Dynamical Mass Generation in Wick Cutkosky Model

Abstract

Studying extent of dynamical generation of mass in a quantum field theory, which may have non-perturbative attributes, is an essential step towards complete understanding of the theory. It has historic relevance to interactions including fermions. However, as search of further fundamental scalars continues, inquiring into the possibility of dynamical generation of mass becomes crucial for scalars with masses much lower than the electroweak scale. This paper addresses Yukawa interaction between a complex doublet field, conveniently named the Higgs, and a scalar singlet studied in terms of correlation functions and the dynamical masses produced in the parameter space of the model. The study is conducted using the method of Dyson Schwinger equation. The Higgs is found to be receiving negative squared masses while the scalar singlet field receives positive squared mass. Higgs propagators are found to be significantly more sensitive to couplings in comparison to the scalar propagators. The vertices are relatively more stable against the cutoff used in comparison to the propagators and dynamically generated masses. No indication of a critical coupling is found within the explored range of coupling values. The model is found to have strong cutoff effects until the cutoff is raised to 100 TeV. The model suggests no sign of triviality.

17 pages, 7 figures

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