Abstract
In an external magnetic field, the energy of the electroweak sphaleron---representing the energy barrier to baryon and lepton number violation---decreases but remains nonzero until the upper Ambjorn-Olesen critical field strength set by the Higgs mass and the electric charge, where it vanishes. We demonstrate this by numerically computing the sphaleron configuration in the presence of an external magnetic field, over the full range of field strengths until the energy barrier vanishes. We discuss the implications for baryogenesis in the early universe, and the possibility of observing of baryon and lepton number violation in heavy-ion collisions.
Highlights
The electroweak sphaleron [1,2] is a static, unstable solution to the field equations of electroweak theory, a saddle point of the energy functional
In this paper we study this phenomenon beyond the weak-field limit by numerically computing sphaleron solutions over the full range of relevant magnetic field strengths
We find that when Bext is increased, the sphaleron energy initially decreases linearly for Bext ≪ Bðc1riÞt, more rapidly until Bext 1⁄4 Bðc1riÞt
Summary
The electroweak sphaleron [1,2] is a static, unstable solution to the field equations of electroweak theory, a saddle point of the energy functional. Previous numerical evaluations of the sphaleron solution in zero or weak external fields have shown that it has a significant magnetic dipole moment [2,5,6,7,8] This suggests that the energy barrier to sphaleron transitions is lowered in the presence of a weak external magnetic field. As the external field increases in strength above Bðc1riÞt, the mean value of the Higgs field magnitude decreases continuously until, at Bðc2riÞt, the symmetry of the Higgs vacuum is restored It has been shown [12] that in the symmetric Higgs phase there is the potential for unsuppressed B þ L violation, meaning that strong magnetic fields could provide the first observations of this elusive phenomenon. We confirm that the sphaleron energy vanishes precisely at Bext 1⁄4 Bðc2riÞt and not below
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