Effect ofCP-odd Planck-scale-induced operators on the Majoron scale

We extend a recent work on the effect of nonperturbative Planck scale effects on models with spontaneously broken global B-L symmetry, where it was shown that the scale ${\mathit{V}}_{\mathit{B}\mathit{L}}$ of this symmetry must be less than 10 TeV. We show that, if the Planck scale effects break CP invariance, an allowed window for ${\mathit{V}}_{\mathit{B}\mathit{L}}$ appears where ${10}^8$ GeV≤${\mathit{V}}_{\mathit{B}\mathit{L}}$≤5×${10}^{10}$ GeV.