[Paper Review] Technicolorful Supersymmetry

Hitoshi Murayama|ArXiv.org|Jul 23, 2003

Particle physics theoretical and experimental studies4 citations

TL;DR

This paper proposes a supersymmetric technicolor model that achieves electroweak symmetry breaking dynamically via strong interactions, eliminating the need for an elementary Higgs boson. By embedding technicolor in a supersymmetric framework with a superconformal window, it enables exact calculations of $e^+e^-$ production cross sections for techni-resonances while solving the alignment problem and suppressing flavor-changing neutral currents via a renormalizable techni-GIM mechanism.

ABSTRACT

Technicolor achieves electroweak symmetry breaking (EWSB) in an elegant and natural way, while it suffers from severe model building difficulties. I propose to abandon its secondary goal to eliminate scalar bosons in exchange of solving numerous problems using supersymmetry. It helps to understand walking dynamics much better with certain exact results. In the particular model presented here, there is no light elementary Higgs boson and the EWSB is fully dynamical, hence explaining the hierarchy; There is no alignment problem and no light pseudo-Nambu-Goldstone bosons exist; The fermion masses are generated by a ultraviolet-complete renormalizable extended technicolor sector with techni-GIM mechanism and hence the sector is safe from flavor-changing-neutral-current constraints; The "e+ e-'' production of techni-states in the superconformal window is calculable; The electroweak precision observables are (un)fortunately not calculable.

Motivation & Objective

• To resolve long-standing problems in technicolor models—such as the alignment problem, light pseudo-Nambu-Goldstone bosons, and flavor-changing neutral currents—by embedding technicolor in a supersymmetric framework.
• To achieve a natural hierarchy in the electroweak scale not via supersymmetry alone, but through dynamical electroweak symmetry breaking in a strongly coupled technicolor sector.
• To enable exact predictions for observables such as $e^+e^-$ production cross sections in the superconformal regime, leveraging exact results from supersymmetric dynamics.
• To construct a UV-complete, renormalizable extended technicolor sector that generates fermion masses while avoiding FCNC constraints through the techni-GIM mechanism.

Proposed method

• Introduce a supersymmetric extension of technicolor with a superconformal window above the technicolor scale $\Lambda_{TC} \sim 2$ TeV, enabling exact calculations of anomalous dimensions and $S$-matrix elements.
• Implement a UV-complete, renormalizable extended technicolor (ETC) sector with a techni-GIM mechanism to suppress flavor-changing neutral currents, even at a low ETC scale ($\Lambda_{ETC} \sim 2$ TeV).
• Utilize exact results from supersymmetric gauge theories to compute the $e^+e^-$ production cross section of techni-resonances, despite the ill-defined $S$-matrix in conformal field theories.
• Assume supersymmetry breaking is a small perturbation at the $\sim$0.2 TeV scale, with the hierarchy stabilized by technicolor dynamics rather than supersymmetry.
• Leverage the improved theoretical control of supersymmetric non-Abelian gauge theories to avoid the model-building difficulties of non-supersymmetric walking technicolor.
• Postulate that the coincidence of $m_{SUSY} \sim \Lambda_{TC} \sim \Lambda_{ETC}$ is a new analog of the $\mu$-problem in the MSSM, requiring further explanation.

Experimental results

Research questions

• RQ1 Can electroweak precision observables such as the $S$ and $T$ parameters be reliably calculated in this supersymmetric technicolor framework?
• RQ2 Is there a reliable way to relate the techni-pion decay constant to the technicolor scale $\Lambda_{TC}$?
• RQ3 How high can the supersymmetry breaking scale be pushed before losing theoretical control, and can it be pushed beyond $\Lambda_{TC}$?
• RQ4 Can the ETC scale be raised further while maintaining consistency with flavor physics and the techni-GIM mechanism?
• RQ5 How can the origin of flavor be consistently implemented in this framework, possibly via a Froggatt-Nielsen mechanism at the ETC scale?

Key findings

• The model eliminates the alignment problem and avoids light pseudo-Nambu-Goldstone bosons, which are ruled out by experiment.
• Fermion masses are generated via a UV-complete, renormalizable extended technicolor sector with the techni-GIM mechanism, suppressing flavor-changing neutral currents despite a low ETC scale of $\sim$2 TeV.
• The $e^+e^-$ production cross section for techni-states in the superconformal window is exactly calculable, even though the $S$-matrix is ill-defined in conformal theories.
• The hierarchy problem is stabilized by the dynamical electroweak symmetry breaking in the technicolor sector, not by supersymmetry, allowing the supersymmetry breaking scale to be pushed up to $\Lambda_{TC} \sim$2 TeV.
• The model avoids the little hierarchy problem by decoupling the supersymmetry breaking scale from the electroweak scale, with the potential to push it beyond $\Lambda_{TC}$.
• The coincidence of $m_{SUSY} \sim \Lambda_{TC} \sim \Lambda_{ETC} \sim$2 TeV is identified as a new $\mu$-problem analog, suggesting a deeper underlying symmetry or mechanism.