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We discuss two Higgs doublet models with a softly-broken discrete $mathbb{S}_3$ symmery, where the mass matrix for charged-leptons is predicted as the diagonal form in the weak eigenbasis of lepton fields. Similar to an introduction of $mathbb{Z}_2$ symmetry, the tree level flavor changing neutral current can be forbidden by imposing the $mathbb{S}_3$ symmetry to the model. Under the $mathbb{S}_3$ symmetry, there are four types of Yukawa interactions depending on the $mathbb{S}_3$ charge assignment to right-handed fermions. We find that extra Higgs bosons can be muon and electron specific in one of four types of the Yukawa interaction. This property does not appear in any other two Higgs doublet models with a softly-broken ${mathbb Z}_2$ symmetry. We discuss the phenomenology of the muon and electron specific Higgs bosons at the Large Hadron Collider; namely we evaluate allowed parameter regions from the current Higgs boson search data and discovery potential of such a Higgs boson at the 14 TeV run.
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We study the Two-Higgs-Doublet Model with the aligned Yukawa sector (A2HDM) in light of the observed excess measured in the muon anomalous magnetic moment. We take into account the existing theoretical and experimental constraints with up-to-date values and demonstrate that a phenomenologically interesting region of parameter space exists. With a detailed parameter scan, we show a much larger region of viable parameter space in this model beyond the limiting case Type X 2HDM as obtained before. It features the existence of light scalar states with masses $3$ GeV $lesssim m_H^{} lesssim 50$ GeV, or $ 10$ GeV $lesssim m_A^{} lesssim 130$ GeV, with enhanced couplings to tau leptons. The charged Higgs boson is typically heavier, with $200$ GeV $ lesssim m^{}_{H^+} lesssim 630$ GeV. The surviving parameter space is forced into the CP-conserving limit by EDM constraints. Some Standard Model observables may be significantly modified, including a possible new decay mode of the SM-like Higgs boson to four taus. We comment on future measurements and direct searches for those effects at the LHC as tests of the model.
We present the first complete two loop calculation of the electron EDM in the complex two-Higgs doublet model. We confirm gauge-independence by demonstrating analytic cancellation of the gauge parameter $xi$ in the background field gauge and the t Hooft $R_xi$ gauge. We also investigate the behavior of the electron EDM near the decoupling limit, and determine the short- and long-distance contributions by matching onto an effective field theory. Compared with earlier studies of the electron EDM in the complex two-Higgs doublet model, we note disagreements in several places and provide diagnoses where possible. We also provide expressions for EDMs of light quarks.
The CP violating two-Higgs doublet model of type-X may enhance significantly the electric and magnetic moment of leptons through two-loop Barr-Zee diagrams. We analyze the general parameter space of the type-X 2HDM consistent with the muon $g-2$ and the electron EDM measurements to show how strongly the CP violating parameter is constrained in the region explaining the muon $ g-2$ anomaly.
Recent progress on muon $g-2$ measurement prompts one to take it even more seriously. In the general two Higgs doublet model that allows extra Yukawa couplings, we take a simplified approach of single enhanced coupling. We fix the charged lepton flavor violating coupling, $rho_{taumu} = rho_{mutau}$, via the one-loop mechanism, for illustrative masses of the heavy scalar $H$ and pseudoscalar $A$, where we assume $m_A = m_{H^+}$. Since extra top Yukawa couplings are plausibly the largest, we turn on $rho_{tt}$ and find that LHC search for $gg to H,,A to taumu$ gives more stringent bound than from $tauto mugamma$ with two-loop mechanism. Turning on a second extra top Yukawa coupling, $rho_{tc}$, can loosen the bound on $rho_{tt}$, but LHC constraints can again be more stringent than from $B to Dmu u$ vs $De u$ universality. This means that evidence for $H,,A to taumu$ may yet emerge with full LHC Run 2 data, while direct search for $tau^pmmu^mp bW^+$ or $tbar cbW^+$ (plus conjugate) may also bear fruit.
The new round of experiments, MEG II, COMET/Mu2e, and Mu3e, would soon start to push the $mu to egamma$, $mu N to eN$ conversion, and $mu to 3e$ frontier, while Belle II would probe $tau to mugamma$ and $tau to 3mu$. In the general two Higgs doublet model with extra Yukawa couplings, we show that all these processes probe the lepton flavor violating (LFV) dipole transition that arises from the two loop mechanism, with scalar-induced contact terms subdominant. This is because existing data suggest the extra Yukawa couplings $rho_{mu e},, rho_{ee} lesssim lambda_e$, while $rho_{taumu},, rho_{tautau} lesssim lambda_tau$ and $rho_{tt} lesssim lambda_t$, with $lambda_i$ the usual Yukawa coupling of the Standard Model (SM), where $rho_{mu e}rho_{tt}$ and $rho_{taumu}rho_{tt}$ enter the $mu egamma$ and $taumugamma$ two loop amplitudes, respectively. With the $B_s to mumu$ decay rate basically consistent with SM expectation, together with the $B_s$ mixing constraint, we show that $B_s to tautau$ would also be consistent with SM, while $B_s to taumu$ and $B to Ktaumu$ decays would be out of reach of projected sensitivities, in strong contrast with some models motivated by the B anomalies.
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