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

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.

Unitary and causal dynamics based on the chiral Lagrangian

“…5. The possible importance of d-wave amplitudes in the photon asymmetry was pointed out in [29] recently. Within our scheme we have no freedom to significantly increase the asymmetry without destroying the successful description of the photoproduction multipoles at higher energies.…”

Impact of the Delta (1232) resonance in neutral pion photoproduction in chiral perturbation theory.

“…So far we are yet to see any significant change between the three calculations so it appears that D-waves do not play a significant role. This might change with data on other observables more sensitive to higher order partial waves [3].…”

“…They concluded that both theories fail to describe the process beyond energies of E γ ≈ 170 MeV. Two explanations have been suggested for these failures: the need for the ∆(1232) to be included as a degree of freedom; and the possibility that D-waves (or higher) have a greater impact on observables than expected [3]. It should not come as a surprise that the ∆(1232) is required when studying photoproduction well beyond threshold, as the mass difference between it and the nucleon is not large,…”

“…This data has reached unprecedented levels of accuracy from threshold through to the ∆ resonance. Accompanying the experimental work, there has also been a series of publications studying the theory that show that, to go beyond an energy of E γ = 170 MeV, it is necessary to include other aspects, in particular the ∆(1232) as a degree of freedom [2] and possibly higher partial waves [3]. …”

Threshold neutral pion photoproduction off the tri-nucleon to O(q4)

“…We therefore give only a rough estimate of this uncertainty. The extractions of the proton S-wave photoproduction amplitude based on CHPT using various approximations [24] lead to an uncertainty ∆E π 0 p 0+ ≈ ±0.05 × 10 −3 /M π + , which is about 5%. The uncertainty of the neutron S-wave threshold amplitude is estimated to be the same.…”