Abstract
We present an extension of the mass sum rule that applies to renormalizable rigid supersymmetric field theories to the case of the N=1 supersymmetric effective action (the gauged non-linear sigma model) consisting of adjoint scalar superfields and vector superfields possessing a Kähler potential, a set of gauge coupling functions (second prepotential derivatives) and a superpotential, which respectively set their energy scales. The mass sum rule derived is valid for any vacua, including the (metastable) one of broken supersymmetry with the condensates of D-term and/or F-term. We manage to extend these analyses to the cases where superfields in (anti-)fundamental representation are present. The supertrace is shown to vanish in those cases where underlying geometry is special Kähler and theory under concern is anomaly free. Simple phenomenological application is given, providing an upper bound for gaugino masses. We discuss that the effects of the D and/or F condensates can be represented as a set of soft breaking terms with their strengths predicted by the scales.
Highlights
The mass sum rule of renormalizable rigid supersymmetric (SUSY) field theories in four dimensions [1] played an important role in eighties in deciding upon the appropriate use of supersymmetry in particle physics together with the notion of naturalness
Being largely independent of the dynamics, it gives us a general constraint on a pattern of bose-fermi mass splitting when applied to theories with vacua of spontaneously broken supersymmetry and has provided a rationale for the existence of the hidden sector that has affected the SUSY model building till today
It has been demonstrated that dynamical supersymmetry breaking takes place on metastable vacua in the weak-coupling regime: the D-term triggered Hartree-Fock treatment has enabled us to exhibit the condensates of the order parameters of supersymmetry on the metastable vacuum through the gap equation [37,38,39]
Summary
The mass sum rule of renormalizable rigid supersymmetric (SUSY) field theories in four dimensions [1] played an important role in eighties in deciding upon the appropriate use of supersymmetry in particle physics together with the notion of naturalness. We derive a mass sum rule from a prototypical N = 1 supersymmetric effective action (gauged non-linear sigma model). The effective action that we consider consists of adjoint chiral superfields and vector superfields, possessing a Kahler potential, a set of gauge coupling functions (second prepotential derivatives) and a superpotential, which respectively set distinct energy scales. 3) the gauge group can be arbitrary except that it contains an overall U(1) in which all particles in the observable sector are singlets It has been demonstrated [39] the supersymmetry is spontaneously broken in the Hartree-Fock approximation in this system, replacing 3) by. The role played by this effective action in the vacuum of broken supersymmetry is somewhat analogous to that played by the NJL model [45,46] in broken chiral symmetry which connects the confinement scale and the scale of the chiral lagrangian: here, this effective action describes the dynamics in the intermediate energy scale, connecting the low energy dynamics with the high energy inputs
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