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The Lee-Wick Standard Model

Benjamin Grinstein, Donal O'Connell, Mark B. Wise

Abstract

We construct a modification of the standard model which stabilizes the Higgs mass against quadratically divergent radiative corrections, using ideas originally discussed by Lee and Wick in the context of a finite theory of quantum electrodynamics. The Lagrangian includes new higher derivative operators. We show that the higher derivative terms can be eliminated by introducing a set of auxiliary fields; this allows for convenient computation and makes the physical interpretation more transparent. Although the theory is unitary, it does not satisfy the usual analyticity conditions.

The Lee-Wick Standard Model

Abstract

We construct a modification of the standard model which stabilizes the Higgs mass against quadratically divergent radiative corrections, using ideas originally discussed by Lee and Wick in the context of a finite theory of quantum electrodynamics. The Lagrangian includes new higher derivative operators. We show that the higher derivative terms can be eliminated by introducing a set of auxiliary fields; this allows for convenient computation and makes the physical interpretation more transparent. Although the theory is unitary, it does not satisfy the usual analyticity conditions.

Paper Structure

This paper contains 15 sections, 58 equations, 4 figures.

Table of Contents

  1. Introduction
  2. A Toy Model
  3. The Hierarchy Problem and Lee-Wick Theory
  4. Gauge Fields
  5. Scalar Matter
  6. Power Counting
  7. One loop Pole Mass
  8. The normal scalar
  9. The LW-scalar
  10. The LW-vector
  11. Lee-Wick Standard Model Lagrangian
  12. The Higgs Sector
  13. Fermion Kinetic Terms
  14. Fermion Yukawa Interactions
  15. Conclusions

Figures (4)

  • Figure 1: One loop mass renormalization of the normal scalar field. The curly line is a gauge field while the zigzag line is the LW-gauge field. The dashed line represents the scalar field.
  • Figure 2: One loop mass renormalization of the LW-scalar field. The dotted line represents the LW-scalar field while the other propagators are as in Figure \ref{['fig:normscalar']}.
  • Figure 3: One loop mass renormalization of the LW-vector field. The propagators are as in Figure \ref{['fig:normscalar']}.
  • Figure 4: One loop graphs involving fermions which are potentially quadratically divergent. The solid lines represent fermion propagators while the curly and zigzag lines represent gauge bosons and LW-gauge bosons, respectively.