Testing in-medium $\pi N$ dynamics on pionic atoms

TL;DR

This paper tests a new algorithm for handling energy-dependent meson-nucleon interactions in pionic atoms, confirming the in-medium renormalization of the $ ext{b}_1$ amplitude and pion decay constant through extensive data analysis.

Contribution

It applies a novel energy dependence handling algorithm to pionic atoms, validating the in-medium modification of $ ext{b}_1$ and $f_ ext{ extpi}$ with large-scale experimental data.

Findings

Reaffirms density-dependent renormalization of $ ext{b}_1$ amplitude.

Confirms in-medium modification of pion decay constant $f_ ext{ extpi}$.

Validates the algorithm's effectiveness across diverse nuclei.

Abstract

A general algorithm for handling the energy dependence of meson-nucleon amplitudes in the nuclear medium has been recently applied to antikaons and to eta mesons. Here we test this approach on $\pi N$ amplitudes in pionic atoms where direct comparison can be made with ample experimental results. Applying this algorithm to a large-scale fit of 100 pionic-atom data points across the periodic table, which also include the `deeply-bound' states in Sn and Pb, reaffirms earlier conclusions on the density-dependent renormalization of the $\pi N$ threshold isovector amplitude $b_1$, or equivalently the renormalization of the pion decay constant $f_{\pi}$ in the nuclear medium.