Extraction of $\gamma n\to\pi N$ observables from deuteron-target data

TL;DR

This paper analyzes the extraction methods of gamma-neutron to pion-nucleon observables from deuteron-target data, highlighting the importance of invariant mass cuts and FSI corrections for accurate results.

Contribution

It demonstrates that imposing a cut on the final $ ext{W}$ effectively reduces distortions caused by nucleon Fermi motion in the extraction process.

Findings

Using invariant mass cuts improves the accuracy of extracted observables.

Kinematical cuts still require FSI corrections for precise cross sections.

Provides qualitative explanation of FSI effects in recent experiments.

Abstract

An examination is conducted on a commonly used procedure for extracting (un)polarized $\gamma n\to \pi^-p$ and $\gamma n\to \pi^0n$ observables from $d(\gamma,\pi^-)pp$ and $d(\gamma,\pi^0)pn$ data, using a model that consists of the impulse term and the final-state interaction (FSI) terms due to nucleon- and pion-exchange. Recent experimental and theoretical analyses used an extraction method that does not impose a cut on the final $\pi N$ invariant mass $W$. I demonstrate that the use of this method can result in the $\gamma n\to \pi N$ observables that are seriously distorted by the nucleon Fermi motion, and that one can efficiently avoid this problem by imposing a cut on $W$. It is also shown that the use of kinematical cuts of recent experimental analyses can still leave in the selected samples substantial FSI effects that must be corrected in extracting the $\gamma n \to\pi N$ cross sections. In terms of the nucleon- and pion-exchange mechanisms, I give the first qualitative explanation of the FSI corrections, obtained in a recent MAMI experiment, for extracting $\gamma n\to \pi^0 n$ cross sections.