Abstract
The strong CP problem is a compelling motivation for physics beyond the Standard Model. The most popular solutions invoke a global U(1)PQ symmetry, but are challenged by quantum gravitational corrections which are thought to be incompatible with global symmetries, arguing that realistic theories contain additional structure. We explore a construction in which the U(1)PQ symmetry is protected to arbitrary order by virtue of a supersymmetric, confining SU(N)L × SU(N) × SU(N)R × U(1)X product gauge group, achieving left|overline{uptheta}right| < 10−11 for an SU(5) model with fa ≲ 3 × 1011 GeV. This construction leads to low energy predictions such as a U(1)X gauge symmetry, and for X = B − L engineers a naturally mathcal{O} (TeV) value for the μ parameter of the MSSM.
Highlights
Searches for an electric dipole moment of the neutron have so far resulted only in upper limits on its magnitude, implying that θ < 6 × 10−11 [1, 2], where θis the physically relevant combination of CP violating phases, θ = θ + arg det MQ
We explore a model with a composite axion in which an accidental Peccei-Quinn symmetry naturally emerges as a solution to the strong CP problem
Gravitational perturbations to the axion scalar potential are shown to be sufficiently suppressed in the Nc = 5 model to permit an axion decay constant of fa 3 × 1011 GeV, even under the pessimistic assumptions that supersymmetry breaking induces the most dangerous U(1)PQ-violating A-term potential, and that the higher-dimensional operators representing quantum gravitational effects are parameterized by O(1) coupling constants
Summary
A closer inspection of the simple axion model presented above reveals a new set of theoretical difficulties, namely a hierarchy problem and a fine-tuning problem. Arguments from general relativity [13,14,15,16,17,18] suggest that non-perturbative quantum gravitational effects do not respect global symmetries such as baryon number or U(1)PQ. If we assume φ ∼ O(1) is not tuned, the measured value of θ 10−11 is possible only if δV (a) satisfies Satisfying this bound requires that the theory of quantum gravity somehow produce a severe fine-tuning in the λk, such that even the dimension-12 operators in eq (1.9) must have λk 1. Smaller groups can be employed to the same effect in supersymmetric theories [20, 21], if the discrete group is an R symmetry Composite axion models such as [22,23,24] protect U(1)PQ to arbitrarily high order, with the added benefit that the axion scale fa can be generated dynamically. We explore the ability of this model to mediate supersymmetry breaking via composite messengers
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