Implications of asymptotic safety in two minimal Z-prime models

TL;DR

This paper applies the asymptotic-safety paradigm to two minimal Z′ extensions of the Standard Model, G$_{SM}$ × U(1)$_x$ with x = B-L or χ, including hypercharge–U(1) kinetic mixing. By analyzing one-loop gauge beta functions augmented with gravity-induced corrections ($f_g$) and the Yukawa beta functions for $y_t$ and $y_b$, it identifies two UV fixed-point structures for the Abelian sector and imposes the requirement that the top and bottom Yukawas reach nontrivial fixed points. It finds that enforcing nonzero $g_{1*}$ is incompatible with the observed top Yukawa, while the $g_{1*}=0$ case allows viable regions where the fixed-point values determine the low-energy couplings via the UV critical surface, with $f_g$ controlling the values. The results constrain the otherwise free Abelian sector, connect high-scale boundary conditions to low-energy observables, and point to future FRG calculations to predict the gravitational parameters more precisely. Overall, the work demonstrates how asymptotic safety can render minimal Z′ models predictive and testable in future experiments.

Abstract

We consider the implications of asymptotic safety on two U(1) gauge extensions of the standard model that are minimal in the sense that anomaly cancellation only requires the presence of right-handed neutrinos. We study the UV fixed points of the gauge couplings taking into account kinetic mixing between hypercharge and the new U(1) gauge field. We consider the possibility that the top-bottom mass splitting originates from the effect of differing gauge charges on the nontrivial fixed point values of their respective Yukawa couplings and assess the impact of the extended gauge symmetry on the viability of this picture.

Figures (5)

• Figure 1: Fixed points (solid dots) in the $(g,\tilde{g})$ plane for $g_{1*} = g_1(M_{\rm Pl})$ in the B-L model. The solid line connecting the fixed points is the UV critical surface defined by Eq. (\ref{['eq:theline']}).
• Figure 2: Fixed points (solid dot and ellipse) in the $(g,\tilde{g})$ plane for $g_{1*} = 0$ in the B-L model. For the purpose of illustration, we have chosen $\hat{f}_g=5$.
• Figure 3: Running of the couplings in the B-L model, in the case where $g_{1*} =0$, for the case where both $g$ and $\tilde{g}$ reach nontrivial fixed point values. The inset shows the top and bottom Yukawa couplings on a log scale so that the approach of $y_b$ to a nontrivial fixed point is easer to see.
• Figure 4: Predictions for the top quark Yukawa coupling renormalized at the scale $m_{t}$. The solid (dotted) lines refer to the $B-L$ ($\chi$) model. The shaded band between the dashed lines is the 2 standard deviation experimentally allowed range.
• Figure 5: Value of $g(M_{\rm Pl})$ leading to the correct top and bottom quark masses as a function of the parameter $\hat{f}_g$, in the two models of interest in the case where $g_{1*}=0$. The lines shown are linear fits which each have a goodness-of-fit parameter $R$ that exceeds 0.998.