Studies of Wick Cutkosky model in light of its classical ground state using Dyson Schwinger equations

Abstract

Implications of additional fundamental scalar fields are regarded as among the most important avenues to explore after the experimental discovery of the standard model Higgs, particularly when there already exist cogent arguments in favor of their existence. A peculiar observation in Higgs-scalar singlet system is tendency of scalar singlet field to have negative squared physical masses which may be a sign of either a tachyon field or symmetry breaking. Assuming that this feature is due to the presence of a phenomenon similar to the conventionally understood Higgs mechanism, Wick Cutkosky model is studied in the parameter space suggested by the classical ground state of the system at Higgs mass $125.09$ GeV with positive values for both squared bare masses. The results are found to have strong negative contributions to squared scalar masses. For higher cutoff values, the renormalized squared scalar masses and squared bare couplings are found to qualitatively favor a relationship similar to the one in the classical ground state of the system, upto an additive constant. Higgs propagators remain almost unaffected as observed in a previously explored region of parameter space. However, scalar singlet propagators are found to have relatively different qualitative features in comparison to the previous study of the model. Vertices are found to have qualitatively similar features. No sign of triviality is found.