Bounds on QCD axion mass and primordial magnetic field from CMB
  $\mu$-distortion
  The oscillation of the CMB photons into axions can cause CMB spectral
distortion in the presence of large scale magnetic field. With the COBE limit
on the $\mu$ parameter and a homogeneous magnetic field with strength
$B\lesssim 3.2$ nG at the horizon scale, an upper limit on the axion mass is
found to be, $m_a\lesssim 4.8\times 10^{-5}$ eV for the KSVZ axion model. On
the other hand, using the value of excluded axion mass $m_a\simeq 3.5\times
10^{-6}$ eV from the ADMX experiment together with the COBE bound on $\mu$, is
found $B\simeq 46$ nG for the KSVZ axion model and $B\simeq 130$ nG for DFSZ
axion model, for a homogeneous magnetic field with coherence length at the
present epoch $\lambda_B\simeq 1.3$ Mpc. Forecast on $B$ and $m_a$ for
PIXIE/PRISM expected sensitivity on $\mu$ are derived. If CMB $\mu$ distortion
would be detected by the future space missions PIXIE/PRISM and assuming that
the strength of the large scale magnetic field is close to its canonical value,
$B\simeq 1-3$ nG, axions in the mass range $2\, \mu$eV - $3\, \mu$eV would be
potential candidates of CMB $\mu$-distortion.
