English

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

High Energy Physics - Theory 2023-06-19 v2

Abstract

We obtain the β\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 β\beta-functions for the Stuckelberg gauged version of the theory are also obtained.

Keywords

Cite

@article{arxiv.2303.06723,
  title  = {Running couplings and unitarity in a 4-derivative scalar field theory},
  author = {Bob Holdom},
  journal= {arXiv preprint arXiv:2303.06723},
  year   = {2023}
}

Comments

16 pages, 4 figures