Muon-Catalyzed Fusion Effects in the Precision Measurement of Muon Capture on the Deuteron

Abstract

The MuSun experiment will measure the rate of muon capture on the deuteron to 1.5~\% precision. This reaction is related to solar $pp$ fusion and the $\nu d$ scattering reaction at the Sudbury Neutrino Observatory through effective field theories like chiral perturbation theory. The Gamow-Teller transition in all of these processes contains a single unknown low-energy constant that determines the strength of the axial coupling to the two-nucleon system. Muon capture on the deuteron provides a precise and theoretically clean determination of this low-energy constant. The capture rate is determined by comparing the free muon lifetime to a 10~ppm measurement of the lifetime of negative muons stopped in a deuterium target. MuSun achieves this precision by tracking muons with a cryogenic time-projection chamber to ensure they stop in deuterium. This dissertation characterizes and quantifies a systematic measurement error known as fusion interference, which is a class of tracking error caused by muon-catalyzed fusion reactions following the muon stop. An efficiency difference between events with and without fusion leads to a non-exponential decay time distribution and causes a shift in the measured lifetime. The design and operation of the MuSun experiment and the data analysis procedures are summarized. A formalism is developed to describe the parameters of fusion interference and a correction procedure based on a specialized muon tracking algorithm is presented.