Physics

Invariant (physics)

Symmetry (geometry)

Mathematics

Mathematical physics

Particle physics

Mathematical analysis

Maxima and minima

Modulus

Geometry

Homogeneous space

Quark

Journal of High Energy Physics

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.

Modular flavour symmetries and modulus stabilisation