Classification of three-generation models on magnetized orbifolds

TL;DR

This paper classifies parameter combinations in magnetized orbifold models that produce three generations of quarks and leptons, considering nonzero phases, and analyzes specific examples with different Higgs configurations.

Contribution

It provides a comprehensive classification of three-generation models on magnetized orbifolds including nonzero phases, extending previous studies that assumed zero phases.

Findings

Identified parameter sets yielding three generations on various orbifolds.

Analyzed models with nonzero Wilson line and Scherk-Schwarz phases.

Compared Higgs sector differences with previous zero-phase models.

Abstract

We classify the combinations of parameters which lead three generations of quarks and leptons in the framework of magnetized twisted orbifolds on $T^2/Z_2$, $T^2/Z_3$, $T^2/Z_4$ and $T^2/Z_6$ with allowing nonzero discretized Wilson line phases and Scherk-Schwarz phases. We also analyze two actual examples with nonzero phases leading to one-pair Higgs and five-pair Higgses and discuss the difference from the results without nonzero phases studied previously.