Theta angle versus CP violation in the leptonic sector

TL;DR

This paper investigates how large CP-violating phases in the leptonic sector can influence the theta parameter, finding that in certain models, such effects are suppressed or require specific conditions, with implications for supersymmetric theories.

Contribution

It analyzes the radiative transfer of CP violation to the theta parameter across different Higgs models, highlighting the conditions under which large CP phases can significantly affect theta.

Findings

Large theta cannot be induced in one-Higgs-doublet models without at least three loops.

In multi-Higgs models, scalar potential phases dominate theta contributions.

In MSSM, the A_l parameter induces large corrections to theta at one loop, constraining CP phases.

Abstract

Assuming that the axion mechanism of solving the strong CP problem does not exist and the vanishing of theta at tree level is achieved by some model-building means, we study the naturalness of having large CP-violating sources in the leptonic sector. We consider the radiative mechanisms which transfer a possibly large CP-violating phase in the leptonic sector to the theta parameter. It is found that large theta cannot be induced in the models with one Higgs doublet as at least three loops are required in this case. In the models with two or more Higgs doublets the dominant source of theta is the phases in the scalar potential, induced by CP violation in leptonic sector. Thus, in the MSSM framework the imaginary part of the trilinear soft-breaking parameter A_l generates the corrections to the theta angle already at one loop. These corrections are large, excluding the possibility of large phases, unless the universality in the slepton sector is strongly violated.