I provide a pedagogical introduction to supersymmetry. The level of discussion is aimed at readers who are familiar with the Standard Model and quantum field theory, but who have had little or no prior exposure to supersymmetry. Topics covered include: motivations for supersymmetry, the construction of supersymmetric Lagrangians, superspace and superfields, soft supersymmetry-breaking interactions, the Minimal Supersymmetric Standard Model (MSSM), R-parity and its consequences, the origins of supersymmetry breaking, the mass spectrum of the MSSM, decays of supersymmetric particles, experimental signals for supersymmetry, and some extensions of the minimal framework. † Some attacks on the hierarchy problem, not reviewed here, are based on the proposition that the ultimate cutoff scale is actually close to the electroweak scale, rather than the apparent Planck scale. † Other notations in the literature have H1, H2 or H, H instead of Hu, H d . The notation used here has the virtue of making it easy to remember which Higgs VEVs gives masses to which type of quarks.

Hereditary pancreatitis (HP) is a rare, early-onset genetic disorder characterized by epigastric pain and often more serious complications. We now report that an Arg-His substitution at residue 117 of the cationic trypsinogen gene is associated with the HP phenotype. This mutation was observed in all HP affected individuals and obligate carriers from five kindreds, but not in individuals who married into the families nor in 140 unrelated individuals. X-ray crystal structure analysis, molecular modelling, and protein digest data indicate that the Arg 117 residue is a trypsin-sensitive site. Cleavage at this site is probably part of a fail-safe mechanism by which trypsin, which is activated within the pancreas, may be inactivated; loss of this cleavage site would permit autodigestion resulting in pancreatitis.

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We compute the two-loop renormalization group equations for all soft supersymmetry-breaking couplings in a general softly broken N = 1 supersymmetric model. We also specialize these results to the minimal supersymmetric standard model.

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The scalar potential of the Minimal Supersymmetric Standard Model (MSSM) is nearly flat along many directions in field space. We provide a catalog of the flat directions of the renormalizable and supersymmetry-preserving part of the scalar potential of the MSSM, using the correspondence between flat directions and gauge-invariant polynomials of chiral superfields. We then study how these flat directions are lifted by non-renormalizable terms in the superpotential, with special attention given to the subtleties associated with the family index structure.Several flat directions are lifted only by supersymmetry-breaking effects and by supersymmetric terms in the scalar potential of surprisingly high dimensionality.

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.

We discuss the dependence of running couplings on the choice of regularization method in a general softly-broken N = 1 supersymmetric theory.Regularization by dimensional reduction respects supersymmetry, but standard dimensional regularization does not. We find expressions for the differences between running couplings in the modified minimal subtraction schemes of these two regularization methods, to one loop order. We also find the two-loop renormalization group equations for gaugino masses in both schemes, and discuss the application of these results to the Minimal Supersymmetric Standard Model.