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On mass hierarchies in orientifold vacua

Pascal Anastasopoulos, Elias Kiritsis, Andrea Lionetto

TL;DR

We address the origin of fermion mass hierarchies in orientifold vacua using a bottom-up D-brane framework with multiple anomalous U(1)s. Mass textures are generated through three channels—tree-level Yukawa, higher-dimension operators, and D-instantons—yielding three distinct mass scales governed by the string scale $M_s$. The authors classify viable brane configurations (3–5 stacks) and demonstrate several vacua where a three-scale pattern emerges; in some cases CKM/mixing aligns with experimental data, while others face challenges. The work is exploratory, identifying promising brane setups and highlighting the roles of instantons, discrete symmetries, and scalar vevs in shaping fermion hierarchies, with plans to integrate these configurations into broader top-down model catalogs.

Abstract

We analyze the problem of the hierarchy of masses and mixings in orientifold realizations of the Standard Model. We find bottom-up brane configurations that can generate such hierarchies.

On mass hierarchies in orientifold vacua

TL;DR

We address the origin of fermion mass hierarchies in orientifold vacua using a bottom-up D-brane framework with multiple anomalous U(1)s. Mass textures are generated through three channels—tree-level Yukawa, higher-dimension operators, and D-instantons—yielding three distinct mass scales governed by the string scale . The authors classify viable brane configurations (3–5 stacks) and demonstrate several vacua where a three-scale pattern emerges; in some cases CKM/mixing aligns with experimental data, while others face challenges. The work is exploratory, identifying promising brane setups and highlighting the roles of instantons, discrete symmetries, and scalar vevs in shaping fermion hierarchies, with plans to integrate these configurations into broader top-down model catalogs.

Abstract

We analyze the problem of the hierarchy of masses and mixings in orientifold realizations of the Standard Model. We find bottom-up brane configurations that can generate such hierarchies.

Paper Structure

This paper contains 22 sections, 86 equations, 1 table.

Table of Contents

  1. Introduction, motivation and scope
  2. Bottom-up description of D-brane configurations
  3. Mass Matrices of the SM stack
  4. Mass Matrix Forms
  5. Vacua with 3-scales in all fermion mass matrices
  6. Vacuum 1: $a=1, ~b=c=e=h=0, ~d=f=g=2$.
  7. Vacuum 4: $a=c=d=1, ~b=f=h=0, ~e=g=2$.
  8. The KST vacua
  9. A vacuum with five stacks
  10. Branes at singularities and $Z_3$ symmetry
  11. The CKM mixing matrix
  12. Correlations with experimentally unfavorable couplings.
  13. Conclusions
  14. Masses at various scales
  15. D-brane embeddings
  16. ...and 7 more sections