Probing the emission mechanism and nature of the pulsating compact object in the X-ray binary SAX J1324.4-6200

Recently, there has been renewed interest in the Be X-ray binary (Be/XRB) SAX J1324.4-6200 because of its spatial coincidence with a variable gamma-ray source detected by Fermi/LAT. To explore more thoroughly its properties, new X-ray observations were carried out in 2023 by NuSTAR, XMM-Newton, and Swift satellites, jointly covering the energy range from 0.2 - 79 keV. SAX J1324.4-6200 was caught at an X-ray flux of similar to 10(-11) erg cm(-2) s(-1). The X-ray spectrum fits well with an absorbed power law with a high energy cutoff. Other acceptable fits require an additional blackbody component (kT(bb) approximate to 1.1 keV) or a Gaussian in absorption (E-gabs approximate to 6.9 keV). We measured a NuSTAR spin period of 175.8127 +/- 0.0036 s and an XMM-Newton spin period of 175.862 +/- 0.025 s. We show that all the available spin period measurements of SAX J1324.4-6200, spanning 29 yr, are highly correlated with time, resulting in a remarkably stable spin-down of (P) over dot = 6.09 +/- 0.06 x 10(-9) s s(-1). We find that if SAX J1324.4-6200 hosts an accretion-powered pulsar, accretion torque models indicate a surface magnetic field of similar to 10(12 - 13) G. The X-ray properties emerging from our analysis strenghten the hypothesis that SAX J1324.4-6200 belongs to the small group of persistent Be/XRBs. We also performed radio observations with the Parkes Murriyang telescope, to search for radio pulsations. However, no radio pulsations compatible with the rotational ephemeris of SAX J1324.4-6200 were detected. We rule out the hypothesis that SAX J1324.4-6200 is a gamma-ray binary where the emission is produced by interactions between the pulsar and the companion winds. Other models commonly used to account for the production of gamma-rays in accreting pulsars cannot reproduce the bright emission from SAX J1324.4-6200. We examined other possible mechanisms behind the gamma-ray emission and note that there is a similar to 0.5% chance probability that an unknown extragalactic active galactic nucleus (AGN) observed through the Galactic plane may coincidentally fall within the Fermi/LAT error circle of the source and be responsible for the gamma-ray emission.