Complete structure of Z_n Yukawa couplings

TL;DR

This paper provides a comprehensive and explicit calculation of twisted Yukawa couplings in all Z_n orbifold models, including deformations, crucial for understanding fermion masses and flavor structure in string phenomenology.

Contribution

It offers the complete explicit expressions for Z_n orbifold Yukawa couplings, accounting for deformations and moduli dependence, enabling detailed phenomenological analysis.

Findings

Explicit formulas for all Z_n orbifold Yukawa couplings.

Dependence of couplings on moduli expectation values.

Non-diagonal fermion mass matrix entries and their implications.

Abstract

We give the complete twisted Yukawa couplings for all the Z_n orbifold constructions in the most general case, i.e. when orbifold deformations are considered. This includes a certain number of tasks. Namely, determination of the allowed couplings, calculation of the explicit dependence of the Yukawa couplings values on the moduli expectation values (i.e. the parameters determining the size and shape of the compactified space), etc. The final expressions are completely explicit, which allows a counting of the DIFFERENT Yukawa couplings for each orbifold (with and without deformations). This knowledge is crucial to determine the phenomenological viability of the different schemes, since it is directly related to the fermion mass hierarchy. Other facts concerning the phenomenological profile of Z_n orbifolds are also discussed, e.g. the existence of non--diagonal entries in the fermion mass matrices, which is related to a non--trivial structure of the Kobayashi--Maskawa matrix. Finally some theoretical results are given, e.g. the no--participation of (1,2) moduli in twisted Yukawa couplings. Likewise, (1,1) moduli associated with fixed tori which are involved in the Yukawa coupling, do not affect the value of the coupling.