Search for invisible axion dark matter of mass m$_a=43~\mu$eV with the QUAX--$a\gamma$ experiment

A haloscope of the QUAX--$a\gamma$ experiment composed of an oxygen-free high thermal conductivity-Cu cavity inside an 8.1 T magnet and cooled to $\sim200$ mK is put in operation for the search of galactic axion with mass $m_a\simeq43~\mu\text{eV}$. The power emitted by the resonant cavity is amplified with a Josephson parametric amplifier whose noise fluctuations are at the standard quantum limit. With the data collected in about 1 h at the cavity frequency $\nu_c=10.40176$ GHz, the experiment reaches the sensitivity necessary for the detection of galactic QCD-axion, setting the $90\%$ confidence level limit to the axion-photon coupling $g_{a\gamma\gamma}<0.639\times10^{-13}$ GeV$^{-1}$.
Comment: 7 pages, 6 figures. Analysis method changed. The result is almost left unchanged. Consequently, text has been revised in the Analysis section. Added references. Added equations (2), (4), (5)