A formal notion of genericity and term-by-term vanishing superpotentials at supersymmetric vacua from R-symmetric Wess-Zumino models

Abstract

It is known in previous literature that if a Wess-Zumino model with an R-symmetry gives a supersymmetric vacuum, the superpotential vanishes at the vacuum. In this work, we establish a formal notion of genericity, and show that if the R-symmetric superpotential has generic coefficients, the superpotential vanishes term-by-term at a supersymmetric vacuum. This result constrains the form of the superpotential which leads to a supersymmetric vacuum. It may contribute to a refined classification of R-symmetric Wess-Zumino models, and find applications in string constructions of vacua with small superpotentials. A similar result for a scalar potential system with a scaling symmetry is discussed.

Gaugino masses from misaligned supersymmetry breaking and R-symmetry breaking spurions

“…In this work, we have shown that it is possible to generate gaugino masses, using multiple SUSY breaking and R-symmetry breaking spurions with a proper R-charge arrangement satisfying the condition (19). The magnitude of resulting gaugino masses ( 22) is suppressed ψ1 M , provided that all VEV's of Y 's and all messenger masses are at the universal scale M .…”

“…Messenger masses must be determined from eigenvalues of the messenger mass matrix, and the mass eigenstates are generally not aligned with the Rcharge eigenstates of messengers. There may also be more than one combinations of X's and Y 's satisfying the condition (19), corresponding to multiple different loop diagrams which contribute to the gaugino masses. Therefore the actual gaugino masses require more careful calculation depending on these details of the model.…”

“…This is just the no-go statement obtained in [30]: The simplest tree-level R-symmetry breaking model, if successfully generates gaugino masses in gauge mediation, is generically accompanied by same magnitude of loop-level R-symmetry breaking which also contributes to gaugino masses. To generate gaugino masses from misaligned SUSY breaking and R-symmetry breaking spurions in a generic model, it is necessary to have multiple F X 's or multiple φ Y 's inserted in the loop of Figure 4, satisfying the condition (19).…”

“…This section presents simple examples to demonstrate the possibility of generating gaugino masses with multiple spurions satisfying the condition (19). Noticing that both N X and N Y must be odd numbers, the simplest model has either three F X vertices or three φ Y vertices inserted in the loop.…”

“…To build a natural SUSY breaking model in the hidden sector, it is necessary to introduce an R-symmetry which restricts the possible terms appearing in the superpotential [9]. The R-charge assignment of fields determines the generic form of the superpotential which has R-charge 2, and SUSY or SUSY breaking vacua can be obtained by a proper R-charge assignment satisfying certain conditions [10,11,12,13,14,15,16,17,18,19,20]. SUSY breaking effects are then transferred to the visible sector through the coupling of messenger fields.…”