The CKM Phase in Heterotic Orbifold Models

TL;DR

This paper investigates the conditions under which the CKM phase appears in heterotic orbifold models, finding it vanishes in prime orbifolds but can be non-zero in certain non-prime cases like Z_6-I.

Contribution

It identifies the specific orbifold conditions that allow for a non-zero CKM phase, especially analyzing the Z_6-I orbifold and its modular properties.

Findings

CKM phase vanishes at the renormalizable level for prime orbifolds

Non-prime orbifolds like Z_6-I can have a non-zero CKM phase

CKM phase vanishes when moduli are stabilized at Im T_i = ±1/2

Abstract

We consider properties of the CKM phase in the heterotic orbifold models. We find that at the renormalizable level the CKM phase vanishes identically for the prime orbifolds, whereas it can be non-zero for some non-prime orbifolds. In particular, we study in detail the Z_6-I orbifold which allows for a non-trivial CKM phase and analyze the modular properties of the corresponding Jarlskog invariant. The CKM phase is shown to vanish if the moduli fields are stabilized at Im T_i=\pm 1/2.