Renormalization and running in the 2D $CP(1)$ model
High Energy Physics - Theory
2024-08-26 v1 High Energy Physics - Phenomenology
Abstract
We calculate the scattering amplitude in the two dimensional model in a regularization scheme independent way. When using cutoff regularization, a new Feynman rule from the path integral measure is required if one is to preserve the symmetry. The physical running of the coupling with renormalization scale arises from a UV finite Feynman integral in all schemes. We reproduce the usual result with asymptotic freedom, but the pathway to obtaining the beta function can be different in different schemes. We also comment on the way that this model evades the classic argument by Landau against asymptotic freedom in non-gauge theories.
Cite
@article{arxiv.2408.13142,
title = {Renormalization and running in the 2D $CP(1)$ model},
author = {Diego Buccio and John F. Donoghue and Gabriel Menezes and Roberto Percacci},
journal= {arXiv preprint arXiv:2408.13142},
year = {2024}
}
Comments
11 pages, 1 figure