Grand unification and heavy axion

We argue that sufficiently complex grand unified theories involving extra strong intractions that confine at very short distances, may lead to a heavy axion solution of the CP problem of QCD. This axion may have a mass within accessible energy range, and its low energy interactions emerge through mixing with axial Higgs boson(s). Another signature of this scenario is softly broken Peccei—Quinn symmetry in the electroweak Higgs sector. We present a toy GUT exhibiting these features. In QCD, the effective θ-parameter θ̄ = θ + arg detMquark breaks CP [1] and is experimentally constrained to be unnaturally small, θ̄ ∼< 10 (for reviews see, e.g., ref. [2]). An elegant solution to this strong CP problem is based on the Peccei— Quinn (PQ) symmetry [3] and predicts a light particle, axion. In view of constraints from experimental searches for the Weinberg—Wilczek [4] axion, a widely accepted option is an extremely light invisible axion [5]. A potential problem with the latter comes from possible non-renormalizable terms in the low energy Lagrangian which may be due to very high (say, Planckian) scales and need not respect PQ symmetry [6]. Negligible for other purposes, these terms would introduce extra axion potential and ruin the Peccei—Quinn mechanism precisely because the QCD contribution into the axion potential is tiny. From this point of view it is more safe to have axion heavy enough.