  We propose to measure the weak decay constant $\alpha_-$ for the decay
$\Lambda\rightarrow p\pi^-$ 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 $\alpha_-$ which will be left as a free
parameter in the fit. We expect to determine $\alpha_-$ 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.
