A bstract We consider a supergravity model that has the modular A 4 symmetry and discuss the interplay between the neutrino mixing and inflation. The model contains right- handed neutrinos that have the Majorana masses and additional Yukawa couplings to the waterfall field. In the model an active neutrino is massless and we find that only the inverted hierarchy is allowed and the Majorana phase is predicted to be around ± (120–180)° from the observed neutrino mixing data. In the early universe, one of right-handed sneutrinos plays the role of the inflaton field. Focusing on the subcritical regime of the hybrid inflation that is consistent with the cosmic microwave background data, we analyze the dynamics of the scalar sector and derive an upper bound (10 10 ) GeV on the scale of the Majorana mass. 

/pdf/subcritical-regime-of-hybrid-inflation-with-modular-a4-23xg5sga.pdf

Subcritical regime of hybrid inflation with modular A4 symmetry

A bstract We study the lepton flavor violation (LFV), the leptonic magnetic moments ( g − 2) μ, e and the electric dipole moment (EDM) of the electron in the Standard-Model Effective Field Theory with the Γ N modular flavor symmetry. We employ the stringy Ansatz on coupling structure that 4-point couplings of matter fields are written by a product of 3-point couplings of matter fields. We take the level 3 finite modular group, Γ 3 for the flavor symmetry, and discuss the dipole operators at nearby fixed point τ = i , where observed lepton masses and mixing angles are well reproduced. Suppose the anomaly of the anomalous magnetic moment of the muon to be evidence of the new physics (NP), we have related it with ( g − 2) e , LFV decays, and the electron EDM. It is found that the NP contribution to ( g − 2) e is proportional to the lepton masses squared likewise the naive scaling. We also discuss the correlations among the LFV processes μ → eγ , τ → μγ and τ → eγ , which are testable in the future. The electron EDM requires the tiny imaginary part of the relevant Wilson coefficient in the basis of real positive charged lepton masses, which is related to the μ → eγ transition in our framework. 

/pdf/lepton-flavor-violation-lepton-g-2-m-e-and-electron-edm-in-12yq80px.pdf

Lepton flavor violation, lepton (g − 2)μ, e and electron EDM in the modular symmetry

A bstract We study a symmetry breaking of residual flavor symmetries realized at fixed points of the moduli space. In the supersymmetric modular invariant theories, a small departure of the modulus from fixed points is required to realize fermion mass hierarchies and sizable CP-breaking effects. We investigate whether one can dynamically fix the moduli values in the vicinity of the fixed points in the context of Type IIB string theory. It is found that the string landscape prefers | δτ | ≃ 10 − 5 for the deviation of the complex structure modulus from all fixed points and the CP-breaking vacuum is statistically favored. To illustrate phenomenological implications of distributions of moduli values around fixed points, we analyze the lepton sector on a concrete A 4 modular flavor model. 

/pdf/residual-flavor-symmetry-breaking-in-the-landscape-of-1vbfharv.pdf

Residual flavor symmetry breaking in the landscape of modular flavor models

A bstract We study the vacua of 4 d heterotic toroidal orbifolds using effective theories consisting of an overall Kähler modulus, the dilaton, and non-perturbative corrections to both the superpotential and Kähler potential that respect modular invariance. We prove three de Sitter no-go theorems for several classes of vacua and thereby substantiate and extend previous conjectures. Additionally, we provide evidence that extrema of the scalar potential can occur inside the PSL(2, ℤ) fundamental domain of the Kähler modulus, in contradiction of a separate conjecture. We also illustrate a loophole in the no-go theorems and determine criteria that allow for metastable de Sitter vacua. Finally, we identify inherently stringy non-perturbative effects in the dilaton sector that could exploit this loophole and potentially realize de Sitter vacua. 

/pdf/heterotic-de-sitter-beyond-modular-symmetry-r9h8g3rk.pdf

Heterotic de Sitter beyond modular symmetry


 We study the CP violation and the CP phase of quark mass matrices in modular flavor symmetric models. The CP symmetry remains at τ = e2πi/3 by a combination of the T-symmetry of the modular symmetry. However, the T-symmetry breaking may lead to the CP violation at the fixed point τ = e2πi/3. We study such a possibility in magnetized orbifold models as examples of modular flavor symmetric models. These models, in general, have more than one candidates for Higgs modes, while generic string compactifications also lead to several Higgs modes. These Higgs modes have different behaviors under the T-transformation. The light Higgs mode can be a linear combination of those modes so as to lead to realistic quark mass matrices. The CP phase of mass matrix does not appear in a certain case, which is determined by the T-transformation behavior. Deviation from it is important to realize the physical CP phase. We discuss an example leading to non-vanishing CP phase at the fixed point τ = e2πi/3.

/pdf/mass-matrices-with-cp-phase-in-modular-flavor-symmetry-3me8b0ks.pdf

Mass matrices with CP phase in modular flavor symmetry

A bstract We study the problem of modulus stabilisation in the framework of the modular symmetry approach to the flavour problem. By analysing simple UV-motivated CP-invariant potentials for the modulus τ we find that a class of these potentials has (non-fine-tuned) CP-breaking minima in the vicinity of the point of $$ {\mathrm{\mathbb{Z}}}_3^{ST} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>ℤ</mml:mi> <mml:mn>3</mml:mn> <mml:mi>ST</mml:mi> </mml:msubsup> </mml:math> residual symmetry, τ ≃ e 2 πi /3 . Stabilising the modulus at these novel minima breaks spontaneously the CP symmetry and can naturally explain the mass hierarchies of charged leptons and possibly of quarks. 

/pdf/modular-flavour-symmetries-and-modulus-stabilisation-3juoes7q.pdf

Турсунов Озодбек Бадалович

Papers

Modular flavour symmetries and modulus stabilisation