D-TERM DYNAMICAL SUPERSYMMETRY BREAKING GENERATING SPLIT ${\mathcal N} = 2$ GAUGINO MASSES OF MIXED MAJORANA–DIRAC TYPE

Abstract

Under a few mild assumptions, [Formula: see text] supersymmetry (SUSY) in four dimensions is shown to be spontaneously broken in a metastable vacuum in a self-consistent Hartree–Fock approximation of Bardeen–Cooper–Schrieffer/Nambu–Jona-Lasinio (BCS/NJL) type to the leading order, in the gauge theory specified by the gauge kinetic function and the superpotential of adjoint chiral superfields, in particular, that possess [Formula: see text] extended SUSY spontaneously broken to [Formula: see text] at tree level. We derive an explicit form of the gap equation, showing the existence of a nontrivial solution. The [Formula: see text] gauginos in the observable sector receive mixed Majorana–Dirac masses and are split due to both the nonvanishing 〈D0〉 and 〈F0〉 induced with 〈D0〉. It is argued that proper physical applications and assessment of the range of the validity of our framework are made possible by rendering the approximation into [Formula: see text] expansion.