Measurement of the Formation Rate of Muonic Hydrogen Molecules

Background: The rate lambda(pp mu) characterizes the formation of pp mu molecules in collisions of muonic p mu atoms with hydrogen. In measurements of the basic weak muon capture reaction on the proton to determine the pseudoscalar coupling g(P), capture occurs from both atomic and molecular states. Thus knowledge of lambda(pp mu) is required for a correct interpretation of these experiments. Purpose: Recently the MuCap experiment has measured the capture rate Lambda(S) from the singlet p mu atom, employing a low-density active target to suppress pp mu 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 lambda(pp mu) 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 pp mu formation was introduced, which allowed the extraction of pp mu from the observed time distribution of decay electrons. Results: The pp mu formation rate was measured as lambda(pp mu) = (2.01 +/- 0.06(stat) +/- 0.03(sys)) x 10(6) s(-1). This result updates the pp mu value used in the abovementioned MuCap publication. Conclusions: The 2.5x 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 lambda(pp mu) to a minor contribution to the overall uncertainty of Lambda(S) and g(P), as determined in the MuCap experiment. Our final value for lambda(pp mu) shifts Lambda(S) and g(P) by less than one-tenth of their respective uncertainties compared to our results published earlier.