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We have carried out exclusive measurements for the photoproduction of an$\eta$ meson from a proton target with an egg-shaped calorimeter made of BGOcrystals (BGOegg) and forward charged-particle detectors at the SPring-8 LEPS2beamline. The differential cross sections and photon beam asymmetries of the$\gamma p \to \eta p$ reaction are measured in a center-of-mass energy ($W$)range of $1.82$-$2.32$ GeV and a polar angle range of $-1.0 <\cos{\theta^{\eta}_{\mathrm{c.m.}}} < 0.6$. The reaction is identified byselecting a proton and two $\gamma$'s produced by an $\eta$-meson decay. Thekinematic fit method was employed to select the reaction candidate with theconfidence level larger than $1$\%. A bump structure at $W$ = $2.0$-$2.3$ GeVin the differential cross section is confirmed at extremely backward $\eta$polar angles, where the existing data are inconsistent with each other. Thisbump structure is likely associated with high-spin resonances that couple with$s\bar{s}$ quarks. The results of the photon beam asymmetries in a wide $\eta$polar angle range are new for the photon beam energies exceeding $2.1$ GeV.These results are not reproduced by the existing partial wave analyses. Theyprovide an additional constraint to nucleon resonance studies at high energies.

Differential cross sections and photon beam asymmetries of $\eta$ photoproduction on the proton at $E_\gamma$ = 1.3-2.4 GeV