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Register a new userIs the magnitude of the Peccei-Quinn scale set by the landscape?
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Rather general considerations of the string theory landscape imply a mild statistical draw towards large soft SUSY breaking terms tempered by the requirement of proper electroweak symmetry breaking where SUSY contributions to the weak scale are not too far from m(weak)~ 100 GeV. Such a picture leads to the prediction that m_h~ 125 GeV while most sparticles are beyond current LHC reach. Here we explore the possibility that the magnitude of the Peccei-Quinn (PQ) scale f_a is also set by string landscape considerations within the framework of a compelling SUSY axion model. First, we examine the case where the PQ symmetry arises as an accidental approximate global symmetry from a more fundamental gravity-safe Z(24)^R symmetry and where the SUSY mu parameter arises from a Kim-Nilles operator. The pull towards large soft terms then also pulls the PQ scale as large as possible. Unless this is tempered by rather severe (unknown) cosmological or anthropic bounds on the density of dark matter, then we would expect a far greater abundance of dark matter than is observed. This conclusion cannot be negated by adopting a tiny axion misalignment angle theta_i because WIMPs are also overproduced at large f_a. Hence, we conclude that setting the PQ scale via anthropics is highly unlikely. Instead, requiring soft SUSY breaking terms of order the gravity-mediation scale m_{3/2}~ 10-100 TeV places the mixed axion-neutralino dark matter abundance into the intermediate scale sweet zone where f_a~ 10^{11}-10^{12} GeV. We compare our analysis to the more general case of a generic SUSY DFSZ axion model with uniform selection on theta_i but leading to the measured dark matter abundance: this approach leads to a preference for f_a~ 10^{12} GeV.
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A scan of soft SUSY breaking parameters within the string theory landscape with the MSSM assumed as the low energy effective field theory -- using a power-law draw to large soft terms coupled with an anthropic selection of a derived weak scale to be within a factor four of our measured value -- predicts a peak probability of m_h~125 GeV with sparticles masses typically beyond the reach of LHC Run 2. Such multiverse simulations usually assume a fixed value of the SUSY conserving superpotential mu parameter to be within the assumed anthropic range, mu<~ 350 GeV. However, depending on the assumed solution to the SUSY mu problem, the expected mu term distribution can actually be derived. In this paper, we examine two solutions to the SUSY mu problem. The first is the gravity-safe-Peccei-Quinn (GSPQ) model based on an assumed Z_{24}^R discrete R-symmetry which allows a gravity-safe accidental, approximate Peccei-Quinn global symmetry to emerge which also solves the strong CP problem. The second case is the Giudice-Masiero solution wherein the mu term effectively acts as a soft term and has a linear draw to large values. For the first case, we also present the expected landscape distribution for the PQ scale f_a; in this case, weak scale anthropics limits its range to the cosmological sweet zone of around f_a~ 10^{11} GeV.
We show that, for values of the axion decay constant parametrically close to the GUT scale, the Peccei-Quinn phase transition may naturally occur during warm inflation. This results from interactions between the Peccei-Quinn scalar field and the ambient thermal bath, which is sustained by the inflaton field through dissipative effects. It is therefore possible for the axion field to appear as a dynamical degree of freedom only after observable CMB scales have become super-horizon, thus avoiding the large-scale axion isocurvature perturbations that typically plague such models. This nevertheless yields a nearly scale-invariant spectrum of axion isocurvature perturbations on small scales, with a density contrast of up to a few percent, which may have a significant impact on the formation of gravitationally-bound axion structures such as mini-clusters.
The relaxation mechanism, which solves the electroweak hierarchy problem without relying on TeV scale new physics, crucially depends on how a Higgs-dependent back-reaction potential is generated. In this paper, we suggest a new scenario in which the scalar potential induced by the QCD anomaly is responsible both for the relaxation mechanism and the Peccei-Quinn mechanism to solve the strong CP problem. The key idea is to introduce the relaxion and the QCD axion whose cosmic evolutions become quite different depending on an inflaton-dependent scalar potential. Our scheme raises the cutoff scale of the Higgs mass up to 10^7 GeV, and allows reheating temperature higher than the electroweak scale as would be required for viable cosmology. In addition, the QCD axion can account for the observed dark matter of the universe as produced by the conventional misalignment mechanism. We also consider the possibility that the couplings of the Standard Model depend on the inflaton and become stronger during inflation. In this case, the relaxation can be implemented with a sub-Planckian field excursion of the relaxion for a cutoff scale below 10 TeV.
In the Standard Model, the renormalization of the QCD vacuum angle $theta$ is extremely tiny, and small $theta$ is technically natural. In the general Standard Model effective field theory (SMEFT), however, $Deltatheta$ is quadratically divergent, reflecting the fact that new sources of hadronic CP-violation typically produce $mathcal O(1)$ threshold corrections to $theta$. The observation of such CP-violating interactions would therefore be in tension with solutions to the strong CP problem in which $theta=0$ is an ultraviolet boundary condition, pointing to the Peccei-Quinn mechanism as the explanation for why $theta$ is small in the infrared. We study the quadratic divergences in $theta$ arising from dimension-6 SMEFT operators and discuss the discovery prospects for these operators at electric dipole moment experiments, the LHC, and future proton-proton colliders.
We consider extensions of the Standard Model in which a spontaneously broken global chiral Peccei-Quinn (PQ) symmetry arises as an accidental symmetry of an exact $Z_N$ symmetry. For $N = 9$ or $10$, this symmetry can protect the accion - the Nambu-Goldstone boson arising from the spontaneous breaking of the accidental PQ symmetry - against semi-classical gravity effects, thus suppressing gravitational corrections to the effective potential, while it can at the same time provide for the small explicit symmetry breaking term needed to make models with domain wall number $N_{rm DW}>1$, such as the popular Dine-Fischler-Srednicki-Zhitnitsky (DFSZ) model ($N_{rm DW}=6$), cosmologically viable even in the case where spontaneous PQ symmetry breaking occurred after inflation. We find that $N=10$ DFSZ accions with mass $m_A approx 3.5$-$4.2,mathrm{meV}$ can account for cold dark matter and simultaneously explain the hints for anomalous cooling of white dwarfs. The proposed helioscope International Axion Observatory - being sensitive to solar DFSZ accions with mass above a few meV - will decisively test this scenario.
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