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Abstract |
Some time ago it was claimed in “Spontaneous breaking of lepton number and cosmological domain wall problem” [Lazarides et al. Phys. Rev. Lett. 122, 151301 (2019)] that nonperturbative instantons of the weak interaction SU(2)W lead to the formation of domain walls in Majoron models owing to the anomaly of the spontaneously broken global lepton number L symmetry U(1)L with respect to SU(2)W. We point out that it has long been known that this effect can be completely rotated away unless there is a source of explicit B + L breaking present, where B denotes the baryon number. We further estimate the tiny instanton-induced Majoron mass from B + L breaking and analyze the cosmological impact of such domain walls. In general, this scenario does not lead to a cosmological catastrophe, and we demonstrate that the tiny instanton-induced mass can act as a bias term to collapse walls induced by a larger source of lepton number breaking. Alternatively, this electroweak Majoron could act as dynamical dark energy. |
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