Likelihood \& Correlation Analysis of $π^o$ Electroproduction for Proton Tensor Charge Extraction

Abstract

We present a likelihood analysis of observables in deeply virtual exclusive $π^o$ electro-production off the proton. We use experimental data for the cross section as well as the beam and target spin asymmetries measured in various longitudinal polarization configurations at Jefferson Lab Hall A and Hall B. Performing a local extraction, for each kinematic bin, we derive a joint likelihood for the various helicity amplitudes defining the different polarization configurations. We subsequently extract the Compton form factors that parameterize the underlying QCD scattering amplitudes in the chiral-odd sector. Markov chain Monte Carlo (MCMC) methods are employed to explore the full parameter space, extracting the parameter uncertainties, correlations and credible intervals. The joint likelihood analysis of the cross-section and asymmetry data constrains the parameter space indicating that a larger kinematic coverage and additional polarization configurations, {\it e.g.} in the transverse sector, will improve the precision of the parameters. We also report a determination of the proton tensor charge and tensor anomalous magnetic moment extracted in a Bayesian statistical framework using deeply virtual exclusive scattering data.