Eur. Phys. J. C (2013) 73: 2652
https://doi.org/10.1140/epjc/s10052-013-2652-y

Regular Article - Theoretical Physics

An asymptotic safety scenario for gauged chiral Higgs–Yukawa models

¹ Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universität Jena, 07743, Jena, Germany
² Institut für Physik, Johannes-Gutenberg-Universität Mainz, 55099, Mainz, Germany
³ Faculty of Science (IMAPP), Radboud University Nijmegen, 6500 GL, Nijmegen, The Netherlands
⁴ Institut für Theoretische Physik, Universität Heidelberg, 69120, Heidelberg, Germany
⁵ Dip. di Fisica, Università degli Studi di Bologna, INFN Sez. di Bologna via Irnerio 46, 40126, Bologna, Italy

^* e-mail: holger.gies@uni-jena.de

Received: 14 July 2013
Revised: 23 September 2013
Published online: 28 November 2013

Abstract

We investigate chiral Higgs–Yukawa models with a non-abelian gauged left-handed sector reminiscent to a sub-sector of the standard model. We discover a new weak-coupling fixed-point behavior that allows for ultraviolet complete RG trajectories which can be connected with a conventional long-range infrared behavior in the Higgs phase. This non-trivial ultraviolet behavior is characterized by asymptotic freedom in all interaction couplings, but a quasi conformal behavior in all mass-like parameters. The stable microscopic scalar potential asymptotically approaches flatness in the ultraviolet, however, with a non-vanishing minimum increasing inversely proportional to the asymptotically free gauge coupling. This gives rise to non-perturbative—though weak-coupling—threshold effects which induce ultraviolet stability along a line of fixed points. Despite the weak-coupling properties, the system exhibits non-Gaußian features which are distinctly different from its standard perturbative counterpart: e.g., on a branch of the line of fixed points, we find linear instead of quadratically running renormalization constants. Whereas the Fermi constant and the top mass are naturally of the same order of magnitude, our model generically allows for light Higgs boson masses. Realistic mass ratios are related to particular RG trajectories with a “walking” mid-momentum regime.