Unexpected impact of D waves in low-energy neutral pion photoproduction from the proton and the extraction of multipoles

TL;DR

This paper investigates the significant role of D waves in low-energy neutral pion photoproduction from the proton, revealing their impact on observables and the extraction of multipoles, with implications for theoretical models and experimental measurements.

Contribution

It demonstrates that D waves are essential in analyzing low-energy pion photoproduction and must be considered for accurate multipole extraction, challenging previous dismissals.

Findings

D waves significantly affect double-polarization observables

Different theoretical approaches agree on D wave contributions

F waves are negligible near threshold

Abstract

Contributions of $D$ waves to physical observables for neutral pion photoproduction from the proton in the near-threshold region are studied and means to isolate them are proposed. Various approaches to describe the multipoles are employed --a phenomenological one, a unitary one, and heavy baryon chiral perturbation theory. The results of these approaches are compared and found to yield essentially the same answers. $D$ waves are seen to enter together with $S$ waves in a way that any means which attempt to obtain the $E_{0+}$ multipole accurately must rely on knowledge of $D$ waves and that consequently the latter cannot be dismissed in analyses of low-energy pion photoproduction. It is shown that $D$ waves have a significant impact on double-polarization observables that can be measured. This importance of $D$ waves is due to the soft nature of the $S$ wave and is a direct consequence of chiral symmetry and the Nambu--Goldstone nature of the pion. $F$-wave contributions are shown to be negligible in the near-threshold region.