Proposal for PAC 52: Measurement of $α_-$ for $Λ\rightarrow pπ^-$
We propose to measure the weak decay constant $α_-$ for the decay $Λ\rightarrow pπ^-$ using a both circularly and linearly polarized photon beam with the GlueX spectrometer in Hall D. The measurement will take advantage of the fact that a measurement with both linear and circular photon beam polarization results in an over-constrained set of amplitudes which can be fitted to data and used to extract $α_-$ which will be left as a free parameter in the fit. We expect to determine $α_-$ with statistical uncertainties comparable to existing measurements and independent systematic uncertainties. This measurement can be performed alongside GlueX-II running and requires no new hardware or new beam time. The measurement requires that a sufficient fraction of the electron beam polarization be longitudinal in the Hall D tagger.