We propose to measure the rate Rd for muon capture on the deuteron to better than 1.5% precision. This process is the simplest weak interaction process on a nucleus that can both be calculated and measured to a high degree of precision. The measureme
nt will provide a benchmark result, far more precise than any current experimental information on weak interaction processes in the two-nucleon system. Moreover, it can impact our understanding of fundamental reactions of astrophysical interest, like solar pp fusion and the $ u+d$ reactions observed by the Sudbury Neutrino Observatory. Recent effective field theory calculations have demonstrated, that all these reactions are related by one axial two-body current term, parameterized by a single low-energy constant. Muon capture on the deuteron is a clean and accurate way to determine this constant. Once it is known, the above mentioned astrophysical, as well as other important two-nucleon reactions, will be determined in a model independent way at the same precision as the measured muon capture reaction.
