The Quest for an Intermediate-Scale Accidental Axion and Further ALPs
  The recent detection of the cosmic microwave background polarimeter
experiment BICEP2 of tensor fluctuations in the B-mode power spectrum basically
excludes all plausible axion models where its decay constant is above $10^{13}$
GeV. Moreover, there are strong theoretical, astrophysical, and cosmological
motivations for models involving, in addition to the axion, also axion-like
particles (ALPs), with decay constants in the intermediate scale range, between
$10^9$ GeV and $10^{13}$ GeV. Here, we present a general analysis of models
with an axion and further ALPs and derive bounds on the relative size of the
axion and ALP photon (and electron) coupling. We discuss what we can learn from
measurements of the axion and ALP photon couplings about the fundamental
parameters of the underlying ultraviolet completion of the theory. For the
latter we consider extensions of the Standard Model in which the axion and the
ALP(s) appear as pseudo Nambu-Goldstone bosons from the breaking of global
chiral $U(1)$ (Peccei-Quinn (PQ)) symmetries, occuring accidentally as low
energy remnants from exact discrete symmetries. In such models, the axion and
the further ALP are protected from disastrous explicit symmetry breaking
effects due to Planck-scale suppressed operators. The scenarios considered
exploit heavy right handed neutrinos getting their mass via PQ symmetry
breaking and thus explain the small mass of the active neutrinos via a seesaw
relation between the electroweak and an intermediate PQ symmetry breaking
scale. We show some models that can accommodate simultaneously an axion dark
matter candidate, an ALP explaining the anomalous transparency of the universe
for $\gamma$-rays, and an ALP explaining the recently reported 3.55 keV gamma
line from galaxies and clusters of galaxies, if the respective decay constants
are of intermediate scale.
