Abstract
In general two Higgs doublet models (2HDMs) without scalar flavour changing neutral couplings (SFCNC) in the lepton sector, the electron, muon and tau interactions can be decoupled in a robust framework, stable under renormalization group evolution. In this framework, the breaking of lepton flavour universality (LFU) goes beyond the mass proportionality, opening the possibility to accommodate a different behaviour among charged leptons. We analyze the electron and muon $(g-2)$ anomalies in the context of these general flavour conserving models in the leptonic sector (g$\ell$FC). We consider two different models, I-g$\ell$FC and II-g$\ell$FC, in which the quark Yukawa couplings coincide, respectively, with the ones in type I and in type II 2HDMs. We find two types of solutions that fully reproduce both $(g-2)$ anomalies, and which are compatible with experimental constraints from LEP and LHC, from LFU, from flavour and electroweak physics, and with theoretical constraints in the scalar sector. In the first type of solution, all the new scalars have masses in the 1--2.5 TeV range, the vacuum expectation values (vevs) of both doublets are quite similar in magnitude, and both anomalies are dominated by two loop Barr-Zee contributions. This solution appears in both models. In a second type of solution, one loop contributions are dominant in the muon anomaly, all new scalars have masses below 1 TeV, and the ratio of vevs is in the range 10--100. The second neutral scalar $H$ is the lighter among the new scalars, with a mass in the 210--390 GeV range while the pseudoscalar $A$ is the heavier, with a mass in the range 400--900 GeV. The new charged scalar $H^\pm$ is almost degenerate either with the scalar or with the pseudoscalar. This second type of solution only appears in the I-g$\ell$FC model. Both solutions require the soft breaking of the $\mathbb{Z}_{2}$ symmetry of the Higgs potential.
Highlights
INTRODUCTIONAfter an improved determination of the fine structure constant [1], a new anomaly has emerged [2] concerning the anomalous magnetic moment of the electron ae 1⁄4 ðge − 2Þ=2: there is a discrepancy among the experimental determination and the Standard Model (SM) prediction [3,4,5,6,7,8], δae ≡ aEexp − aSeM 1⁄4 −ð8.7 Æ 3.6Þ × 10−13: ð1Þ
Solution [B] corresponds instead to large tβ, lighter new scalars, with δae obtained through two loop Barr-Zee contributions while in δaμ the most important contributions are one loop and H-mediated
Lepton flavor universality is broken beyond the mass proportionality, and a different behavior among charged leptons can be accommodated in a simple way, without introducing highly constrained scalar flavor changing neutral couplings (SFCNC)
Summary
After an improved determination of the fine structure constant [1], a new anomaly has emerged [2] concerning the anomalous magnetic moment of the electron ae 1⁄4 ðge − 2Þ=2: there is a discrepancy among the experimental determination and the Standard Model (SM) prediction [3,4,5,6,7,8], δae ≡ aEexp − aSeM 1⁄4 −ð8.7 Æ 3.6Þ × 10−13: ð1Þ. As in the A2HDM, it has been shown that the charged lepton sector of the gFC-2HDM is one loop stable under RGE, in the sense that SFCNC, absent at tree level, are not generated at one loop [45]. This implies that a well behaved and minimal 2HDM that can implement the effective decoupling among μ and e is a gFC-2HDM in the leptonic sector. H:c:; ð10Þ where Mf are the diagonal fermion mass matrices for f 1⁄4 u; d; l and Nf are the new flavor structures that may be able to explain the electron and muon anomalies in Eqs.
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