Extracting Supersymmetry-Breaking Effects from Wave-Function Renormalization

TL;DR

This paper develops a simple, RG-driven method to compute soft SUSY-breaking terms in theories where breaking is transmitted by renormalizable interactions, by promoting the messenger scale $M$ to the spurion superfield $X$ and deriving soft terms from derivatives of wave-function renormalizations. The approach yields compact expressions for gaugino masses, scalar masses, and $A$-terms at leading order, with two-loop sfermion masses determined from one-loop RG data, and it extends to subleading Higgs mass corrections, messenger–matter couplings, and gauge-mauge (vector) messengers. It demonstrates new phenomenologically relevant results, including a notable ${\cal O}(\alpha_t\alpha_s^2)$ correction to $m_H^2$ and nontrivial contributions from messenger–matter interactions and gauge messengers, which can substantially affect the superpartner spectrum and viability of certain models. The method highlights both its practicality for calculating soft terms and the need for careful threshold and higher-order considerations when extending beyond leading order.

Abstract

We show that in theories in which supersymmetry breaking is communicated by renormalizable perturbative interactions, it is possible to extract the soft terms for the observable fields from wave-function renormalization. Therefore all the information about soft terms can be obtained from anomalous dimensions and beta functions, with no need to further compute any Feynman diagram. This method greatly simplifies calculations which are rather involved if performed in terms of component fields. For illustrative purposes we reproduce known results of theories with gauge-mediated supersymmetry breaking. We then use our method to obtain new results of phenomenological importance. We calculate the next-to-leading correction to the Higgs mass parameters, the two-loop soft terms induced by messenger-matter superpotential couplings, and the soft terms generated by messengers belonging to vector supermultiplets.