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Register a new userPoincare recurrence theorem and the strong CP-problem
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The existence in the physical QCD vacuum of nonzero gluon condensates, such as $<g^2F^2>$, requires dominance of gluon fields with finite mean action density. This naturally allows any real number value for the unit ``topological charge $q$ characterising the fields approximating the gluon configurations which should dominate the QCD partition function. If $q$ is an irrational number then the critical values of the $theta$ parameter for which CP is spontaneously broken are dense in $mathbb{R}$, which provides for a mechanism of resolving the strong CP problem simultaneously with a correct implementation of $U_{rm A}(1)$ symmetry. We present an explicit realisation of this mechanism within a QCD motivated domain model. Some model independent arguments are given that suggest the relevance of this mechanism also to genuine QCD.
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We derive sufficient conditions that guarantee a robust solution of the strong CP problem in theories with spontaneous CP violation, and introduce a class of models satisfying these requirements. In the simplest scenarios the dominant contribution to the topological angle arises at 3-loop order in the Yukawa couplings. A variety of realizations are possible on a warped extra dimension, which can simultaneously address the Planck-TeV hierarchy. Experimental signatures of this approach to the strong CP problem include flavor violation and vector-like partners of the top or bottom quarks.
Current upper bounds of the neutron electric dipole moment constrain the physically observable quantum chromodynamic (QCD) vacuum angle $|bartheta| lesssim 10^{-11}$. Since QCD explains vast experimental data from the 100 MeV scale to the TeV scale, it is better to explain this smallness of $|bartheta|$ in the QCD framework, which is the strong CaPa problem. Now, there exist two plausible solutions to this problem, one of which leads to the existence of the very light axion. The axion decay constant window, $10^9 {gev}lesssim F_alesssim 10^{12} gev$ for a ${cal O}(1)$ initial misalignment angle $theta_1$, has been obtained by astrophysical and cosmological data. For $F_agtrsim 10^{12}$ GeV with $theta_1<{cal O}(1)$, axions may constitute a significant fraction of dark matter of the universe. The supersymmetrized axion solution of the strong CaPa problem introduces its superpartner the axino which might have affected the universe evolution significantly. Here, we review the very light axion (theory, supersymmetrization, and models) with the most recent particle, astrophysical and cosmological data, and present prospects for its discovery.
Many meson processes are related to the U_A(1) axial anomaly, present in the Feynman graphs where fermion loops connect axial vertices with vector vertices. However, the coupling of pseudoscalar mesons to quarks does not have to be formulated via axial vertices. The pseudoscalar coupling is also possible, and this approach is especially natural on the level of the quark substructure of hadrons. In this paper we point out the advantages of calculating these processes using (instead of the anomalous graphs) the graphs where axial vertices are replaced by pseudoscalar vertices. We elaborate especially the case of the processes related to the Abelian axial anomaly of QED, but we speculate that it seems possible that effects of the non-Abelian axial anomaly of QCD can be accounted for in an analogous way.
We construct a theory in which the solution to the strong CP problem is an emergent property of the background of the dark matter in the Universe. The role of the axion degree of freedom is played by multi-body collective excitations similar to spin-waves in the medium of the dark matter of the Galactic halo. The dark matter is a vector particle whose low energy interactions with the Standard Model take the form of its spin density coupled to $G widetilde{G}$, which induces a potential on the average spin density inducing it to compensate $overline{theta}$, effectively removing CP violation in the strong sector in regions of the Universe with sufficient dark matter density. We discuss the viable parameter space, finding that light dark matter masses within a few orders of magnitude of the fuzzy limit are preferred, and discuss the associated signals with this type of solution to the strong CP problem.
For all the success of the Standard Model (SM), it is on the verge of being surpassed. In this regard we argue, by showing a minimal flavor-structured model based on the non-Abelian discrete $SL_2(F_3)$ symmetry, that $U(1)$ mixed-gravitational anomaly cancellation could be of central importance in constraining the fermion contents of a new chiral gauge theory. Such anomaly-free condition together with the SM flavor structure demands a condition $k_1,X_1/2=k_2,X_2$ with $X_i$ being a charge of $U(1)_{X_i}$ and $k_i$ being an integer, both of which are flavor dependent. We show that axionic domain-wall condition $N_{rm DW}$ with the anomaly free-condition depends on both $U(1)_X$ charged quark and lepton flavors; the seesaw scale congruent to the scale of Peccei-Quinn symmetry breakdown can be constrained through constraints coming from astrophysics and particle physics. Then the model extended by $SL_2(F_3)times U(1)_X$ symmetry can well be flavor-structured in a unique way that $N_{rm DW}=1$ with the $U(1)_X$ mixed-gravitational anomaly-free condition demands additional Majorana fermion and the flavor puzzles of SM are well delineated by new expansion parameters expressed in terms of $U(1)_X$ charges and $U(1)_X$-$[SU(3)_C]^2$ anomaly coefficients. And the model provides remarkable results on neutrino (hierarchical mass spectra and unmeasurable neutrinoless-double-beta decay rate together with the predictions on atmospheric mixing angle and leptonic Dirac CP phase favored by the recent long-baseline neutrino experiments), QCD axion, and flavored-axion.
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