Advertisement

A new formulation of Lee-Wick quantum field theory

  • Damiano Anselmi
  • Marco Piva
Open Access
Regular Article - Theoretical Physics

Abstract

The Lee-Wick models are higher-derivative theories that are claimed to be unitary thanks to a peculiar cancelation mechanism. In this paper, we provide a new formulation of the models, to clarify several aspects that have remained quite mysterious, so far. Specifically, we define them as nonanalytically Wick rotated Euclidean theories. The complex energy plane is divided into disconnected regions, which can be related to one another by a well-defined, albeit nonanalytic procedure. Working in a generic Lorentz frame, the models are intrinsically equipped with the right recipe to treat the pinchings of the Lee-Wick poles, with no need of external ad hoc prescriptions. We describe these features in detail by calculating the one-loop bubble diagram and explaining how the key properties generalize to more complicated diagrams. The physical results of our formulation are different from those of the previous ones. The unusual behaviors of the physical amplitudes lead to interesting phenomenological predictions.

Keywords

Beyond Standard Model Models of Quantum Gravity 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

References

  1. [1]
    T.D. Lee and G.C. Wick, Negative metric and the unitarity of the S matrix, Nucl. Phys. B 9 (1969) 209 [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  2. [2]
    T.D. Lee and G.C. Wick, Finite theory of quantum electrodynamics, Phys. Rev. D 2 (1970) 1033 [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  3. [3]
    R.E. Cutkosky, P.V. Landshoff, D.I. Olive and J.C. Polkinghorne, A non-analytic S matrix, Nucl. Phys. B 12 (1969) 281 [INSPIRE].ADSCrossRefGoogle Scholar
  4. [4]
    R.E. Cutkosky, Singularities and discontinuities of Feynman amplitudes, J. Math. Phys. 1 (1960) 429 [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    M.J.G. Veltman, Unitarity and causality in a renormalizable field theory with unstable particles, Physica 29 (1963) 186 [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  6. [6]
    G. ’t Hooft, Renormalization of massless Yang-Mills fields, Nucl. Phys. B 33 (1971) 173 [INSPIRE].
  7. [7]
    G. ’t Hooft, Renormalizable Lagrangians for massive Yang-Mills fields, Nucl. Phys. B 35 (1971) 167 [INSPIRE].
  8. [8]
    K.S. Stelle, Renormalization of higher derivative quantum gravity, Phys. Rev. D 16 (1977) 953 [INSPIRE].ADSMathSciNetGoogle Scholar
  9. [9]
    E.S. Fradkin and A.A. Tseytlin, Renormalizable asymptotically free quantum theory of gravity, Nucl. Phys. B 201 (1982) 469 [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  10. [10]
    U.G. Aglietti and D. Anselmi, Inconsistency of Minkowski higher-derivative theories, Eur. Phys. J. C 77 (2017) 84 [arXiv:1612.06510] [INSPIRE].ADSCrossRefGoogle Scholar
  11. [11]
    N. Nakanishi, Lorentz noninvariance of the complex-ghost relativistic field theory, Phys. Rev. D 3 (1971) 811 [INSPIRE].ADSGoogle Scholar
  12. [12]
    B. Grinstein, D. O’Connell and M.B. Wise, Causality as an emergent macroscopic phenomenon: the Lee-Wick O(N ) model, Phys. Rev. D 79 (2009) 105019 [arXiv:0805.2156] [INSPIRE].ADSGoogle Scholar
  13. [13]
    B. Grinstein, D. O’Connell and M.B. Wise, The Lee-Wick Standard Model, Phys. Rev. D 77 (2008) 025012 [arXiv:0704.1845] [INSPIRE].ADSGoogle Scholar
  14. [14]
    C.D. Carone and R.F. Lebed, Minimal Lee-Wick extension of the Standard Model, Phys. Lett. B 668 (2008) 221 [arXiv:0806.4555] [INSPIRE].ADSCrossRefGoogle Scholar
  15. [15]
    J.R. Espinosa and B. Grinstein, Ultraviolet properties of the Higgs sector in the Lee-Wick Standard Model, Phys. Rev. D 83 (2011) 075019 [arXiv:1101.5538] [INSPIRE].ADSGoogle Scholar
  16. [16]
    C.D. Carone and R.F. Lebed, A higher-derivative Lee-Wick Standard Model, JHEP 01 (2009) 043 [arXiv:0811.4150] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  17. [17]
    B. Grinstein and D. O’Connell, One-loop renormalization of Lee-Wick gauge theory, Phys. Rev. D 78 (2008) 105005 [arXiv:0801.4034] [INSPIRE].ADSGoogle Scholar
  18. [18]
    C.D. Carone, Higher-derivative Lee-Wick unification, Phys. Lett. B 677 (2009) 306 [arXiv:0904.2359] [INSPIRE].ADSCrossRefGoogle Scholar
  19. [19]
    E. Tomboulis, 1/N expansion and renormalization in quantum gravity, Phys. Lett. B 70 (1977) 361 [INSPIRE].ADSCrossRefGoogle Scholar
  20. [20]
    E. Tomboulis, Renormalizability and asymptotic freedom in quantum gravity, Phys. Lett. B 97 (1980) 77 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  21. [21]
    L. Modesto and I.L. Shapiro, Superrenormalizable quantum gravity with complex ghosts, Phys. Lett. B 755 (2016) 279 [arXiv:1512.07600] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  22. [22]
    L. Modesto, Super-renormalizable or finite Lee-Wick quantum gravity, Nucl. Phys. B 909 (2016) 584 [arXiv:1602.02421] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  23. [23]
    D. Anselmi and M. Piva, Perturbative unitarity of Lee-Wick quantum field theory, arXiv:1703.05563 [INSPIRE].

Copyright information

© The Author(s) 2017

Authors and Affiliations

  1. 1.Dipartimento di Fisica “Enrico Fermi”Università di PisaPisaItaly
  2. 2.INFN, Sezione di PisaPisaItaly

Personalised recommendations