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Fermion Masses and Mixing in Extended Technicolor Models

Thomas Appelquist, Maurizio Piai, Robert Shrock

Abstract

We study fermion masses and mixing angles, including the generation of a seesaw mechanism for the neutrinos, in extended technicolor (ETC) theories. We formulate an approach to these problems that relies on assigning right-handed $Q=-1/3$ quarks and charged leptons to ETC representations that are conjugates of those of the corresponding left-handed fermions. This leads to a natural suppression of these masses relative to the $Q=2/3$ quarks, as well as the generation of quark mixing angles, both long-standing challenges for ETC theories. Standard-model-singlet neutrinos are assigned to ETC representations that provide a similar suppression of neutrino Dirac masses, as well as the possibility of a realistic seesaw mechanism with no mass scale above the highest ETC scale of roughly $10^3$ TeV. A simple model based on the ETC group SU(5) is constructed and analyzed. This model leads to non-trivial, but not realistic mixing angles in the quark and lepton sectors. It can also produce sufficiently light neutrinos, although not simultaneously with a realistic quark spectrum. We discuss several aspects of the phenomenology of this class of models.

Fermion Masses and Mixing in Extended Technicolor Models

Abstract

We study fermion masses and mixing angles, including the generation of a seesaw mechanism for the neutrinos, in extended technicolor (ETC) theories. We formulate an approach to these problems that relies on assigning right-handed quarks and charged leptons to ETC representations that are conjugates of those of the corresponding left-handed fermions. This leads to a natural suppression of these masses relative to the quarks, as well as the generation of quark mixing angles, both long-standing challenges for ETC theories. Standard-model-singlet neutrinos are assigned to ETC representations that provide a similar suppression of neutrino Dirac masses, as well as the possibility of a realistic seesaw mechanism with no mass scale above the highest ETC scale of roughly TeV. A simple model based on the ETC group SU(5) is constructed and analyzed. This model leads to non-trivial, but not realistic mixing angles in the quark and lepton sectors. It can also produce sufficiently light neutrinos, although not simultaneously with a realistic quark spectrum. We discuss several aspects of the phenomenology of this class of models.

Paper Structure

This paper contains 41 sections, 156 equations, 14 figures, 2 tables.

Table of Contents

  1. Introduction
  2. General Framework
  3. Technicolor and Extended Technicolor
  4. Conventional ETC Mass Generation for Fermions
  5. Intra-generational Mass Splittings
  6. Quark Mixing
  7. Progenitors
  8. AT94
  9. AS02
  10. Models with Extended Strong-Electroweak Gauge Groups
  11. A Model for Quarks and Leptons
  12. Ingredients
  13. Symmetry Breaking -- The First Stage
  14. Neutrino Mass Matrix
  15. Symmetry-Breaking Sequence 1
  16. ...and 26 more sections

Figures (14)

  • Figure 1: Graphs generating $\bar{f}_{i,L} M^{(f)}_{ij} f^j_R$ where $i=1,2,3$, assuming that the indicated one-loop mixings of ETC gauge bosons occur, for the case in which $f_L$ and $f_R$ both transform according to the same (fundamental) representation of SU(5)$_{ETC}$. The index $t$ takes on the values 4 and 5. Here, $f^i$ is an up-type quark for $1 \le i \le 3$ and techniquark for $i=4,5$.
  • Figure 2: Graphs generating $\bar{d}_{i,L} M^{(d)}_{ij} d_{j,R}$ where $i=1,2,3$, assuming that the indicated, one-loop mixings of ETC gauge bosons occur, for the case in which $d_L$ and $d_R$ transform according to the fundamental and conjugate fundamental representation of SU(5)$_{ETC}$. Here $d^i$ is a down-type quark (techniquark) for $1 \le i \le 3$ ($i=4,5$). As indicated, the graph with the indices 4 and 5 interchanged also contributes.
  • Figure 3: Graphs generating $\bar{n}^i_L b_{ij} \alpha^{1j}_R$ for $i=1,2,3$ and $j=2,3$, provided that the indicated mixings of ETC gauge bosons occur.
  • Figure 4: Graphs for $\alpha^{12 \ T}_R C r_{23} \alpha^{13}_R$.
  • Figure 5: Graphs that yield contributions to the Dirac bilinear $\bar{n}^i_L d_{i,jk} \xi^{jk}_R$ for $j,k=4,5$ and (a) $i=1$, (b) $i=2,3$. In the latter case, the mixing of ETC gauge bosons that is necessary is indicated.
  • ...and 9 more figures