Supersymmetry-Breaking Loops from Analytic Continuation into Superspace

TL;DR

The paper develops a general framework to compute SUSY-breaking effects by analytically continuing renormalization group flow into superspace, treating renormalized couplings as superfields and linking soft-term evolution to SUSY beta functions and anomalous dimensions. It demonstrates that gaugino masses can be computed and remain screened from strong messenger dynamics up to high loop orders, while scalar masses generally receive higher-loop contributions sensitive to messenger details. The formalism is implemented with regulators (notably dimensional reduction and the SDR/DR' scheme) to yield regulator-consistent, all-orders relations for soft terms, including explicit next-to-leading order results in gauge mediation and threshold-induced effects. This approach clarifies the connection between holomorphic and real gauge couplings, provides precise predictions for GMSB spectra, and offers a powerful, general method for evaluating soft terms in a broad class of SUSY theories.

Abstract

We extend to all orders in perturbation theory a method to calculate supersymmetry-breaking effects by analytic continuation of the renormalization group into superspace. 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 consider these issues for a number of regulators, including dimensional reduction. With this method, the renormalization group equations for soft supersymmetry breaking terms are directly related to supersymmetric beta functions and anomalous dimensions to all orders in perturbation theory. However, the real power of the formalism lies in computing finite soft breaking effects corresponding to high-loop component calculations. We prove that the gaugino mass in gauge-mediated supersymmetry 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.

Figures (2)

• Figure 1: One-loop diagrams contributing to the vector field propagator.
• Figure 2: NLO correction to the gluino pole mass, as a function of the messenger mass scale $M$, for messenger index $N=1,3,5$. We have taken a leading-order value of the gluino mass of 600 GeV and $\tan\beta=2$, but the results are rather insensitive to these choices. The curves are interrupted at values of $M$ that require $F = M^2$ to obtain the required gluino mass.