Measurement of the Formation Rate of Muonic Hydrogen Molecules

Background: The rate λppμ characterizes the formation of ppμ molecules in collisions of muonic pμ atoms with hydrogen. In measurements of the basic weak muon capture reaction on the proton to determine the pseudoscalar coupling gP, capture occurs from both atomic and molecular states. Thus knowledge of λppμ is required for a correct interpretation of these experiments. Purpose: Recently the MuCap experiment has measured the capture rate ΛS from the singlet pμ atom, employing a low-density active target to suppress ppμ formation [V. Andreev et al. (MuCap Collaboration), Phys. Rev. Lett. 110, 012504 (2013)]. Nevertheless, given the unprecedented precision of this experiment, the existing experimental knowledge in λppμ had to be improved. Method: The MuCap experiment derived the weak capture rate from the muon disappearance rate in ultrapure hydrogen. By doping the hydrogen with 20 ppm of argon, a competing process to ppμ formation was introduced, which allowed the extraction of λppμ from the observed time distribution of decay electrons. Results: The ppμ formation rate was measured as λppμ=(2.01±0.06stat±0.03sys)×106s−1. This result updates the λppμ value used in the abovementioned MuCap publication. Conclusions: The 2.5× higher precision compared to earlier experiments, and the fact that the measurement was performed under nearly identical conditions as the main data taking, reduces the uncertainty induced by λppμ to a minor contribution to the overall uncertainty of ΛS and gP, as determined in the MuCap experiment. Our final value for λppμ shifts ΛS and gP by less than one-tenth of their respective uncertainties compared to our results published earlier