. The capture rate from the hyperfine singlet ground state of the $mu p$ atom is measured to be $Lambda_S=725.0 pm 17.4 s^{-1}$, from which the induced pseudoscalar coupling of the nucleon, $g_P(q^2=-0.88 m_mu^2)=7.3 pm 1.1$, is extracted. This result is consistent with theoretical predictions for $g_P$ that are based on the approximate chiral symmetry of QCD.