The role of angle dependent phase rotations of reaction amplitudes in $\eta$ photoproduction on protons

It was recently proved that the invariance of observables with respect to angle-dependent phase rotations of reaction amplitudes mixes multipoles, changing also their relative strength [A. Svarc et al., Phys. Rev. C 97, 054611 (2018)]. Modern partial wave analyses (PWAs) in eta photoproduction on protons in the center-of-mass energy range 1.5 <= W <= 2.0 GeV, either energy-dependent (ED) or single-energy (SE) ones, do not take this effect into consideration. It is commonly accepted that all PWAs give very similar results for the E0+ multipole, but notable differences in this and all other partial waves still remain. In this paper we demonstrate that once these phase rotations are properly taken into account, all ED and SE partial wave analysis in eta photoproduction become almost identical for the dominant E0+ multipole, and the agreement among all other multipoles becomes much better. We also show that measured observables are almost equally well reproduced in all PWAs, and the remaining differences among multipoles can be attributed solely to the difference in predictions for unmeasured observables. So, new measurements are needed.