Modular flavour symmetries and modulus stabilisation

TLDR: In this article , the authors study the problem of modulus stabilisation in the framework of the modular symmetry approach to the flavour problem and find that a class of these potentials has (non-fine-tuned) CP-breaking minima in the vicinity of the point of

Abstract: 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.