**Implications of Attractive Fixed
Manifolds of the**

Renormalization Group Equations

The renormalization group (RG) flow of *ratios*
of Yukawa and Higgs couplings [or also of ratios of parton densities]
is often strongly attracted towards certain *fixed points, fixed
lines, fixed surfaces i*n the space of dependent variables. Unlike generic
solutions, these *fixed manifolds* represent solutions of the RG-equations,
which are *independent of initial values*. For example, in a typical
RG evolution of ratios of Yukawa and Higgs couplings from a high ultra-violet
(UV) momentum scale down to the presently accessible infra-red (IR) region,
this implies a certain decoupling of the UV physics from IR physics along
with model independent *strong constraints among quark and Higgs
masses. *This general mechanism may be explored in the Standard Model
as well as in popular extensions thereof, like minimal or next-to-minimal
Supersymmetry...

##
Publications

- Barbara Schrempp and Fridger Schrempp,

*A Renormalization Group Invariant Line and an Infrared Attractive
Top-Higgs Mass Relation,*

DESY-92-147; published in **Phys.
Lett. B 299 (1993) 321-328**

- Barbara Schrempp,

*Infrared Fixed Points and Fixed Lines in the Top Bottom Tau Sector
in Supersymmetric Grand Unification,*

DESY-94-193; hep-ph/9411241;
published in **Phys. Lett. B 344 (1995) 193-200**

##
Review

- Barbara Schrempp and Michael Wimmer,

*Top Quark and Higgs Boson Masses: Interplay Between Infrared and
Ultraviolet Physics,*

DESY-96-109; hep-ph/9606386;
published in **Prog. Part. Nucl. Phys. 37 (1996) 1-98**

*Last modified: July 19, 2002*

Fridger Schrempp (fridger.schrempp@desy.de)