Abstract
Working within the context of PT-symmetric quantum mechanics, we begin by describing a non-Hermitian extension of QED that is both Lorentz invariant and consistent with unitarity. We show that the non-Hermitian Dirac mass matrix of this theory exhibits an exceptional point, corresponding to an effectively massless theory whose conserved current is either right- or left-chiral dominated. With this inspiration, we are able to construct a non- Hermitian model of light Dirac neutrino masses from Hermitian and anti-Hermitian Yukawa couplings that are both of order unity. We finish by highlighting potential phenomenological implications of this model.
Highlights
The observation of neutrino flavour oscillations has provided compelling empirical evidence that the neutrinos of the Standard Model (SM) of particle physics have nonzero masses [1]
We are able to construct a nonHermitian model of light Dirac neutrino masses from Hermitian and anti-Hermitian Yukawa couplings that are both of order unity
Concluding remarks We have described a U (1) gauge theory coupled to a fermion with an anti-Hermitian, parityviolating mass term
Summary
The observation of neutrino flavour oscillations has provided compelling empirical evidence that (at least two of) the neutrinos of the Standard Model (SM) of particle physics have nonzero masses [1]. We show that the non-Hermitian Dirac mass matrix of this theory exhibits an exceptional point, corresponding to an effectively massless theory whose conserved current is either right- or left-chiral dominated. We are able to construct a nonHermitian model of light Dirac neutrino masses from Hermitian and anti-Hermitian Yukawa couplings that are both of order unity.
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