Abstract
Motivated by the intimate connection between the strong CP problem and the flavor structure of the Standard Model, we present a flavor model that revives and extends the classic mu = 0 solution to the strong CP problem. QCD is embedded into a SU(3)1 × SU(3)2 × SU(3)3 gauge group, with each generation of quarks charged under the respective SU(3). The non-zero value of the up-quark Yukawa coupling (along with the strange quark and bottom-quark Yukawas) is generated by contributions from small instantons at a new scale M ≫ ΛQCD. The Higgsing of SU(3)3 → SU(3)c allows dimension-5 operators that generate the Standard Model flavor structure and can be completed in a simple renormalizable theory. The smallness of the third generation mixing angles can naturally emerge in this picture, and is connected to the smallness of threshold corrections to overline{theta} . Remarkably, overline{theta} is essentially fixed by the measured quark masses and mixings, and is estimated to be close to the current experimental bound and well within reach of the next generation of neutron and proton EDM experiments.
Highlights
Not a priori inconsistent with current algebra since non-perturbative effects can generate an effective up-quark mass [10,11,12,13]
Motivated by the intimate connection between the strong CP problem and the flavor structure of the Standard Model, we present a flavor model that revives and extends the classic mu = 0 solution to the strong CP problem
This mechanism for “factoring” the Strong CP problem was first presented in ref. [18], where all of the quarks are charged under a single SU(3) factor, and the PQ symmetry is realized by a heavy axion in each sector
Summary
For example for α ≈ 0.1, as in the SM near the weak scale, the non-perturbative contribution to yu is |yu|/|yd| 10−16 This simple 2-flavor example shows that instanton effects can generate large nonperturbative contributions to a perturbatively vanishing Yukawa coupling. 2+1 flavor lattice QCD results fully include all instanton configurations and can be interpreted as a calculation of the 2nd order term in the Chiral Lagrangian giving an effective up-quark mass proportional to m∗dm∗s/ΛQCD — these results suggest that the size of the desired non-perturbative effect is only ∼ 10–40% of the experimentally required value [14]. Qualitatively non-perturbative effects in the SM near the scale ΛQCD are nearly the right size to allow mu = 0 solution to the strong CP problem, quantitatively the possibility is strongly disfavored by precision lattice results. We will describe an extension to the SM in which non-perturbative effects can become important again at a high energy scale M ΛQCD, and these additional contributions allow a solution to the strong CP problem reminiscent of the massless up quark solution
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