Measurement of Muon Capture on the Proton to 1% Precision and Determination of the Pseudoscalar Coupling $g_P$

The MuCap experiment at the Paul Scherrer Institute has measured the rate ${\Lambda }_S$ of muon capture from the singlet state of the muonic hydrogen atom to a precision of 1%. A muon beam was stopped in a time projection chamber filled with 10-bar, ultrapure hydrogen gas. Cylindrical wire chambers and a segmented scintillator barrel detected electrons from muon decay. ${\Lambda }_S$ is determined from the difference between the ${\mu }^{-}$ disappearance rate in hydrogen and the free muon decay rate. The result is based on the analysis of $1.2\times {10}^{10}$ ${\mu }^{-}$ decays, from which we extract the capture rate ${\Lambda }_S=(714.9\pm {5.4}_{\mathrm{stat}}\pm {5.1}_{\mathrm{syst}}){\mathrm{s}}^{-1}$ and derive the proton’s pseudoscalar coupling $g_P(q_0^2=-0.88m_{\mu }^2)=8.06\pm 0.55$.

Figure 1

Upper panel: (a) Cross-sectional side view of the MuCap detector showing a typical muon stop and decay electron. Lower panels: Zoomed-in special event topologies. (b) Rare large-angle $\mu \mathrm{\text{−}}p$ scatter event with $\sim {10}^{-2}/\mu$ probability. (c) Very rare delayed capture on impurity in $\mu O\to N^{*}\nu$ with $\sim 3.4\times {10}^{-6}/\mu$ probability. The interpretation of the event displays is described in the text.

Figure 2

Extracted values for $g_P$ as a function of the poorly known molecular transition rate ${\lambda }_{\mathrm{op}}$ [12, 13, 34]. In contrast to earlier experiments (OMC [11], RMC [14]), MuCap is rather insensitive to this parameter.