Diagram dependance of the $\mathbb{CP}(1)$ beta function
Kasra Kiaee, Alexander Monin
TL;DR
This paper examines how different Feynman diagrams contribute to the beta function in the 2D $ ext{CP}(1)$ sigma model, highlighting scheme-dependent diagrammatic roles and their relation to scattering amplitudes.
Contribution
It reveals the scheme dependence of diagram contributions to the beta function and discusses their connection to scattering amplitude energy dependence.
Findings
Different schemes attribute the running to different diagrams.
Tadpoles and UV-finite bubbles can both drive the beta function.
The relation between beta functions and scattering amplitudes is analyzed.
Abstract
We revisit the computation of the beta function in the two-dimensional sigma model. We show that in different schemes, different diagrams are responsible for the running, such as momentum-independent tadpoles or even UV-finite bubble diagrams. We also comment on the relation between the beta functions and the energy dependence of scattering amplitudes.
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Taxonomy
TopicsNumerical Methods and Algorithms · Particle physics theoretical and experimental studies