Natural solution of SUSY $\mu$ problem from modulus stabilization in modular flavor model

Abstract

We propose a solution to the SUSY $\mu$-problem within the framework of modular flavor symmetry. The explicit $\mu$-term is prohibited by modular symmetry, and an effective $\mu$-term is regenerated following the stabilization of the modulus field. We examine the stabilization mechanism of a single modulus field with the presence of SUSY breaking contributions described by the non-linear SUSY realization scheme involving a nilpotent Goldstino ${\text{X}}_{nl}$ superfield. A natural small ${\mu }_{eff}$, significantly smaller than the SUSY scale, can result from either the expansion of typical modular forms using a small deviation parameter near the fixed point $\omega$, or from the combined effects of suppression by powers of $q^{1/24}$ [or $(2\Im \tau {)}^{-1}$] along with the asymptotic suppression behavior of typical modular forms away from the fixed point $i\infty$, taking the form of appropriate power of the tiny deviation parameter. A natural small ${\mu }_{eff}$ can also be achieved by a weighton-like mechanism for $H_u{H}_d$ bilinear.

Version accepted in PRD; major changes, discussions added; 40 pages, 2 figures

References in corpus (12)

• Combined results of searches for the standard model Higgs boson in pp collisions at sqrt(s) = 7 TeV
• Combined search for the Standard Model Higgs boson using up to 4.9 fb-1 of pp collision data at sqrt(s) = 7 TeV with the ATLAS detector at the LHC
• From Linear SUSY to Constrained Superfields
• Unification of Flavor, CP, and Modular Symmetries
• Landscape of Modular Symmetric Flavor Models
• Revisiting the SUSY mu problem and its solutions in the LHC era
• SUSY Breaking Constraints on Modular flavor $S_3$ Invariant $SU(5)$ GUT Model
• Challenge for spontaneous CP violation in Type IIB orientifolds with fluxes
• Adjoint SU(5) GUT model with Modular $S_4$ Symmetry
• Leptogenesis in $SO(10)$ Models with $A_4$ Modular Symmetry
• Flavor mixing and CP violation from the interplay of $S_4$ modular group and gCP
• Two A5 modular symmetries for Golden Ratio 2 mixing