Howard E. Haber

The search for supersymmetry: Probing physics beyond the standard model

Abstract In this paper we survey methods by which supersymmetry (or other new physics) could be observed in experiments at present and future accelerators. We review some of the motivation for supposing supersymmetry might be a symmetry of nature even though there is presently no evidence for it. We try to systematize the necessary new notation, and discuss in some detail how to calculate results, with considerable emphasis on pedagogical completeness. We summarize present limits on the existence of supersymmetric partners of ordinary particles, and show how to get improved quantitative limits if supersymmetric particles are not detected, so that eventually it is possible to be sure they are either detected or do not exist on the mass scale accessible to experiments.

The Snowmass points and slopes: Benchmarks for SUSY searches

Abstract. The ”Snowmass Points and Slopes” (SPS) are a set of benchmark points and parameter lines in the MSSM parameter space corresponding to different scenarios in the search for Supersymmetry at present and future experiments. This set of benchmarks was agreed upon at the 2001 ”Snowmass Workshop on the Future of Particle Physics” as a consensus based on different existing proposals.

Higgs Bosons in Supersymmetric Models. 1.

Abstract We describe the properties of Higgs bosons in a class of supersymmetric theories. We consider models in which the low-energy sector contains two weak complex doublets and perhaps one complex gauge-singlet Higgs field. Supersymmetry is assumed to be either softly or spontaneously broken, thereby imposing a number of restrictions on the Higgs boson parameters. We elucidate the Higgs boson masses and present Feynman rules for their couplings to the gauge bosons, fermions and scalars of the theory. We also present Feynman rules for vertices which are related by supersymmetry to the above couplings. Exact analytic expressions are given in two useful limits — one corresponding to the absence of the gauge-singlet Higgs field and the other corresponding to the absence of a supersymmetric Higgs mass term.

The CP conserving two Higgs doublet model: The Approach to the decoupling limit

A CP-even neutral Higgs boson with standard-model-like couplings may be the lightest scalar of a two-Higgs-doublet model. We study the decoupling limit of the most general CP-conserving two-Higgs-doublet model, where the mass of the lightest Higgs scalar is significantly smaller than the masses of the other Higgs bosons of the model. In this case, the properties of the lightest Higgs boson are nearly indistinguishable from those of the standard model Higgs boson. The first nontrivial corrections to Higgs boson couplings in the approach to the decoupling limit are also evaluated. The importance of detecting such deviations in precision Higgs boson measurements at future colliders is emphasized. We also clarify the case in which a neutral Higgs boson can possess standard-model-like couplings in a regime where the decoupling limit does not apply. The two-Higgs-doublet sector of the minimal supersymmetric model illustrates many of the above features.

Higgs boson theory and phenomenology

Abstract Precision electroweak data presently favors a weakly-coupled Higgs sector as the mechanism responsible for electroweak symmetry breaking. Low-energy supersymmetry provides a natural framework for weakly-coupled elementary scalars. In this review, we summarize the theoretical properties of the Standard Model (SM) Higgs boson and the Higgs sector of the minimal super-symmetric extension of the Standard Model (MSSM). We then survey the phenomenology of the SM and MSSM Higgs bosons at the Tevatron, LHC and a future e+e− linear collider. We focus on the Higgs discovery potential of present and future colliders and stress the importance of precision measurements of Higgs boson properties.

Reconciling the two loop diagrammatic and effective field theory computations of the mass of the lightest CP - even Higgs boson in the MSSM

The mass of the lightest CP-even Higgs boson of the minimal supersymmetric extension of the Standard Model (MSSM) has previously been computed including O(ααs) twoloop contributions by an on-shell diagrammatic method, while approximate analytic results have also been obtained via renormalization-group-improved effective potential and effective field theory techniques. Initial comparisons of the corresponding two-loop results revealed an apparent discrepancy between terms that depend logarithmically on the supersymmetry-breaking scale, and different dependences of the non-logarithmic terms on the squark mixing parameter, Xt. In this paper, we determine the origin of these differences as a consequence of different renormalization schemes in which both calculations are performed. By re-expressing the on-shell result in terms of MS parameters, the logarithmic two-loop contributions obtained by the different approaches are shown to coincide. The remaining difference, arising from genuine non-logarithmic two-loop contributions, is identified, and its effect on the maximal value of the lightest CP-even Higgs boson mass is discussed. Finally, we show that in a simple analytic approximation to the Higgs mass, the leading two-loop radiative corrections can be absorbed to a large extent into an effective one-loop expression by evaluating the running top quark mass at appropriately chosen energy scales.

Two-component spinor techniques and Feynman rules for quantum field theory and supersymmetry

Two-component spinors are the basic ingredients for describing fermions in quantum field theory in 3 + 1 spacetime dimensions. We develop and review the techniques of the twocomponent spinor formalism and provide a complete set of Feynman rules for fermions using two-component spinor notation. These rules are suitable for practical calculations of crosssections, decay rates, and radiative corrections in the Standard Model and its extensions, including supersymmetry, and many explicit examples are provided. The unified treatment presented in this review applies to massless Weyl fermions and massive Dirac and Majorana fermions. We exhibit the relation between the two-component spinor formalism and the more traditional four-component spinor formalism, and indicate their connections to the spinor helicity method and techniques for the computation of helicity amplitudes.

Renormalization-group-improved Higgs sector of the minimal supersymmetric model.

In the minimal supersymmetric model all Higgs self-coupling parameters are related to gauge couplings at the tree level. Leading-logarithmic radiative corrections to these quantities can be summed using renormalization-group techniques. By this procedure we obtain complete leading-logarithmic radiative corrections to the Higgs boson masses, the CP-even Higgs boson mixing angle, and trilinear Higgs boson couplings. Additional corrections due to squark mixing can be explicitly incorporated into this formalism. These results incorporate nearly all potentially large corrections. Mass shifts to the neutral CP-even Higgs bosons grow with the fourth power of the top-quark mass and can be significant. The phenomenological consequences of these results are examined

Higgs bosons in supersymmetric models (II). Implications for phenomenology

Abstract We discuss a wide range of phenomenological issues involving the production and decay of Higgs bosons. We focus on a minimal two-doublet supersymmetry model with soft supersymmetry breaking.

Charge / Color Breaking Minima and a-Parameter Bounds in Supersymmetric Models

In supersymmetric models, the requirement that the global potential minimum not violate color and/or electric charge invariance implies restrictions on the parameters of the model. We reassess and improve upon constraints on the A parameter that have been obtained previously in the literature. In particular, we demonstrate that no universally applicable bound which is either necessary or sufficient can be given.