Evading Weinberg's no-go theorem to construct mass dimension one fermions: Constructing darkness

Recent theoretical work reporting the construction of a new quantum field of spin one half fermions with mass dimension one requires that Weinberg's no go theorem must be evaded. Here we show how this comes about. The essence of the argument is to first define a quantum field with due care being taken in fixing the locality phases attached to each of the expansion coefficients. The second ingredient is to systematically construct the adjoint/dual of the field. The Feynman-Dyson propagator constructed from the vacuum expectation value of the field and its adjoint then yields the mass dimensionality of the field. For a quantum field constructed from a complete set of eigenspinors of the charge conjugation operator, with locality phases judiciously chosen, the Feynman-Dyson propagator has mass dimension one. The Lorentz symmetry is preserved, locality anticommutators are satisfied, without violating fermionic statistics as needed for the spin one half field.Comment: 8 pages, significantly extended published versio

Elko under spatial rotations

Under a rotation by an angle $\vartheta$, both the right- and left- handed Weyl spinors pick up a phase factor ${\exp(\pm\, i \vartheta/2)}$. The upper sign holds for the positive helicity spinors, while the lower sign for the negative helicity spinors. For $\vartheta = 2\pi$ radians this produces the famous minus sign. However, the four-component spinors are built from a direct sum of the indicated two-component spinors. The effect of the rotation by $2\pi$ radians on the eigenspinors of the parity - that is, the Dirac spinors -- is the same as on Weyl spinors. It is because for these spinors the right- and left- transforming components have the same helicity. And the rotation induced phases, being same, factor out. But for the eigenspinors of the charge conjugation operator, i.e. Elko, the left- and right- transforming components have opposite helicities, and therefore they pick up opposite phases. As a consequence the behaviour of the eigenspinors of the charge conjugation operator (Elko) is more subtle: for $0<\vartheta<2\pi$ a self conjugate spinor becomes a linear combination of the self and antiself conjugate spinors with $\vartheta$ dependent superposition coefficients - and yet the rotation preserves the self/antiself conjugacy of these spinors! This apparently paradoxical situation is fully resolved. This new effect, to the best of our knowledge, has never been reported before. The purpose of this communication is to present this result and to correct an interpretational error of a previous version.Comment: 7 pages, Two new sections, and significantly new material. An error in v1 and v2 correcte

Magnetic field creation by solar mass neutrino jets

Parity violation and its effects for neutrinos in astrophysical contexts have been considered earlier in pioneering papers of Hawking and Vilenkin. But because even the largest magnetic moments predicted by physics beyond the Standard Model are some twelve orders of magnitude smaller than the Bohr magneton, their implications for magnetic field generation and neutrino oscillations are generally considered insignificant. Here we show that since in astrophysical scenarios a huge number of neutrinos may be emitted, the smallness of the magnetic moment, when coupled with parity violation, is compensated by the sheer number of neutrinos. The merger of neutron stars would leave behind a short pulse of electromagnetic synchrotron radiation even if the neutrino jet in the merger points away from the neutrino detectors. We show that the magnetic field can be as large as 10^6\,\mbox{Gauss} and comment on the possibility of direct detection. Observation of such a pulse would lend strong support for neutrino magnetic moments and resolve the missing neutrino problem in neutron star mergers.Comment: 5 pages, version accepted for publication in Europhysics Letters (EPL