Measurement of the Muon Capture Rate in Hydrogen Gas and Determination of the Proton’s Pseudoscalar Coupling $g_P$

The rate of nuclear muon capture by the proton has been measured using a new technique based on a time projection chamber operating in ultraclean, deuterium-depleted hydrogen gas, which is key to avoiding uncertainties from muonic molecule formation. The capture rate from the hyperfine singlet ground state of the $\mu p$ atom was obtained from the difference between the ${\mu }^{-}$ disappearance rate in hydrogen and the world average for the ${\mu }^{+}$ decay rate, yielding ${\Lambda }_S=725.0\pm 17.4{\mathrm{s}}^{-1}$, from which the induced pseudoscalar coupling of the nucleon, $g_P(q^2=-0.88m_{\mu }^2)=7.3\pm 1.1$, is extracted.

Figure 1

Experimental and theoretical determinations of $g_P$, presented vs the ortho-para transition rate ${\lambda }_{\mathrm{op}}$ in the $p\mu p$ molecule. The most precise previous OMC experiment [10] and the RMC experiment [6] both depend significantly on the value of ${\lambda }_{\mathrm{op}}$, which itself is poorly known due to mutually inconsistent experimental (${\lambda }_{\mathrm{op}}^{\mathrm{Ex}1}$ [7], ${\lambda }_{\mathrm{op}}^{\mathrm{Ex}2}$ [8]) and theoretical (${\lambda }_{\mathrm{op}}^{\mathrm{Th}}$ [9]) results. In contrast, the MuCap result for $g_P$ is nearly independent of molecular effects.

Figure 2

Simplified cross-sectional diagram of the MuCap detector. The detector components are described in the text.

Figure 3

Lifetime spectra of negative muons. The signal-to-background ratio improves with tighter cuts on the $\mu \mathrm{\text{−}}e$ vertex.