Renormalization Group Fixed Point with a Fourth Generation: Higgs-induced Bound States and Condensates

TL;DR

This paper explores how a fourth generation in the Standard Model can lead to a fixed point in renormalization group equations, enabling bound state formation and condensates at TeV scales without new interactions.

Contribution

It demonstrates the existence of a fixed point in the two-loop RG equations for a four-generation Standard Model, leading to Higgs-induced bound states and condensates at accessible energy scales.

Findings

A fixed point scale $\, ext{few TeV to 100 TeV}$ is identified.

Heavy fourth-generation Yukawa couplings can form bound states.

Condensates form without Technicolor or new interactions.

Abstract

In the Standard Model with four generations, the two-loop renormalization group equations for the Higgs quartic and Yukawa couplings have a fixed point structure. If the masses of the fourth family are sufficiently heavy, it will contain a natural scale $\Lambda_{FP}$ in the range of a few TeV to the order of $10^2$ TeV, above which the Higgs quartic and Yukawa couplings become practically constant. We found that around $\Lambda_{FP}$ the strong Yukawa couplings make it possible for the fourth generation to form bound states, including composite extra Higgs doublets. In this scenario the fourth generation condensates are obtained without introducing Technicolor or other unknown interactions.