Top quark and Higgs boson masses: Interplay between infrared and ultraviolet physics

Abstract

We review recent efforts to explore the information on masses of heavy matter particles, notably of the top quark and the Higgs boson, as encoded at the quantum level in the renormalization group equations. The Standard Model (SM) and the Minimal Supersymmetric Standard Model (MSSM) are considered in parallel throughout. First, the question is addressed to which extent the infrared physics of the “top-down” renormalization group flow is independent of the ultraviolet physics. The central issues are i) infrared attractive fixed point values for the top and the Higgs mass, the most outstanding one being m t = O(190 GeV) sin β in the MSSM, ii) infrared attractive relations between parameters, the most prominent ones being an infrared fixed top-Higgs mass relation in the SM, leading to m H =O(140 GeV) for the experimental top mass, and an infrared fixed relation between the top mass and the parameter tan β in the MSSM, and iii) a systematical analytical assessment of their respective strengths of attraction. The triviality and vacuum stability bounds on the Higgs and top masses in the SM as well as the upper bound on the mass of the lightes Higgs boson in the MSSM are reviewed. The mathematical backbone for all these features, the rich structure of infrared attractive fixed points, lines, surfaces,… in the corresponding multiparameter space, is made transparent. Interesting hierarchies emerge: i) infrared attraction in the MSSM is systematically stronger than in the SM, ii) generically, nontrivial higher dimensional fixed manifolds are more strongly infrared attractive than the lower dimensional ones. Tau-bottom-(top) Yukawa coupling unification as an ultraviolett symmetry property of supersymmetric grand unified theories and its power to focus the “top-down” renormalization group flow into the IR top mass fixed point and, more generally, onto the infrared fixed line in the m t -tan β-plane is reviewed. The program of reduction of parameters, a systematic search for renormalization group invariant relations between couplings, guided by the requirement of asymptotically free couplings in the complementary “bottom-up” renormalization group evolution, is summarized; its interrelations with the search for IR attractive fixed manifolds are pointed out.