Likelihood and Correlation Analysis of Compton Form Factors for Deeply Virtual Exclusive Scattering on the Nucleon

TL;DR

This paper develops a likelihood-based method to analyze Compton form factors in deeply virtual exclusive scattering, using unpolarized data from Jefferson Lab, to better understand the underlying QCD processes and improve the precision of form factor extraction.

Contribution

It introduces a joint likelihood approach for extracting Compton form factors from experimental data, incorporating twist-two and twist-three corrections, and employs MCMC for uncertainty quantification.

Findings

Likelihood method constrains three CFFs with unpolarized data.

Inclusion of twist-three corrections impacts form factor estimates.

Proposed techniques can reduce error bars in future analyses.

Abstract

A likelihood analysis of the observables in deeply virtual exclusive photoproduction off a proton target, $ep \rightarrow e' p' \gamma'$, is presented. Two processes contribute to the reaction: deeply virtual Compton scattering, where the photon is produced at the proton vertex, and the Bether-Heitler process, where the photon is radiated from the electron. We consider the unpolarized process for which the largest amount of data with all the kinematic dependences are available from corresponding datasets with unpolarized beams and unpolarized targets from Jefferson Lab. We provide and use a method which derives a joint likelihood of the Compton form factors, which parametrize the deeply virtual Compton scattering amplitude in QCD, for each observed combination of the kinematic variables defining the reaction. The unpolarized twist-two cross section likelihood fully constrains only three of the Compton form factors (CFFs). The impact of the twist-three corrections to the analysis is also explored. The derived likelihoods are explored using Markov chain Monte Carlo (MCMC) methods. Using our proposed method we derive CFF error bars and covariances. Additionally, we explore methods which may reduce the magnitude of error bars/contours in the future.