Asymptotic Safety in the Conformal Hidden Sector?

TL;DR

This paper explores the integration of asymptotic safety and conformal invariance in a hidden sector beyond the Standard Model, using RG equations to connect high-energy boundary conditions with low-energy physics, exemplified in a leptophobic $U(1)'$ model.

Contribution

It introduces a novel framework combining asymptotic safety with conformal invariance in a hidden sector, providing predictive scenarios and detailed RG analysis for a leptophobic $U(1)'$ model.

Findings

Identified an asymptotic safety scenario with strong predictive power.

Established relationships between UV boundary conditions, couplings, and the transition scale.

Linked the UV fixed point scale to the top quark Yukawa coupling.

Abstract

We combine the notion of asymptotic safety (AS) with conformal invariance in a hidden sector beyond the Standard Model. We use the renormalization group (RG) equations as a bridge to connect UV boundary conditions and EW/TeV scale physics and furnish a detailed example in the context of a leptophobic $U(1)'$ model. A broad selection of UV boundary conditions are formulated corresponding to differing AS scenarios, and we find an AS scenario with very strong predictive power, allowing unique determination of most of the parameters in the model. We obtain the interrelationships among the couplings, the transition scale of the fixed point $M_{UV}$ and the generations of quarks coupled to the $Z'$, and especially the correlation between $M_{UV}$ and the top quark Yukawa coupling $Y_t$. Several phenomenological implications of our results are presented for selected $Z'$ masses.