Renormalization Properties of Softly Broken SUSY Gauge Theories

In the present review we show that renormalizations in a softly broken SUSY gauge theory are not independent but directly follow from those of an unbroken or rigid theory. This is a consequence of a treatment of a softly broken theory as a rigid one in external spurion superfield. This enables one to get the singular part of effective action in a broken theory from a rigid one by a simple modification of the couplings. Substituting the modified couplings into renormalization constants, RG equations, solutions to these equations, approximate solutions, fixed points, etc., one can get corresponding relations for the soft terms by a simple Taylor expansion over the Grassmannian variables. Some examples including the MSSM in low and high $\tan\beta$ regime, SUSY GUTs and the N=2 Seiberg-Witten model are considered.Comment: LaTeX, 25pp, 2 eps figures. Talk at "Continuous Advances in QCD 2002/Arkadyfest

Beyond The Standard Model

The present lectures contain an introduction to possible new physics beyond the Standard Model. Having in mind first of all accelerator experiments of the nearest future we concentrate on supersymmetry, a new symmetry that relates bosons and fermions, as the first target of experimental search. Since supersymmetry is widely covered in the literature, we mostly consider novel developments and applications to hadron colliders. We describe then the so-called extra dimensional models in less detail and discuss their possible manifestations.Comment: 52 pages, 51 eps figures, Lectures given at the European School on High Energy Physics, May-June 2004, Sant Feliu de Guixols, Spai

Renormalization Group Treatment of Nonrenormalizable Interactions

The structure of the UV divergencies in higher dimensional nonrenormalizable theories is analysed. Based on renormalization operation and renormalization group theory it is shown that even in this case the leading divergencies (asymptotics) are governed by the one-loop diagrams the number of which, however, is infinite. Explicit expression for the one-loop counter term in an arbitrary D-dimensional quantum field theory without derivatives is suggested. This allows one to sum up the leading asymptotics which are independent of the arbitrariness in subtraction of higher order operators. Diagrammatic calculations in a number of scalar models in higher loops are performed to be in agreement with the above statements. These results do not support the idea of the na\"ive power-law running of couplings in nonrenormalizable theories and fail (with one exception) to reveal any simple closed formula for the leading terms.Comment: LaTex, 11 page