Proposal for PAC 52: Measurement of $\alpha_-$ for $\Lambda\rightarrow p\pi^-$

TL;DR

This paper proposes a method to measure the weak decay constant alpha_- for Lambda decay using polarized photon beams at GlueX, aiming for precise results without additional hardware or beam time.

Contribution

It introduces a novel measurement approach utilizing both linear and circular photon polarization to extract alpha_- with minimal additional resources.

Findings

Expected statistical uncertainties comparable to existing measurements

Independent systematic uncertainties achieved

Feasibility of measurement during GlueX-II without new hardware

Abstract

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.