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Register a new userA Composite Axion from a Supersymmetric Product Group
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A global $U(1)_text{PQ}$ symmetry is protected from gravitational effects in the s-confining $SU(N)^k$ product group theory with $A+4Q +Noverline{Q}$ matter. If the $SU(4)$ family symmetry is gauged and an appropriate tree-level superpotential is added, then the dynamically generated superpotential spontaneously breaks $SU(4)times U(1)_text{PQ} rightarrow SU(3)_c$ and produces a QCD axion. Small values of the $CP$-violating $theta$ parameter are then possible without any fine-tuning, as long as the product group is suitably large. By introducing a second copy of the s-confining $SU(N)$ product group also coupled to the gauged $SU(4)$, we find that values as small as $N=7$ are consistent with $bartheta<10^{-10}$, even under the pessimistic assumption that the dominant contribution to the axion quality is at tree level.
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We consider the strong dynamics associated with a composite Higgs model that simultaneously produces dynamical axions and solves the strong CP problem. The strong dynamics arises from a new $Sp$ or $SU(4)$ hypercolor gauge group containing QCD colored hyperfermions that confines at a high scale. The hypercolor global symmetry is weakly gauged by the Standard Model electroweak gauge group and an enlarged color group, $SU(N+3) times SU(N)$. When hyperfermion condensates form, they not only lead to an $SU(5)/SO(5)$ composite Higgs model but also spontaneously break the enlarged color group to $SU(3)_c times SU(N)_D$. At lower energies, the $SU(N)_D$ group confines, producing two dynamical axions that eliminates all CP violation. Furthermore, small instantons from the $SU(N)$ group can enhance the axion mass, giving rise to TeV scale axion masses that can be detected at collider experiments. Our model provides a way to unify the composite Higgs with dynamical axions, without introducing new elementary scalar fields, while also extending the range of axion masses that addresses the strong CP problem.
The strong CP problem is a compelling motivation for physics beyond the Standard Model. The most popular solutions invoke a global Peccei-Quinn 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 Peccei-Quinn symmetry is protected to arbitrary order by virtue of a supersymmetric, confining $SU(N)_L times SU(N) times SU(N)_R times U(1)_X$ product gauge group, achieving $bartheta < 10^{-11}$ for an $SU(5)$ model with $f_a lesssim 3 times 10^{11}$ GeV. This construction leads to low energy predictions such as a $U(1)_X$ gauge symmetry, and for $X = B-L$ engineers a naturally order ~TeV value for the $mu$ parameter of the MSSM.
We describe a realistic, renormalizable, supersymmetric ``quindecuplet model in which the top quark, left handed bottom quark, and up-type Higgs boson are composite, with a compositeness scale $sim 1-3$ TeV. The top-Higgs Yukawa coupling is a dynamically generated strong interaction effect, and is naturally much larger than any other Yukawa coupling. The light quark doublets and right-handed up-type quarks are also composite but at higher energies; the hierarchy of quark masses and mixings is due to a hierarchy in the compositeness scales. Flavor changing neutral currents are naturally suppressed, as is baryon number violation by Planck-scale dimension five operators. The model predicts that the most easily observable effects would be on $b$-quark physics and on the $rho$ parameter. In particular a small negative $Deltarho=-epsilon$ leads to $Delta R_b> +2epsilon$. There are effects on $B$ meson mixing and on flavor-changing neutral-current $b$-quark decays to leptons which might be detectable, but not on $brightarrow sgamma$. The model also suggests the supersymmetry-breaking mass for the right handed top squark might be considerably larger than that of the left handed top squark.
A mechanism is suggested by which the dynamics of confinement could be responsible for the fermion mass matrix. In this approach the large top quark Yukawa coupling is generated naturally during confinement, while those of the other quarks and leptons stem from non-renormalizable couplings at the Planck scale and are suppressed. Below the confinement scale(s) the effective theory is minimal supersymmetric $SU(5)$ or the supersymmetric standard model. Particles in the $bar 5$ representations of $SU(5)$ are fundamental while those in the $10$ and $5$ are composite. The standard model gauge group is weakly coupled and predictions of unification can be preserved. A hierarchy in confinement scales helps generate a hierarchical spectrum of quark and lepton masses and ensures the Kobayashi-Maskawa matrix is nearly diagonal. However, the most natural outcome is that the strange quark is heavier than the charm quark; additional structure is required to evade this conclusion. No attempt has been made to address the issues of $SU(5)$ breaking, SUSY breaking, doublet/triplet splitting or the $mu$ parameter. While the models presented here are neither elegant nor complete, they are remarkable in that they can be analyzed without uncontrollable dynamical assumptions.
Motivated by the flavored Peccei-Quinn symmetry for unifying the flavor physics and string theory, we construct an explicit model by introducing a $U(1)$ symmetry such that the $U(1)_X$-$[gravity]^2$ anomaly-free condition together with the standard model flavor structure demands additional sterile neutrinos as well as no axionic domain-wall problem. Such additional sterile neutrinos play the role of a realization of baryogenesis via a new Affleck-Dine leptogenesis. We provide grounds for that the $U(1)_X$ symmetry could be interpreted as a fundamental symmetry of nature. The model will resolve rather recent, but fast-growing issues in astro-particle physics, including leptonic mixings and CP violation in neutrino oscillation, high-energy neutrinos, QCD axion, and axion cooling of stars. The QCD axion decay constant, through its connection to the astrophysical constraints of stellar evolution and the SM fermion masses, is shown to be fixed at $F_A=1.30^{+0.66}_{-0.54}times10^{9}$ GeV (consequently, its mass is $m_a=4.34^{+3.37}_{-1.49}$ meV and axion-photon coupling is $|g_{agammagamma}|=1.30^{+1.01}_{-0.45}times10^{-12},{rm GeV}^{-1}$). Interestingly enough, we show that neutrino oscillations at low energies could be connected to astronomical-scale baseline neutrino oscillations. The model predicts non-observational neutrinoless double beta ($0 ubetabeta$) decay rate as well as a remarkable pattern between leptonic Dirac CP phase ($delta_{CP}$) and atmospheric mixing angle ($theta_{23}$); {it e.g.} $delta_{CP}simeq220^{circ}-240^{circ}$, $120^{circ}-140^{circ}$ for $theta_{23}=42.3^{circ}$ for normal mass ordering, and $delta_{CP}simeq283^{circ},250^{circ},100^{circ},70^{circ}$ for $theta_{23}=49.5^{circ}$ for inverted one.
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