Abstract
We study the contributions of supersymmetric models with a U(1) horizontal symmetry and only spontaneous CP breaking to various lepton flavor observables, such as μ → eγ and the electron electric dipole moment. We show that both a horizontal symmetry and a lack of explicit CP violation can alleviate the existing bounds from such observables. The undetermined mathcal{O} (1) coefficients in such mass matrix models muddle the interpretation of the bounds from various flavor observables. To overcome this, we define a new fine-tuning measure for different observables in such setups. This allows us to study how naturally the observed IR flavor observables can emerge from a given mass matrix model. We use our flavor-naturalness measure in study of our supersymmetric models and quantify the degree of fine tuning required by the bounds from various lepton flavor observables at each mass scale of sleptons, neutralinos, and charginos.
Highlights
In nature, it must be broken; SUSY breaking can radiatively drive the higgs mass-squared parameter negative so that the electroweak symmetry is dynamically broken
We study the contributions of supersymmetric models with a U(1) horizontal symmetry and only spontaneous CP breaking to various lepton flavor observables, such as μ → eγ and the electron electric dipole moment
While the discovery of the higgs boson with the mass of around 125 GeV at the Large Hadron Collider (LHC) indicates that the superpartner of the top quark is significantly heavier than the weak scale, to avoid a severe tuning, the mass scale of supersymmetric particles should be within just a few orders of magnitude above the electroweak scale (for a recent study of tuning of the minimal supersymmetric SM (MSSM) or other SUSY extensions of the SM, see ref. [11])
Summary
The quark masses span five orders of magnitude. The diagonal elements of the CKM matrix are of order one, while off-diagonal elements are suppressed. Those hierarchies suggest the existence of a structure with a fundamental small parameter λ ∼ 0.2, originally introduced by Wolfenstein [40] for the CKM matrix elements, and later applied to the quark masses hierarchies [21]. In contrast to the CKM matrix, the PMNS matrix of the lepton sector does not show any clear structure or hierarchy [41]. The PMNS matrix has one (three) CPV phase in the case of Dirac (Majorana) neutrinos. The Dirac phase δCP can be measured by oscillation experiments. The NOνA [29] experiment favors δCP < π, still allowing a CP-conserving phase, while T2K [30] favors δCP > π and disfavors CP-violation at the level of 2σ
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