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Contributions of $D$ waves to physical observables for neutral pionphotoproduction from the proton in the near-threshold region are studied andmeans to isolate them are proposed. Various approaches to describe themultipoles are employed  --a phenomenological one, a unitary one, and heavy baryon chiral perturbationtheory. The results of these approaches are compared and found to yieldessentially the same answers. $D$ waves are seen to enter together with $S$waves in a way that any means which attempt to obtain the $E_{0+}$ multipoleaccurately must rely on knowledge of $D$ waves and that consequently the lattercannot be dismissed in analyses of low-energy pion photoproduction. It is shownthat $D$ waves have a significant impact on double-polarization observablesthat can be measured. This importance of $D$ waves is due to the soft nature ofthe $S$ wave and is a direct consequence of chiral symmetry and theNambu--Goldstone nature of the pion. $F$-wave contributions are shown to benegligible in the near-threshold region.

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