Related papers: Modular invariance and the QCD angle
We formulate general conditions under which the strong CP problem is solved by spontaneous CP violation. Quark-mass matrix elements are polynomials in the CP-breaking order parameters, engineered such that their determinant is a real…
We show that solutions to the strong CP problem based on modular invariance can be extended to incorporate features that appear in string compactifications: quarks with mostly positive modular weights and non-trivial gauge kinetic…
Modular transformations of string theory are shown to play a crucial role in the discussion of discrete flavor symmetries in the Standard Model. They include CP transformations and provide a unification of CP with traditional flavor…
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 $\tau$ we find that a class of these potentials…
Modular flavor symmetries have been proposed as a new way to address the flavor problem. It is known that they can emerge from string compactifications. We discuss this connection in detail, and show how the congruence subgroups of SL(2,Z),…
It is shown that in the scheme with a rotating fermion mass matrix (i.e. one with a scale-dependent orientation in generation space) suggested earlier for explaining fermion mixing and mass hierarchy, the theta-angle term in the QCD action…
We propose a minimal extension of the Standard Model by incorporating sterile neutrinos and a QCD axion to account for the mass and mixing hierarchies of quarks and leptons and to solve the strong CP problem, and by introducing $G_{\rm…
We review the modular flavor symmetric models of quarks and leptons focusing on our works. We present some flavor models of quarks and leptons by using finite modular groups and discuss the phenomenological implications. The modular flavor…
Supersymmetric theories involving a spontaneously broken flavor symmetry can lead to fermion masses which vanish at tree level but are generated by radiative corrections. In the context of supersymmetric theories with minimal low energy…
Recently, it was shown that modular symmetry may solve the strong CP problem without axions, by producing a vanishing QCD angle while generating a large quark CP violation phase. We extend this framework to finite modular groups,…
We study the modular invariance in magnetized torus models. Modular invariant flavor model is a recently proposed hypothesis for solving the flavor puzzle, where the flavor symmetry originates from modular invariance. In this framework…
We present a calculating method for the quark and lepton mixing angles. After a general discussion in field theoretic models, we present a working model from a string compactification through $Z_{12-I}$ orbifold compactification. It is…
One of the historical suggestions to tackle the strong CP problem is to take the up quark mass to zero while keeping $m_d$ finite. The $\theta$ angle is then supposed to become irrelevant, i.e. the topological susceptibility vanishes.…
The formalism of combined finite modular and generalised CP (gCP) symmetries for theories of flavour is developed. The corresponding consistency conditions for the two symmetry transformations acting on the modulus $\tau$ and on the matter…
We investigate theories of flavour based on genus $g=2$ modular invariance and analyze how fermion mass hierarchies can be generated in this context, in the vicinity of invariant points or regions in moduli space where a residual symmetry…
We propose a theory for fermion masses and mixings in which an $A_4$ family symmetry arises naturally from a six-dimensional spacetime after orbifold compactification. The flavour symmetry leads to the successful "golden" quark-lepton…
I briefly review solutions to the strong CP problem based on axions, parity invariance, CP-invariance, and present a new idea based on CP as part of a spontaneously broken flavour symmetry such as a U(1) or modular invariance.
We promote the usual QCD $\theta$-parameter to a field and interpret it as the phase of the quark condensate, which becomes nontrivial when topological defects, vortices in our formulation, are induced in the quark condensate by the QCD…
We show that the observed structure of quark and lepton masses and mixing angles can arise entirely geometrically from superstring constructions, at the renormalizable level. The model we consider is a $Z_3$ orbifold compactification of…
We argue that flavour mixing, both in the quark and charged lepton sector, is basically determined by the lightest family mass generation mechanism. So, in the chiral symmetry limit when the up and down quark masses vanish, all the quark…