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We run all the couplings of the minimal supersymmetric (SUSY) extension of the standard model, taking account of the Yukawa sector. After identifying the scale at which the gauge couplings unify, we place bounds on the top-quark mass by requiring equality of the bottom-quark and r Yukawa couplings at that scale. For MSUSY = 1 TeV, M b =4.6 GeV, we find 139

Peripheral arterial occlusive disease (PAOD) results from atherosclerosis of large and medium peripheral arteries, as well as the aorta, and has many risk factors, including smoking, diabetes, hypertension, and hyperlipidemia. PAOD often coexists with coronary artery disease and cerebrovascular disease. Cross-matching a population-based list of Icelandic patients with PAOD who had undergone angiography and/or revascularization procedures with a genealogy database of the entire Icelandic nation defined 116 extended families containing 272 patients. A genomewide scan with microsatellite markers revealed significant linkage to chromosome 1p31 with an allele-sharing LOD score of 3.93 (P=1.04 x 10(-5)). We designate this locus as "PAOD1." Subtracting 35 patients with a history of stroke increased the LOD score to 4.93. This suggests that, although PAOD and other vascular diseases share risk factors, genetic factors specific to subtypes of vascular disease may exist.

Using renormalization group techniques, we examine several interesting relations among masses and mixing angles of quarks and leptons in the standard model. We extend the analysis to the minimal supersymmetric extension to determine its effect on these mass relations. Remarkably supersymmetry allows for these relations to be satisfied at a single grand unified scale. PACS number(s): 12.15Ff, 11.30Pb, 12.10 Dm

We survey mechanisms which introduce lepton-number violation into the standard model. These mechanisms involve extensions in the fermion or scalar sectors. We present a minimal model with explicit lepton-number breaking and an invisible axion. Neutrino masses are generated at one loop. For a reasonable range of parameters the model provides a solution to the strong CP and solarneutrino problems. I. NEUTRINO MASSES AND THE STANDARD MODELIn the standard model, as formulated by Weinberg and Salam, left-handed neutrinos appear without righthanded partners. As neutrinos are electrically neutral, they can still have a Majorana mass, unlike a Dirac mass which requires two helicities. However, Majorana masses break lepton number by two units, while Dirac masses do not.The neutrino Majorana mass appears in the symmetric product of the lepton weak left-handed isodoublets L, and so breaks weak isospin as an isovector, AIw= 1, and hypercharge by two units, A Y =2. Thus, in the absence of an isotriplet Higgs particle, the standard model does not allow tree-level neutrino Majorana masses. In higher-loop order, electroweak gauge symmetry is no longer sufficient to forbid neutrino masses, since com- binations of the Higgs doublets with A I w = l , A Y =2quantum numbers can readily be constructed, for instance, H T r 2 r H and its complex conjugate, leading to a dimension-five operator in the effective Lagrangian. Here H refers to the standard Higgs doublet with Y = 1, and LL is the lepton lefthanded doublet with Y = -1.However, this interaction can never be generated in perturbation theory since it breaks lepton number by two units ( A L = 2 ) . Thus it is lepton-number conservation alone which forbids neutrino masses from appearing in the standard model. In the nonperturbative regime, it is well known that both L and B (baryon number) are broken, while B -L is preserved. Thus one could, in principle, look for a combination of the form where O is an operator which violates B by two units and has a nonzero vacuum value; it would have to be a sixquark condensate, but such an operator does not exist. Thus massless neutrinos are a signature of the standard model.Although direct experimental searches for the consequences of massive neutrinos, e.g., oscillations, have so far failed to turn up anything, the deficit in the expected number of neutrinos from the indicates an explanation in terms of massive neutrinos.' Interpretations of this deficit are about to be clarified by new experiments using gallium.4 On the other hand, theorists do not view global symmetries, such as baryon and lepton numbers, in the same way as local symmetries. Most theorists expect global symmetries to be approximate symmetries, their apparent conservation being explained by the appearance of tiny ratios, as happens in grand unified theories (GUT'S), axion theories, or theories that involve gravity.Since the mass of the W boson is 17 orders of magnitude smaller than the Planck mass, there is ample room for such ratios.In order to incorporate neutrino masses in...