Muon-Capture Rates in Deuterium and the Weak Form Factors in the Timelike Region

The rates for muon capture in deuterium from the doublet and quartet states are calculated by the use of the elementary-particle treatment. The matrix elements of the vector and axial-vector currents are each constructed in terms of two independent form factors. The form factors describing the matrix element of the vector current are obtained in the spacelike region from electrodistintegration and photodisintegration data by the use of the conserved-vector-current hypothesis. The form factors describing the matrix element of the axial-vector current are obtained in the spacelike region by the use of the hypothesis of partial conservation of axial-vector current and arguments based on the impulse approximation. The capture rates are found to be sensitive to the behavior of the form factors near q²=-m_μ². The capture rates are from the doublet and quartet states are found to be Γd=374±18 sec^-1 and Γq=6.07±0.04 sec^-1. It is shown that 25.6% of the contribution to Γd comes from the timelike region and that an analytic continuation of the dipole fit for the form factors to the timelike region from the spacelike region is consistent with experimental data.