Serendipitous supersymmetric solution to the strong CP problem

Abstract

The Minimal Supersymmetric Standard Model (MSSM) has several problems: 1. its mu term must be forbidden, then regenerated at the weak scale, 2. it allows for R-parity violating superpotential terms which lead to rapid proton decay, 3. it allows for dimension-5 proton decay operators. The usual imposition of R- or matter parity P_M solves only the second of these, whereas anomaly-free discrete Z_n^R symmetries (consistent with grand unification) address all of them. Once the mu-term is forbidden, the MSSM develops an accidental global U(1)_{PQ} symmetry. By coupling the Higgs fields to PQ-charged gauge singlet fields X, Y (in the Kim-Nilles mechanism), and imposing SUSY breaking, one regenerates mu at the weak scale whilst breaking the discrete Z_n^R and the U(1)_{PQ}. The broken global U(1)_{PQ} develops a pseudo-Goldstone boson, the DFSZ axion, thus (perhaps inadvertently) solving the strong CP problem. In this setting, SUSY develops a dark matter candidate, the SUSY DFSZ axion, and possibly, though not necessarily, a WIMP dark matter candidate as well, depending on the order of the induced R-parity violating operators.