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We consider the relations between the gauge couplings at the electroweak scale and the high scale where unification of the three gauge couplings is expected. Threshold corrections are incorporated both at the supersymmetric and at the grand unified scale and, where available, three-loop running and two-loop decoupling are employed. We study the impact of the current experimental uncertainties of the coupling constants and the supersymmetric mass spectrum on the prediction of the superheavy masses within the socalled minimal supersymmetric SU(5). As a main result of the three-loop analysis we confirm that minimal supersymmetric SU(5) cannot be ruled out by the current experimental data on proton decay rates.

The three Laser Interferometer Space Antenna (LISA) spacecraft are going to be placed in a triangular formation in an Earth-trailing or Earth-leading orbit. They will be launched together on a single rocket and transferred to that science orbit using Solar Electric Propulsion. Since the transfer Δv depends on the chosen science orbit, both transfer and science orbit have been optimised together. For a thrust level of 90 mN, an allocation of 1092 m/s per spacecraft is sufficient for an all-year launch in 2034. For every launch month a dedicated science orbit is designed with a corner angle variation of 60° ± 1.0° and an arm length rate of maximum 10 m/s. Moreover, a detailed navigation analysis of the science orbit insertion and the impact on insertion errors on the constellation stability has been conducted. The analysis shows that Range/Doppler measurements together with a series of correction manoeuvres at the beginning of the science orbit phase can reduce insertion dispersions to a level where corner angle variations remain at about 60° ± 1.1° at 99% C.L. However, the situation can become significantly worse if the self-gravity accelerations acting during the science orbit phase are not sufficiently characterised prior to science orbit insertion.

In supersymmetric grand-unified models, the lepton mixing matrix can possibly affect flavor-changing transitions in the quark sector. We present a detailed analysis of a model proposed by Chang, Masiero and Murayama, in which the near-maximal atmospheric neutrino mixing angle governs large new b → s transitions. Relating the supersymmetric low-energy parameters to seven new parameters of this SO(10) GUT model, we perform a correlated study of several flavor-changing neutral current (FCNC) processes. We find the current bound on B(τ → µγ) more constraining than B(B → X s γ). The LEP limit on the lightest Higgs boson mass implies an important lower bound on tan β, which in turn limits the size of the new FCNC transitions. Remarkably, the combined analysis does not rule out large effects in B s −B s mixing and we can easily accomodate the large CP phase in the B s −B s system which has recently been inferred from a global analysis of CDF and DØ data. The model predicts a particle spectrum which is different from the popular Constrained Minimal Supersymmetric Standard Model (CMSSM). B(τ → µγ) enforces heavy masses, typically above 1 TeV, for the sfermions of the degenerate first two generations. However, the ratio of the third-generation and first-generation sfermion masses is smaller than in the CMSSM and a (dominantly right-handed) stop with mass below 500 GeV is possible.

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