Towards a theory of quark masses, mixings and CP-violation

TL;DR

This paper explores how D-brane models in string theory can naturally produce realistic quark masses, mixings, and CP-violation by analyzing Yukawa couplings derived from geometric configurations and world-sheet instantons.

Contribution

It provides a detailed computation of Yukawa couplings in D-brane models, linking geometric data to fermion mass hierarchies and CP-violation, with a focus on realistic three-generation models.

Findings

Reproduces observed quark mass spectrum and mixings.

Identifies geometric brane configurations that explain small quark masses.

Shows CP-violation arises from U(1) Wilson lines in compact dimensions.

Abstract

We discuss the structure of Yukawa couplings in D-brane models in which the SM fermion spectrum appears at the intersections of D-branes wrapping a compact space. In simple toroidal realistic examples one can explicitly compute the Yukawa couplings as a function of the geometrical data summing over world-sheet instanton contributions. A particular simple model with a N = 1 SUSY spectrum and three quark-lepton generations is studied in some detail. Remarkably, one can reproduce the observed spectrum of quark masses and mixings for particular choices of the compact radii and brane locations. In order to reproduce the smallness of up- and down-quark masses branes should be located in simple geometric configurations leading to some accidental global symmetries. We also find that the brane configurations able to reproduce the observed data may be considered as a deformation (by brane translation) of a configuration with Pati-Salam gauge symmetry. The origin of CP-violation in this formalism is quite elegant. It appears as a consequence of the generic presence of U(1) Wilson line backgrounds in the compact dimensions. One can reproduce the observed results for the CP-violation Jarlskog invariant J as long as the compact radii are of order of the string scale. DISCLAIMER: This paper is going to be substantially revised. Althought the physics and general concepts are still valid, the Yukawa couplings of the particular model presented in this paper have a simpler form than discussed here, as we recently pointed out in hep-th/0302105. A properly revised version will be eventually sent as the paper is appropriately corrected.