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Supersymmetry-Breaking Loops from Analytic Continuation into Superspace


We extend to all orders in perturbation theory a method to calculate supersymmetry-breaking effects by analytic continuation of the %RG renormalization group into superspace. %It was recently demonstrated by two of the present authors that %an interesting class of leading 1- and 2-loop calculations in \susy-breaking %theories could be performed by ``analytic continuation'' of \rg %equations into superspace. %The present work extends these methods both to higher orders %in perturbation theory, important for computing next-to-leading %order (NLO) quatities, as well as to the most general %form for soft breakings. %We give definitions of the renormalized couplings %in \susc gauge theories that can be treated as %superfields to all orders in perturbation theory. A central observation is that the renormalized gauge coupling can be extended to a real vector superfield, thereby including soft breaking effects in the gauge sector. We explain the relation between this vector superfield coupling and the ``holomorphic" gauge coupling, which is a chiral superfield running only at 1 loop. %We explain in detail how this is %consistent with perturbative results %that apparently violate holomorphy of coupling constants. We consider these issues for a number of regulators, including %the practically useful case of Dimensional Reduction. dimensional reduction. %In particular, the renormalized gauge coupling is a holomorphic %object whose renormalization group equation is purely one-loop. %We explain in detail how this is consistent with perturbative results %that apparently violate holomorphy of coupling constants. With this method, the %RG flow renormalization group equations for soft supersymmetry breaking terms are directly %obtained from the related to \susc beta functions and anomalous dimensions to all orders in perturbation theory. However, the real power of the formalism lies %, however, in computing finite soft breaking effects corresponding to high-loop component calculations. We prove that the gaugino mass in gauge-mediated \susy breaking is ``screened'' from strong interactions in the messenger sector. We present the complete next-to-leading calculation of gaugino masses (2 loops) and sfermion masses (3 loops) in minimal gauge mediation, and several other calculations of phenomenological relevance. %as well as the leading contribution %to gaugino masses in ``mediator" models of gauge-mediation (5 loops). %We also compute the gauge-mediated effective potential %induced along classically flat directions, both for $D$ flat directions (2 %loops) as well as for the scalar partner of the axion (3 loops). %We also compute interesting effects in gauge-mediated models, some %of which correspond to finite parts of 5-loop diagrams in components.

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