Abstract
The "gauged'' Peccei-Quinn (PQ) mechanism of Fukuda, Ibe, Suzuki and Yanagida is implemented in the flavorful axion model of Carone and Merchand. This model of flavor is similar to other successful ones based on the double tetrahedral group, but the flavor symmetry includes a global U(1) factor that leads to the presence of a flavorful axion. Here we gauge that U(1) symmetry and introduce a heavy sector that includes (1) the fermions necessary to cancel anomalies and (2) a second scalar flavon field that spontaneously breaks the U(1) symmetry. The full theory has an accidental U(1)$\times$U(1)$'$ global symmetry, anomalous with respect to QCD; U(1)$_\text{PQ}$ emerges as a linear combination. The gauged flavor symmetry restricts the possible PQ symmetry-breaking higher-dimension operators so that sufficient axion quality is preserved. We provide a model of the quark sector, as a proof of principle, and then a model which incorporates the standard model charged leptons as well. In both cases, the charge assignments that lead to acceptable axion quality also lead to a multiplicity of some of the heavy sector states; we check that the Landau pole for hypercharge remains above the cut off of the effective theory. We consider relevant phenomenological constraints on these models including those on the predicted axion couplings.
Highlights
The absence of a CP-violating term quadratic in the gluon field-strength tensor, i.e., one proportional to GμνGμν, remains one of the puzzles of the standard model
It has been long argued that the Peccei-Quinn (PQ) solution to the strong CP problem could be spoiled by the presence of higher-dimension operators that violate the PQ symmetry explicitly unless their accompanying dimensionless coefficients are unnaturally small or if the operators arise at sufficiently high order [15]
We have extended the flavorful axion model presented in our previous work [10] to address this problem by implementing a general strategy for preserving axion quality proposed in Ref. [17], the “gauged Peccei-Quinn” mechanism
Summary
The absence of a CP-violating term quadratic in the gluon field-strength tensor, i.e., one proportional to GμνGμν, remains one of the puzzles of the standard model. A Uð1ÞF flavor symmetry, spontaneously broken by a “flavon” field, φ, provides an origin for both the axion field and Yukawa coupling hierarchies [9]. It is believed that quantum gravitational effects generally break all global symmetries [16], in this case, through operators that would reintroduce the strong CP problem by triggering a nonzero value of the θparameter We will review this more explicitly later.
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