In theories with the large extra dimensions beyond the standard 4-dimensional spacetime, axions could propagate in such extra dimensions, and acquire Kaluza-Klein (KK) excitations. These KK axions are produced in the Sun and could solve unexplained heating of the solar corona. While most of the solar KK axions escape from the solar system, a small fraction is gravitationally trapped in orbits around the Sun. They would decay into two photons inside a terrestrial detector. The event rate is expected to modulate annually depending on the distance from the Sun. We have searched for the annual modulation signature using $832times 359$ kg$cdot$days of XMASS-I data. No significant event rate modulation is found, and hence we set the first experimental constraint on the KK axion-photon coupling of $4.8 times 10^{-12}, mathrm{GeV}^{-1}$ at 90% confidence level for a KK axion number density of $bar{n}_mathrm{a} = 4.07 times 10^{13}, mathrm{m}^{-3}$, the total number of extra dimensions $n = 2$, and the number of extra dimensions $delta = 2$ that axions can propagate in.
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