Peccei-Quinn symmetry from a gauged discrete R symmetry

The axion solution to the strong CP problem calls for an explanation as to why the Lagrangian should be invariant under the global Peccei-Quinn (PQ) symmetry, U(1)PQ, to such a high degree of accuracy. In this paper, we point out that the U(1)PQ can indeed survive as an accidental symmetry in the low-energy effective theory, if the standard model gauge group is supplemented by a gauged and discrete R symmetry, ZR N, forbidding all dangerous operators that explicitly break the Peccei-Quinn symmetry. In contrast to similar approaches, the requirement that the ZR N symmetry be anomaly-free forces us, in general, to extend the supersymmetric standard model by new matter multiplets. Surprisingly, we find a large landscape of viable scenarios that all individually fulfill the current experimental constraints on the QCD vacuum angle as well as on the axion decay constant. In particular, choosing the number of additional multiplets appropriately, the order N of the ZR N symmetry can take any integer value larger than 2. This has interesting consequences with respect to possible solutions of the mu problem, collider searches for vectorlike quarks and axion dark matter.