A new two-body relativistic potential model for pionic hydrogen

TL;DR

This paper introduces a novel two-body relativistic potential model for pionic hydrogen, incorporating spin and magnetic effects, and uses it to evaluate pion-nucleon scattering lengths from experimental data.

Contribution

The paper develops a new relativistic two-body potential model based on an extended group symmetry to describe pionic hydrogen, including spin and magnetic effects, and extracts scattering lengths from experimental data.

Findings

Evaluated pion-nucleon scattering lengths: a_{π^- p} = 0.0860(6)m_π^{-1} and a_{π^0 n} = -0.1223(19)m_π^{-1}.

The model accurately describes the energy level shifts and widths in pionic hydrogen.

Incorporates quantum electrodynamics effects via an extended symmetry group.

Abstract

The new potential model for pionic hydrogen, constructed with the employment of the two-body relativistic equation, is offered. The relativistic equation, based on the extension of the $SL(2,C)$ group to the $Sp(4,C)$ one, describes the effect of the proton spin and anomalous magnetic moment in accordance with the results of the quantum electrodynamics. Within this approach, using the experimental data on the strong energy level shift and width of the $1s$ state in pionic hydrogen as input, the pion-nucleon scattering lengths have been evaluated to be $a_{\pi^{-}p}=0.0860(6)m_{\pi}^{-1}$ and $a_{\pi^{0}n}=-0.1223(19)m_{\pi}^{-1}$.