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Renormalization and running in the 2D $CP(1)$ model

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arxiv 2408.13142 v1 pith:DW7KZZSH submitted 2024-08-23 hep-th hep-ph

Diego Buccio , John F. Donoghue , Gabriel Menezes , Roberto Percacci This is my paper · ORCID
classification hep-thhep-ph
keywords modelasymptoticdifferentfeynmanfreedomintegralregularizationrenormalization
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abstract

We calculate the scattering amplitude in the two dimensional $CP(1)$ 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.

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Cited by 1 Pith paper

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  1. Standard Running, "Physical Running", Cosmological Constant and Newton Coupling

    hep-th 2025-05 conditional novelty 5.0 of 10

    Standard beta functions remain valid with a proper scale choice, and vacuum energy plus Newton coupling can run in curved spacetime.

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