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Towards an Asymptotic-Safety Scenario for Chiral Yukawa Systems · Around

2009

Towards an Asymptotic-Safety Scenario for Chiral Yukawa Systems

Gies, Holger, Rechenberger, Stefan, Scherer, Michael M.

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We search for asymptotic safety in a Yukawa system with a chiral $U(N_L)_L\otimes U(1)_R$ symmetry, serving as a toy model for the standard-model Higgs sector.

Using the functional RG as a nonperturbative tool, the leading-order derivative expansion exhibits admissible non-Ga\ssian fixed-points for $1 \leq N_L \leq 57$ which arise from a conformal threshold behavior induced by self-balanced boson-fermion fluctuations.
If present in the full theory, the fixed-point would solve the triviality problem.
Moreover, as one fixed point has only one relevant direction even with a reduced hierarchy problem, the Higgs mass as well as the top mass are a prediction of the theory in terms of the Higgs vacuum expectation value.

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