Modular symmetry of soft supersymmetry breaking terms

Abstract

We study the modular symmetry of soft supersymmetry breaking terms. Soft scalar masses and A-term coefficients are invariant under the modular symmetry when we regard F-term as a spurion with the modular weight −2. Their flavor structure is determined by the same symmetry as Yukawa couplings, i.e., fermion masses. The modular symmetric behavior of μ-term and B-term depends on how the μ-term is generated.

Soft supersymmetry breaking terms and lepton flavor violations in modular flavor models

“…Even if we incorporate the radiative corrections, the sign of modular weight will be unchanged as discussed in Ref. [58]. Indeed, in the opposite case k < 0, φ(0) will not be the modular form but rather a singular function.…”

“…For example, one can derive mass matrices such as m ij ∼ u r i +r j and m ij ∼ ε (r i +r j )/N depending on Z N charges of matter fields. Indeed, viable lepton and quark mass matrices are obtained without fine-tuning of parameters [140,[143][144][145][146][147][148][149].…”

“…Further phenomenology has been developed in many works , while theoretical investigations have been also proceeded [210][211][212][213][214][215][216][217][218][219][220][221][222][223][224][225][226][227].…”

“…See, Refs. [68,69], for a realization of modular-invariant effective field theory after the soft supersymmetry breaking.…”

Dispersive constraints on fermion masses

“…For example, a flavor U(1) symmetry with a scalar field called flavon was introduced and then spontaneously broken in the Froggatt-Nielsen model [1]. The aforementioned flavor structures were generated in various models with modular flavor symmetry [2], which has attracted great attention [3][4][5][6][7]. The smooth confinement mechanism without chiral symmetry breaking [8][9][10] was implemented to explain the small Yukawa couplings of the first-and second-family fermions, which are composite of ultraviolet fields, while the third family fermions are elementary to be consistent with the O(1) top Yukawa coupling [11].…”