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The QCD axion mass may receive contributions from small-size instantons or other Peccei-Quinn breaking effects. We show that it is possible for such a heavy QCD axion to induce slow-roll inflation if the potential is sufficiently flat near its maximum by balancing the small instanton contribution with another Peccei-Quinn symmetry breaking term. There are two classes of such axion hilltop inflation, each giving a different relation between the axion mass at the minimum and the decay constant. The first class predicts the relation $m_phi sim 10^{-6}f_phi$, and the axion can decay via the gluon coupling and reheat the universe. Most of the predicted parameter region will be covered by various experiments such as CODEX, DUNE, FASER, LHC, MATHUSLA, and NA62 where the production and decay proceed through the same coupling that induced reheating. The second class predicts the relation $m_phi sim 10^{-6} f^2_phi/M_{rm pl}$. In this case, the axion mass is much lighter than in the previous case, and one needs another mechanism for successful reheating. The viable decay constant is restricted to be $10^8,{rm GeV}lesssim f_phi lesssim 10^{10},{rm GeV}$, which will be probed by future experiments on the electric dipole moment of nucleons. In both cases, requiring the axion hilltop inflation results in the strong CP phase that is close to zero.
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The novel PQ mechanism replaces the strong CP problem with some challenges in a model building. In particular, the challenges arise regarding i) the origin of an anomalous global symmetry called a PQ symmetry, ii) the scale of the PQ symmetry breaking, and iii) the quality of the PQ symmetry. In this letter, we provide a natural and simple UV completed model that addresses these challenges. Extra quarks and anti-quarks are separated by two branes in the Randall-Sundrum ${bf R}^4 times S^1 / {bf Z}_2$ spacetime while a hidden SU($N_H$) gauge field condensates in the bulk. The brane separation is the origin of the PQ symmetry and its breaking scale is given by the dynamical scale of the SU($N_H$) gauge interaction. The (generalized) Casimir force of SU($N_H$) condensation stabilizes the 5th dimension, which guarantees the quality of the PQ symmetry.
We attempt to identify a phenomenologically viable solution to the strong $CP$ problem in which the axion is composed entirely out of Standard Model fermion species. The axion consists predominantly of the $eta$ meson with a minuscule admixture of a pseudoscalar bilinear composite of neutrinos, $eta_{ u}$. The Peccei-Quinn symmetry is an axial symmetry that acts on the up quark and the neutrino species and is spontaneously broken by the QCD condensate of quarks as well as the condensate of neutrinos triggered by chiral gravitational anomaly. The up-quark mass is spontaneously generated by the neutrino condensate which plays the role of an additional composite Higgs doublet with the compositeness scale of the order of the neutrino masses. Such a scenario is highly economical: it solves the strong $CP$ problem, generates the up-quark and neutrino masses from fermion condensates and simultaneously protects the axion shift symmetry against gravitational anomaly. The phenomenology is different from the standard hidden axion case. One of the experimental signatures is the existence of a gravity-competing isotope-dependent attractive force among nucleons at (sub)micron distances.
We study the scalar-tensor-tensor non-Gaussian signal in an inflationary model comprising also an axion coupled with SU(2) gauge fields. In this set-up, metric fluctuations are sourced by the gauge fields already at the linear level providing an enhanced chiral gravitational waves spectrum. The same mechanism is at work in generating an amplitude for the three-point function that is parametrically larger than in standard single-field inflation.
Using the well-known low-energy effective Lagrangian of QCD --valid for small (non-vanishing) quark masses and a large number of colors-- we study in detail the regions of parameter space where $CP$ is spontaneously broken/unbroken for a vacuum angle $theta= pi$. In the $CP$-broken region there are first order phase transitions as one crosses $theta=pi$, while on the (hyper)surface separating the two regions, there are second order phase transitions signaled by the vanishing of the mass of a pseudo Nambu-Goldstone boson and by a divergent QCD topological susceptibility. The second order point sits at the end of a first order line associated with the $CP$ spontaneous breaking, in the appropriate complex parameter plane. When the effective Lagrangian is extended by the inclusion of an axion these features of QCD imply that standard calculations of the axion potential have to be revised when the QCD parameters fall in the above mentioned $CP$-broken region, in spite of the fact that the axion solves the strong-$CP$ problem. These latter results could be of interest for axionic dark matter calculations if the topological susceptibility of pure Yang-Mills theory falls off sufficiently fast when temperature is increased towards the QCD deconfining transition.
We study the reasonable requirements of two anomalous $U(1)$s in a flavored-axion framework for the anomaly cancellations of both $U(1)$-mixed gravity and $U(1)_Ytimes[U(1)]^2$ which in turn determine the $U(1)_Y$ charges where $U(1)_Y$ is the hypercharge gauge symmetry of the standard model. We argue that, with a flavor symmetry group, axion-induced topology in symmetry-broken phases plays crucial roles in describing how quarks and leptons are organized at a fundamental level and make deep connections with each other. A unified model, as an example, is then proposed in a simple way to describe a whole spectrum of particles where both flavored-axion interactions with normal matter and the masses and mixings of fermions emerge from the spontaneous breaking of a given symmetry group. Once a scale of active neutrino mass defined at a seesaw scale is fixed by the commensurate $U(1)$ flavored-PQ charge of fermions, that of QCD axion decay constant $F_A$ is determined. In turn, fundamental physical parameters complementary to each other are predicted with the help of precision flavor experiments. Model predictions are extracted on the characteristics of neutrino and flavored-axion: $F_A=3.57^{,+1.52}_{,-1.53}times10^{10}$ GeV (consequently, QCD axion mass $m_a=1.52^{+1.14}_{-0.46}times10^{-4}$ eV, axion to photon coupling $|g_{agammagamma}|=2.15^{+1.61}_{-0.64}times10^{-14},text{GeV}^{-1}$, axion to electron coupling $g_{Aee}=3.29^{+2.47}_{-0.98}times10^{-14}$, etc.); atmospheric mixing angle $theta_{23}$, Dirac CP phase $delta_{CP}$, and $0 ubetabeta${it-decay rate} for normal mass ordering and inverted one by taking quantum corrections into account.
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