Classification of three-generation models on magnetized orbifolds

We classify the combinations of parameters which lead three generations of quarks and leptons in the framework of magnetized twisted orbifolds on T2/Z2T2/Z2, T2/Z3T2/Z3, T2/Z4T2/Z4 and T2/Z6T2/Z6 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. (Note: this article is registered under preprint number: arXiv:1501.02787 [hep-ph].)