Top Quark and Higgs Boson Masses: Interplay between Infrared and Ultraviolet Physics

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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 (RG) equations. The Standard Model (SM) and the Minimal Supersymmetric Standard Model (MSSM) are considered in parallel. First, the question is addressed to which extent the infrared (IR) physics of the ``top-down'' RG flow is independent of the ultraviolet (UV) physics. The central issues are i) IR attractive fixed point values for the top and the Higgs mass, the most outstanding one being m_t=O(190 GeV)sin(beta) in the MSSM, ii) IR attractive relations between parameters, the most prominent ones being an IR fixed top-Higgs mass relation in the SM, leading to m_H=O(156) GeV for the experimental top mass, and an IR fixed relation between the top mass and tan(beta) in the MSSM, and iii) an analytical assessment of their respective strengths of attraction. The triviality and vacuum stability bounds on the Higgs and top masses in the SM and the upper bound on the lightest Higgs boson mass in the MSSM are reviewed. The mathematical backbone, the rich structure of IR attractive fixed points, lines, surfaces,... in the multiparameter space, is made transparent. Interesting hierarchies emerge, most remarkably: IR attraction in the MSSM is systematically stronger than in the SM. Tau-bottom-(top) Yukawa coupling unification in supersymmetric grand unified theories and its power to focus the ``top-down'' RG flow into the IR top mass fixed point resp. onto the IR fixed line in the m_t-tan(beta) plane is reviewed. The program of reduction of parameters, a search for RG invariant relations between couplings, guided by the requirement of asymptotically free couplings in the UV limit,is summarized; its interrelations with the search for

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