Revisiting the Proton-Radius Problem Using Constrained Gaussian Processes

• Activity Number: 340 - SPEED: Bayesian Methods, Part 1
• Type: Contributed
• Date/Time: Tuesday, July 30, 2019 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Shuang Zhou* and Pablo Giulani and Jorge Piekarewicz and Anirban Bhattacharya and Debdeep Pati
• Companies: Texas A&M University and Florida State University and Florida State University and TAMU and Texas A&M University
• Keywords: Proton-radius problem; shape constrained; function estimation; Nonparametric Bayes; Gaussian Processes

Abstract

The proton radius puzzle is an unanswered problem in physics relating to the size of the proton. Historically the proton radius was measured via two independent methods, which converged to a value of about 0.8768 femtometers (1 fm = 10?15 m). This value was challenged by a 2010 experiment utilizing a third method, called the muonic lamb shift experiment which produced a radius about 5% smaller than this. Although new datasets with high precision measurements confirm that the radius might actually be closer to 0.84 fm, the discrepancy stemming from the original dataset remains unresolved, and is a topic of ongoing research. In this article, we approach this problem from a novel nonparametric Bayesian function estimation perspective, with physical constraints explicitly accounted for in the estimation procedure. Our analysis of the electron-form factor measurements versus potential transfer values data confirms the value obtained from the new datasets (0.84 fm) as the radius. Incorporating the physical constraints substantially reduces the uncertainty and 95 % credible intervals obtained from our method do not contain the previous value of 0.8768 fm.