Improved Measurement of the $pp\mu$ Molecular Formation Rate

The MuCap experiment measures the $\mu^{-}$ lifetime in a gaseous hydrogen TPC to obtain the $\mu$p singlet capture rate $\Lambda_{S}$ by comparing it to the free $\mu^{+}$ lifetime. The motivation is a determination of the pseudoscalar coupling $g_p$ of the proton, which relates linearly to $\Lambda_{S}$. A $\mu^{-}$ atom, formed after a muon stops in the TPC, can form molecular hydrogen at the rate $\lambda_{pp\mu}$, a process that competes with muon capture. Muon capture from the molecular state is slower than from the singlet state and $\lambda_{pp\mu}$ must be known to correctly extract $\Lambda_{S}$ from the data. New results are reported on $\lambda_{pp\mu}$ based on data obtained using an argon-doped hydrogen gas, but under otherwise identical TPC conditions as the un-doped hydrogen data. Argon introduces additional atomic processes involving the muon, which are observed in the muon decay electron and the direct capture neutron time spectra. Fits to these data determine $\lambda_{pp\mu}$ to a precision that is a significant improvement to the current world average. New MuCap data will reduce $\delta\Lambda_{S}$ by a factor of two or more, making the improved measurement of $\lambda_{pp\mu}$ critical.