The QCD axion is an hypothetical particle introduced to solve the strong CP problem of standard model of particle physics and is of interest as a possible component of cold dark matter. In the axion scenario, J.E. Moody and F. Wilczek showed that a new macroscopic long-range force, mediated by axion exchange, acts on electron spins, and that such force can be described in terms of an effective magnetic field. The QUAX-g$_p$g$_s$ experiment, carried out at INFN Laboratori Nazionali di Legnaro, is designed to search for the effects on magnetized samples of the effective field produced by unpolarized mass sources. As this field is macroscopic, it can be detected by measuring the change of magnetization of a paramagnetic Gadolinium silicate (GSO) crystal cooled at liquid helium temperature. The axion effective field induced magnetization can be detected with a SQUID magnetometer. By varying the position of the of source masses, the induced GSO magnetization is modulated at acoustic frequencies. Although the full QUAX-g$_p$g$_s$ sensitivity has not been yet exploited, we are able to measure a magnetization of $10^{-17}~$T at few tens of Hz. With this sensitivity we expect to further improve the upper limit of the coupling of the predicted long-range force in the $10^{-3}$ to $1~$m interval.
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