Intermediate Scale Accidental Axion and ALPs
  We discuss the problem of constructing models containing an axion and axion-like particles, motivated by astrophysical observations, with decay constants at the intermediate scale ranging from $10^9$GeV to $10^{13}$GeV. We present examples in which the axion and axion-like particles arise accidentally as pseudo Nambu-Goldstone bosons of automatic global chiral symmetries, in models having exact discrete symmetries. 
Alex G. Dias
hep-ph