Measurement of the formation rate of muonic hydrogen molecules

Abstract

Background: The rate ${\ensuremath{\lambda}}_{pp\ensuremath{\mu}}^{}$ characterizes the formation of $pp\ensuremath{\mu}$ molecules in collisions of muonic $p\ensuremath{\mu}$ 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 ${\ensuremath{\lambda}}_{pp\ensuremath{\mu}}^{}$ is required for a correct interpretation of these experiments.Purpose: Recently the MuCap experiment has measured the capture rate ${\mathrm{\ensuremath{\Lambda}}}_{\mathrm{S}}^{}$ from the singlet $p\ensuremath{\mu}$ atom, employing a low-density active target to suppress $pp\ensuremath{\mu}$ 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 ${\ensuremath{\lambda}}_{pp\ensuremath{\mu}}^{}$ 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 $pp\ensuremath{\mu}$ formation was introduced, which allowed the extraction of ${\ensuremath{\lambda}}_{pp\ensuremath{\mu}}^{}$ from the observed time distribution of decay electrons.Results: The $pp\ensuremath{\mu}$ formation rate was measured as ${\ensuremath{\lambda}}_{pp\ensuremath{\mu}}^{}=(2.01\ifmmode\pm\else\textpm\fi{}0.{06}_{\mathrm{stat}}\ifmmode\pm\else\textpm\fi{}0.{03}_{\mathrm{sys}})\ifmmode\times\else\texttimes\fi{}{10}^{6}\phantom{\rule{4pt}{0ex}}{\text{s}}^{\ensuremath{-}1}$. This result updates the ${\ensuremath{\lambda}}_{pp\ensuremath{\mu}}^{}$ value used in the abovementioned MuCap publication.Conclusions: The $2.5\ifmmode\times\else\texttimes\fi{}$ 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 ${\ensuremath{\lambda}}_{pp\ensuremath{\mu}}^{}$ to a minor contribution to the overall uncertainty of ${\mathrm{\ensuremath{\Lambda}}}_{\mathrm{S}}^{}$ and ${g}_{P}^{}$, as determined in the MuCap experiment. Our final value for ${\ensuremath{\lambda}}_{pp\ensuremath{\mu}}^{}$ shifts ${\mathrm{\ensuremath{\Lambda}}}_{\mathrm{S}}^{}$ and ${g}_{P}^{}$ by less than one-tenth of their respective uncertainties compared to our results published earlier.