Search for Galactic axions with a high- <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>Q</mml:mi></mml:math> dielectric cavity

A haloscope of the QUAX--$a\gamma$ experiment, composed of an high-Q resonant cavity immersed in a 8 T magnet and cooled to $\sim 4.5$~K is operated to search for galactic axion with mass $m_a\simeq42.8~\mu\text{eV}$. The design of the cavity with hollow dielectric cylinders concentrically inserted in a OFHC Cu cavity, allowed us to maintain a loaded quality-factor Q $\sim 300000$ during the measurements in presence of magnetic field. Through the cavity tuning mechanism it was possible to modulate the resonance frequency of the haloscope in the region $10.35337-10.35345$~GHz and thus acquire different dataset at different resonance frequencies. Acquiring each dataset for about 50 minutes, combining them and correcting for the axion's signal estimation-efficiency we set a limit on the axion-photon coupling $g_{a\gamma\gamma}<0.731\times10^{-13}$ GeV$^{-1}$ with the confidence level set at $90\%$.