Abstract
The strongest upper bounds on the axion mass come from astrophysical observations like the neutrino burst duration of SN1987A, which depends on the axion couplings to nucleons, or the white-dwarf cooling rates and red-giant evolution, which involve the axion-electron coupling. It has been recently argued that in variants of DFSZ models with generation-dependent Peccei-Quinn charges an approximate axion-nucleon decoupling can occur, strongly relaxing the SN1987A bound. However, as in standard DFSZ models, the axion remains in general coupled to electrons, unless an ad hoc cancellation is engineered. Here we show that axion-electron decoupling can be implemented without extra tunings in DFSZ-like models with three Higgs doublets. Remarkably, the numerical value of the quark mass ratio $m_u/m_d\sim 1/2$ is crucial to open up this possibility.
Highlights
It has been recently argued [1] that in variants of DineFischler-Srednicki-Zhitnitsky (DFSZ) [2,3] models with two Higgs doublets and generation-dependent Peccei Quinn (PQ) charges, it is possible to strongly suppress axion couplings to nucleons
By imposing the condition which ensures that the physical axion field is orthogonal to the Goldstone field of hypercharge Uð1ÞY, i.e., X 1v21 þ X 2v22 1⁄4 0, we obtain a relation between the ratio of the vacuum expectation values (VEVs) v1;2 1⁄4 hH1;2i and the ratio of the quark masses that must be satisfied in order to ensure nucleophobia: v22 v21
With only two Higgs doublets responsible for breaking the electroweak symmetry and for providing masses to all the fermions, the lepton sector is unavoidably charged under the PQ symmetry and, as mentioned in the Introduction, electrophobia can only be enforced by tuning a cancellation between the contribution to the axion electron coupling proportional to the electron PQ charge, and corrections arising from lepton flavor mixing [1]
Summary
It has been recently argued [1] that in variants of DineFischler-Srednicki-Zhitnitsky (DFSZ) [2,3] models with two Higgs doublets and generation-dependent Peccei Quinn (PQ) charges, it is possible to strongly suppress axion couplings to nucleons (axion nucleophobia). [1] this type of effect was invoked to arrange for a tuned cancellation between two contributions to the axion-electron coupling: one proportional to the electron PQ charge, and the other coming from intergenerational mixing between the leptons This allows the construction of models of nucleophobic and electrophobic axions that can evade all the tightest astrophysical bounds (astrophobic axions). The tuning of the cancellation required to achieve a significant level of electrophobia is at the level of 10%, astrophobic axion models constructed in this way are admittedly not elegant In this short paper we put forth a more natural way to achieve astrophobia, which requires extending the scalar sector by a third Higgs doublet, but does not involve any ad hoc cancellation between different contributions to the axion-electron coupling. The mechanism can be implemented thanks to the fact that the light quark mass ratio is close to mu=md ≈ 1=2
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