Exploring Softly Broken SUSY Theories via Grassmannian Taylor Expansion

We demonstrate that soft SUSY breaking introduced via replacement of the couplings of a rigid theory by spurion superfields has far reaching consequences. Substituting these modified couplings into renormalization constants, RG equations, solutions to these equations, fixed points, finiteness conditions, etc., one can get corresponding relations for the soft terms by a simple Taylor expansion over the Grassmannian variables. This way one can get new solutions of the RG equations. Some examples including the MSSM, SUSY GUTs and the N=2 Seiberg-Witten model are given.Comment: Latex, 10pp, no figure

Beyond the Standard Model (in search of supersymmetry) [online]

The present lectures contain an introduction to low energy supersymmetry, a new symmetry that relates bosons and fermions, in particle physics. The Standard Model of fundamental interactions is briefly reviewed, and the motivation to introduce supersymmetry is discussed. The main notions of supersymmetry are introduced. The supersymmetric extension of the Standard Model - the Minimal Supersymmetric Standard Model - is considered in more detail. Phenomenological features of the MSSM as well as possible experimental signatures of SUSY are described. An intriguing situation with the supersymmetric Higgs boson is discussed

Renormalizable 1/N_f Expansion for Field Theories in Extra Dimensions

We demonstrate how one can construct renormalizable perturbative expansion in formally nonrenormalizable higher dimensional field theories. It is based on $1/N_f$-expansion and results in a logarithmically divergent perturbation theory in arbitrary high space-time dimension. First, we consider a simple example of $N$-component scalar filed theory and then extend this approach to Abelian and non-Abelian gauge theories with $N_f$ fermions. In the latter case, due to self-interaction of non-Abelian fields the proposed recipe requires some modification which, however, does not change the main results. The resulting effective coupling is dimensionless and is running in accordance with the usual RG equations. The corresponding beta function is calculated in the leading order and is nonpolynomial in effective coupling. It exhibits either UV asymptotically free or IR free behaviour depending on the dimension of space-time. The original dimensionful coupling plays a role of a mass and is also logarithmically renormalized. We analyze also the analytical properties of a resulting theory and demonstrate that in general it acquires several ghost states with negative and/or complex masses. In the former case, the ghost state can be removed by a proper choice of the coupling. As for the states with complex conjugated masses, their contribution to physical amplitudes cancels so that the theory appears to be unitary.Comment: 32 pages, 20 figure

Higher Derivative Operators from Transmission of Supersymmetry Breaking on S_1/Z_2

We discuss the role that higher derivative operators play in field theory orbifold compactifications on S_1/Z_2 with local and non-local (Scherk-Schwarz) breaking of supersymmetry. Integrating out the bulk fields generates brane-localised higher derivative counterterms to the mass of the brane (or zero-mode of the bulk) scalar field, identified with the Higgs field in many realistic models. Both Yukawa and gauge interactions are considered and the one-loop results found can be used to study the ``running'' of the scalar field mass with respect to the momentum scale in 5D orbifolds. In particular this allows the study of the behaviour of the mass under UV scaling of the momentum. The relation between supersymmetry breaking and the presence of higher derivative counterterms to the mass of the scalar field is investigated. This shows that, regardless of the breaking mechanism, (initial) supersymmetry cannot, in general, prevent the emergence of such operators. Some implications for phenomenology of the higher derivative operators are also presented.Comment: 29 pages, LaTeX. Added Section 4 ("Phenomenological implications: living with ghosts?") and Appendix

Higgs Limit and b->s gamma Constraints in Minimal Supersymmetry

New limits on the Higgs mass from LEP and new calculations on the radiative (penguin) decay of the b->s gamma branching ratio restrict the parameter space of the Constrained Minimal Supersymmetric Standard Model (CMSSM). We find that for the low tan(beta) scenario only one sign of the Higgs mixing parameter is allowed, while the high tan(beta scenario is practically excluded, if one requires all sparticles to be below 1 TeV and imposes radiative electroweak symmetry breaking as well as gauge and Yukawa coupling unification. For squarks between 1 and 2 TeV high tan(beta) scenarios are allowed. We consider especially a new high tan(beta)=64 scenario with triple unification of all Yukawa couplings of the third generation, which show an infrared fixed point behaviour. The upper limit on the mass of the lightest Higgs in the low (high) tan(beta) scenarios is 97+-6~(120+-2) GeV, where the errors originate predominantly from the uncertainty in the top mass.Comment: latex + 6 eps figs, 10 pages, IEKP-KA/98-08; References updated in replacement + 1 figure concerning triple Yukawa unification added for final publication in Phys. Let

Renormalization of the Fayet-Iliopoulos Term in Softly Broken SUSY Gauge Theories

It is shown that renormalization of the Fayet-Iliopoulos term in a softly broken SUSY gauge theory, in full analogy with all the other soft terms renormalizations, is completely defined in a rigid or an unbroken theory. However, contrary to the other soft renormalizations, there is no simple differential operator that acts on the renormalization functions of a rigid theory and allows one to get the renormalization of the F-I term. One needs an analysis of the superfield diagrams and some additional diagram calculations in components. The method is illustrated by the four loop calculation of some part of renormalization proportional to the soft scalar masses and the soft triple couplings.Comment: Latex2e, 14 pages, uses axodraw.sty. References adde

Phenomenology of the 1/Nf_f Expansion for Field Theories in Extra Dimensions

In this paper we review the properties of the 1/$N_f$ expansion in multidimensional theories. Contrary to the usual perturbative expansion it is renormalizable and contains only logarithmic divergencies. The price for it is the presence of ghost states which, however, in certain cases do not contribute to physical amplitudes. In this case the theory is unitary and one can calculate the cross-sections. As an example we consider the differential cross section of elastic $eq \to eq$ scattering in $D=7,11,...$-dimensional world. We look also for the unification of the gauge couplings in multidimensional Standard Model and its SUSY extension which takes place at energies lower than in 4 dimensions.Comment: Submitted for the SUSY07 proceedings, 4 pages, LaTeX, 4 eps figures + 3 axodraw figure

A global fit to the anomalous magnetic moment, b -> Xs-gamma and Higgs limits in the constrained MSSM

New data on the anomalous magnetic moment of the muon together with the b -> Xsgamma decay rate are considered within the supergravity inspired constrained minimal supersymmetric model. We perform a global statistical X² analysis of these data and show that the allowed region of parameter space is bounded from below by the Higgs limit, which depends on the trilinear coupling and from above by the anomalous magnetic moment aµ. The newest b ->Xsgamma data deviate 1.7# from recent SM cal­culations and prefer a similar parameter region as the 2.6# deviation from aµ

Supersymmetric Models with Higher Dimensional Operators

In 4D renormalisable theories, integrating out massive states generates in the low energy effective action higher dimensional operators (derivative or otherwise). Using a superfield language it is shown that a 4D N=1 supersymmetric theory with higher derivative operators in either the Kahler or the superpotential part of the Lagrangian and with an otherwise arbitrary superpotential, is equivalent to a 4D N=1 theory of second order (i.e. without higher derivatives) with additional superfields and renormalised interactions. We provide examples where a free theory with trivial supersymmetry breaking provided by a linear superpotential becomes, in the presence of higher derivatives terms and in the second order version, a non-trivial interactive one with spontaneous supersymmetry breaking. The couplings of the equivalent theory acquire a threshold correction through their dependence on the scale of the higher dimensional operator(s). The scalar potential in the second order theory is not necessarily positive definite, and one can in principle have a vanishing potential with broken supersymmetry. We provide an application to MSSM and argue that at tree-level and for a mass scale associated to a higher derivative term in the TeV range, the Higgs mass can be lifted above the current experimental limits.Comment: 36 pages; some clarifications and references adde

Generalization of the BLM procedure and its scales in any order of pQCD

The Brodsky--Lepage--Mackenzie procedure is sequentially and unambiguously extended to any fixed order of perturbative QCD beyond the so called ``large--\beta_0 approximation''. As a result of this procedure, the obtained perturbation series looks like a continued-fraction representation. A subsequent generalization of this procedure is developed, in order to optimize the convergence of the final series, along the lines of the Fastest Convergence Prescription. This generalized BLM procedure is applied to the Adler D function and also to R_{e^+e^-} in QCD at N$^3$LO. A further extension of the sequential BLM is presented which makes use of additional parameters to optimize the convergence of the power-series at any fixed order of expansion.Comment: 24 pages, JHEP3, 4 figures are enclosed as eps-file, final version to be published in JHE