We review the origin of soft supersymmetry-breaking terms in N = 1 supergravity models of particle physics. We first consider general formulae for those terms in general models with a hidden sector breaking supersymmetry at an intermediate energy scale. The results for some simple models are given. We then consider the results obtained in some simple superstring models in which particular assumptions about the origin of supersymmetry breaking are made. These are models in which the seed of supersymmetry breaking is assumed to be originated in the dilaton/moduli sector of the theory.

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We compute the O(α b α s ) two-loop corrections to the neutral Higgs boson masses in the Minimal Supersymmetric Standard Model, using the effective potential approach. Such corrections can be important in the region of parameter space corresponding to tan β ≫ 1 and sizeable µ. In spite of the formal analogy with the O(α t α s ) corrections, there are important differences, since the dominant effects are controlled by the sbottom-Higgs scalar couplings. We propose a convenient renormalization scheme that avoids unphysically large threshold effects associated with the bottom mass, and absorbs the bulk of the O(α b α s + α b α t ) corrections into the one-loop expression. We give general explicit formulae for the O(α b α s ) corrections to the neutral Higgs boson mass matrix. We also discuss the importance of the O(α 2 b ) corrections and derive a formula for their contribution to m h in a simple limiting case.

We compute the O(α 2 t ) two-loop corrections to the neutral CP-even Higgs boson mass matrix in the Minimal Supersymmetric Standard Model, for arbitrary values of m A and of the parameters in the stop sector, in the effective potential approach. In a large region of parameter space these corrections are sizeable, increasing the prediction for m h by several GeV. We present explicit analytical formulae for a simplified case. We discuss the inclusion of momentum-dependent corrections and some possible ways of assigning the input parameters. 2 12

We perform a detailed analysis of several µ-τ lepton flavour violating (LFV) processes, namely τ → µX (X = γ, e + e − , µ + µ − , ρ, π, η, η ′ ), Z → µτ and Higgs boson decays into µτ . First we present a model independent operator analysis relevant to such decays, then we explicitly compute the LFV operator coefficients [and (g µ − 2)] in a general unconstrained MSSM framework, allowing slepton mass matrices to have large µ-τ entries. We systematically study the role and the interplay of dipole and non-dipole operators, showing how the rates and the mutual correlations of those LFV decays change in different regions of the MSSM parameter space. Values of the LFV branching ratios in the experimentally interesting range 10 −9 − 10 −7 can be achieved. For at least two MSSM Higgs bosons, the branching ratio of the LFV decay into µτ can reach values of order 10 −4 . Effective operators and branching ratiosThis section is devoted to the 'model-independent' calculation of the LFV branching ratios. Namely, first we parametrize the basic effective operators (Section 2.1), then construct appropriate effective lagrangians and compute the branching ratios in terms of the coefficients of the effective operators (Section 2.2). We also discuss correlations among different processes in cases of single-operator-dominance (Section 2.3). Parametrization of LFV effective operatorsOur first step, in the derivation of the LFV branching ratios, is the parametrization of the LFV operators that contain a muon, a tau and either a Z boson, or a photon, or an additional f -fermion pair. The leading contributions to these operators arise from d = 6 SU(2) W × U(1) Y -invariant operators [12], possibly with Higgs fields set at their vacuum expectation values (VEVs). It is useful to keep this in mind, although we will not write explicitly the operators in the unbroken phase (except for a few examples). We also recall that the MSSM contains two Higgs doublets H 1 , H 2 , whose VEVs define the ratio tan β = H 0 2 / H 0 1 . We postpone the discussion of d = 4 Higgs-muon-tau effective operators to Section 3.2. The parametrization given below assumes fermions to be on-shell, whereas gauge bosons could also be off-shell. We keep the tau mass m τ at the leading order and neglect m µ , m e as well as the light-quark masses. We adopt two-component spinor notation, so for example µ and τ (μ c andτ c ) are the left-handed (right-handed) components of the muon and tau fields, respectively 1 . Sometimes (e.g. in Figs. 1, 2, 4) symbols like µ, τ, f will generically refer to the particles, not to specific chiralities. Finally, it is understood that the coefficients of all the LFV operators below should carry a flavour subscript µτ , which we omit for brevity.

We consider supersymmetric scenarios in which the scale of SUSY breaking is low, √ F = O(TeV). Instead of studying specific models of this type, e.g. those with extra dimensions and low fundamental scale, we follow a model-independent approach based on a general effective Lagrangian, in which the MSSM supermultiplets are effectively coupled to a singlet associated to SUSY breaking. Our goal is to analyse the interplay bewteen SUSY breaking and electroweak breaking, generalizing earlier results. The conventional MSSM picture can be substantially modified, mainly because the Higgs potential contains additional effective quartic terms and resembles that of two-Higgs-doublet models, with an additional singlet. Novel opportunities to achieve electroweak breaking arise, and the electroweak scale may be obtained in a less fine-tuned way. Also the Higgs spectrum can be strikingly changed, and the lightest state can be much heavier than in usual supersymmetric scenarios. Other effects appear in the chargino and neutralino sectors, which contain the goldstino. Finally, we discuss the role of electroweak breaking in processes in which two goldstinos could be emitted, such as fermion-antifermion annihilation and the invisible decay of a Z boson or of neutral Higgs bosons.

If the gravitinoG is very light and all the other supersymmetric particles are above threshold, supersymmetry may still be found at colliders, by looking at processes with only gravitinos and ordinary particles in the final state. We compute here the cross-section for the process e + e − →GGγ, whose final state can give rise to a distinctive photon plus missing energy signal at present and future e + e − colliders. We describe how the present LEP data can be used to establish a lower bound on the gravitino mass of order 10 −5 eV. We conclude with a critical discussion of our results, comparing them with related ones and outlining possible generalizations.

We study the structure of the soft SUSY-breaking terms obtained from some classes of 4-D strings under the assumption of dilaton/moduli dominance in the process of SUSY-breaking. We generalize previous analyses in several ways and in particular consider the new features appearing when several moduli fields contribute to SUSY breaking (instead of an overall modulus ¹ ). Some qualitative features indeed change in the multimoduli case.