Line shape analysis of the K$\beta$ transition in muonic hydrogen

TL;DR

This study measures the Kβ transition in muonic hydrogen with high-resolution spectroscopy, revealing details about hyperfine splitting, triplet-to-singlet ratio, and kinetic energy distribution, confirming theoretical expectations.

Contribution

It provides a detailed analysis of the Kβ transition in muonic hydrogen, including the first quantification of high-energy components using Bayesian deconvolution.

Findings

Hyperfine splitting and triplet-to-singlet ratio match theoretical predictions.

High-energetic components are present in the kinetic energy distribution.

Both phenomenological and Bayesian methods confirm the kinetic energy features.

Abstract

The K$\beta$ transition in muonic hydrogen was measured with a high-resolution crystal spectrometer. The spectrum is shown to be sensitive to the ground-state hyperfine splitting, the corresponding triplet-to-singlet ratio, and the kinetic energy distribution in the $3p$ state. The hyperfine splitting and triplet-to-singlet ratio are found to be consistent with the values expected from theoretical and experimental investigations and, therefore, were fixed accordingly in order to reduce the uncertainties in the further reconstruction of the kinetic energy distribution. The presence of high-energetic components was established and quantified in both a phenomenological, i.e. cascade-model-free fit, and in a direct deconvolution of the Doppler broadening based on the Bayesian approach.