Using Lepton Pair Photo-production to Determine Beam Linear Polarization and Sensitivity to Nuclear RMS Charge Radii Using the GlueX Detector at JLab

We present measurements of linear photon beam polarization and studies of nuclear RMS charge radii via Bethe-Heitler lepton pairs using the GlueX detector at Jefferson Lab. Analysis of both e⁺e⁻ and µ⁺µ⁻ pairs produced via γ ²⁰⁸Pb → ℓ⁺ℓ⁻(²⁰⁸Pb) provides complementary probes of beam polarization and nuclear charge distributions. The study utilizes data from the Charged Pion Polarizability program at Hall D, using neural nets with six multi-wire proportional chambers for µ/π separation and AI/ML techniques for e/π discrimination. Polarization measurements from azimuthal yield asymmetries in both leptonic channels agree well with triplet polarimeter measurements, with the µ⁺µ⁻ analysis representing the first ever photon beam polarimetry measurement using muons as a probe. The Q² dependence of lepton pair production provides direct sensitivity to the nuclear charge form factor, enabling RMS charge radius extraction of ²⁰⁸Pb. Comparison between electron and muon channels offers a unique test of radiative correction models under identical conditions. These complementary analyses establish a methodology for precision nuclear structure measurements, with future applications to compare electron and muon determinations of the proton charge radius.