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.
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References
T.D. Lee and G.C. Wick, Negative metric and the unitarity of the S matrix, Nucl. Phys. B 9 (1969) 209 [INSPIRE].
T.D. Lee and G.C. Wick, Finite theory of quantum electrodynamics, Phys. Rev. D 2 (1970) 1033 [INSPIRE].
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].
R.E. Cutkosky, Singularities and discontinuities of Feynman amplitudes, J. Math. Phys. 1 (1960) 429 [INSPIRE].
M.J.G. Veltman, Unitarity and causality in a renormalizable field theory with unstable particles, Physica 29 (1963) 186 [INSPIRE].
G. ’t Hooft, Renormalization of massless Yang-Mills fields, Nucl. Phys. B 33 (1971) 173 [INSPIRE].
G. ’t Hooft, Renormalizable Lagrangians for massive Yang-Mills fields, Nucl. Phys. B 35 (1971) 167 [INSPIRE].
K.S. Stelle, Renormalization of higher derivative quantum gravity, Phys. Rev. D 16 (1977) 953 [INSPIRE].
E.S. Fradkin and A.A. Tseytlin, Renormalizable asymptotically free quantum theory of gravity, Nucl. Phys. B 201 (1982) 469 [INSPIRE].
U.G. Aglietti and D. Anselmi, Inconsistency of Minkowski higher-derivative theories, Eur. Phys. J. C 77 (2017) 84 [arXiv:1612.06510] [INSPIRE].
N. Nakanishi, Lorentz noninvariance of the complex-ghost relativistic field theory, Phys. Rev. D 3 (1971) 811 [INSPIRE].
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].
B. Grinstein, D. O’Connell and M.B. Wise, The Lee-Wick Standard Model, Phys. Rev. D 77 (2008) 025012 [arXiv:0704.1845] [INSPIRE].
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].
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].
C.D. Carone and R.F. Lebed, A higher-derivative Lee-Wick Standard Model, JHEP 01 (2009) 043 [arXiv:0811.4150] [INSPIRE].
B. Grinstein and D. O’Connell, One-loop renormalization of Lee-Wick gauge theory, Phys. Rev. D 78 (2008) 105005 [arXiv:0801.4034] [INSPIRE].
C.D. Carone, Higher-derivative Lee-Wick unification, Phys. Lett. B 677 (2009) 306 [arXiv:0904.2359] [INSPIRE].
E. Tomboulis, 1/N expansion and renormalization in quantum gravity, Phys. Lett. B 70 (1977) 361 [INSPIRE].
E. Tomboulis, Renormalizability and asymptotic freedom in quantum gravity, Phys. Lett. B 97 (1980) 77 [INSPIRE].
L. Modesto and I.L. Shapiro, Superrenormalizable quantum gravity with complex ghosts, Phys. Lett. B 755 (2016) 279 [arXiv:1512.07600] [INSPIRE].
L. Modesto, Super-renormalizable or finite Lee-Wick quantum gravity, Nucl. Phys. B 909 (2016) 584 [arXiv:1602.02421] [INSPIRE].
D. Anselmi and M. Piva, Perturbative unitarity of Lee-Wick quantum field theory, arXiv:1703.05563 [INSPIRE].
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ArXiv ePrint: 1703.04584
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Anselmi, D., Piva, M. A new formulation of Lee-Wick quantum field theory. J. High Energ. Phys. 2017, 66 (2017). https://doi.org/10.1007/JHEP06(2017)066
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DOI: https://doi.org/10.1007/JHEP06(2017)066