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arXiv · 2303.06723

Running couplings and unitarity in a 4-derivative scalar field theory

Bob Holdom
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Abstract

We obtain the $\beta$-functions for the two dimensionless couplings of a 4d renormalizable scalar field theory with cubic and quartic 4-derivative interactions. Both couplings can be asymptotically free in the UV, and in some cases also in the IR. This theory illustrates the meaning of unitarity in the presence of a negative norm state. A perturbative calculation that accounts for the new minus signs shows that the optical theorem is identically satisfied. These minus signs also enter a discussion of tree-level scattering. For a certain setup involving colliding beams of particles we find even more intricate cancellations and quite normal behaviour at high energies. The $\beta$-functions for the Stuckelberg gauged version of the theory are also obtained.

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Bob Holdom. 2023-03-12. Running couplings and unitarity in a 4-derivative scalar field theory. https://doi.org/10.1016/j.physletb.2023.138023

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