  Axion-like particles (ALPs) can be produced by thermal processes in a stellar
interior, escape from the star and, if sufficiently light, be converted into
photons in the external Galactic magnetic field. Such a process could produce a
detectable hard X-ray excess in the direction of the star. In this scenario, a
promising class of targets is the red supergiants, massive stars which are
experiencing the late part of their evolution. We report on a search for
ALP-induced X-ray emission from Betelgeuse, produced via the combined processes
of Bremsstrahlung, Compton and Primakoff. Using a 50 ks observation of
Betelgeuse by the \emph{NuSTAR} satellite telescope, we set 95\% C.L. upper
limits on the ALP-electron ($g_{ae}$) and ALP-photon ($g_{a\gamma}$) couplings.
For masses ${m_{a}\leq(3.5-5.5)\times10^{-11}}$ eV, we find $g_{a\gamma} \times
g_{ae}< (0.4-2.8)\times10^{-24}$ GeV$^{-1}$ (depending on the stellar model and
assuming a value of the regular Galactic magnetic field in the direction
transverse to Betelgeuse of $B_T$=1.4 $\mu$G). This corresponds to
${g_{ae}<(0.4-2.8) \times10^{-12}}$ for ${g_{a\gamma}>1.0\times10^{-12}}$
GeV$^{-1}$. This analysis supercedes by over an order of magnitude the limit on
$g_{ae} \times g_{a\gamma}$ placed by the CAST solar axion experiment and is
among the strongest constraints on these couplings.
