48,940 research outputs found
Left-handed completeness
We give a new proof of the completeness of the left-handed star rule of Kleene algebra. The proof is significantly shorter than previous proofs and exposes the rich interaction of algebra and coalgebra in the theory of Kleene algebra
First quantized approaches to neutrino oscillations and second quantization
Neutrino oscillations are treated from the point of view of relativistic
first quantized theories and compared to second quantized treatments. Within
first quantized theories, general oscillation probabilities can be found for
Dirac fermions and charged spin 0 bosons. A clear modification in the
oscillation formulas can be obtained and its origin is elucidated and confirmed
to be inevitable from completeness and causality requirements. The left-handed
nature of created and detected neutrinos can also be implemented in the first
quantized Dirac theory in presence of mixing; the probability loss due to the
changing of initially left-handed neutrinos to the undetected right-handed
neutrinos can be obtained in analytic form. Concerning second quantized
approaches, it is shown in a calculation using virtual neutrino propagation
that both neutrinos and antineutrinos may also contribute as intermediate
particles. The sign of the contributing neutrino energy may have to be chosen
explicitly without being automatic in the formalism. At last, a simple second
quantized description of the flavor oscillation phenomenon is devised. In this
description there is no interference terms between positive and negative
components, but it still gives simple normalized oscillation probabilities. A
new effect appearing in this context is an inevitable but tiny violation of the
initial flavor of neutrinos. The probability loss due to the conversion of
left-handed neutrinos to right-handed neutrinos is also presented.Comment: version accepted for publicatio
What Really Sets the Upper Bound on Quantum Correlations?
The discipline of parallelization in the manifold of all possible measurement
results is shown to be responsible for the existence of all quantum
correlations, with the upper bound on their strength stemming from the maximum
of possible torsion within all norm-composing parallelizable manifolds. A
profound interplay is thus uncovered between the existence and strength of
quantum correlations and the parallelizability of the spheres S^0, S^1, S^3,
and S^7 necessitated by the four real division algebras. In particular,
parallelization within a unit 3-sphere is shown to be responsible for the
existence of EPR and Hardy type correlations, whereas that within a unit
7-sphere is shown to be responsible for the existence of all GHZ type
correlations. Moreover, parallelizability in general is shown to be equivalent
to the completeness criterion of EPR, in addition to necessitating the locality
condition of Bell. It is therefore shown to predetermine both the local
outcomes as well as the quantum correlations among the remote outcomes,
dictated by the infinite factorizability of points within the spheres S^3 and
S^7. The twin illusions of quantum entanglement and non-locality are thus shown
to stem from the topologically incomplete accountings of the measurement
results.Comment: 23 pages; Forthcoming in a FQXi sponsored book on Bell's Theorem and
Quantum Entanglement (2011); Provides foundations to the examples worked out
in arXiv:0904.4259, arXiv:quant-ph/0703179, and arXiv:1005.493
Approximate Flavor Symmetries in the Lepton Sector
Approximate flavor symmetries in the quark sector have been used as a handle
on physics beyond the Standard Model. Due to the great interest in neutrino
masses and mixings and the wealth of existing and proposed neutrino experiments
it is important to extend this analysis to the leptonic sector. We show that in
the see-saw mechanism, the neutrino masses and mixing angles do not depend on
the details of the right-handed neutrino flavor symmetry breaking, and are
related by a simple formula. We propose several ans\"{a}tze which relate
different flavor symmetry breaking parameters and find that the MSW solution to
the solar neutrino problem is always easily fit. Further, the oscillation is unlikely to solve the atmospheric neutrino problem
and, if we fix the neutrino mass scale by the MSW solution, the neutrino masses
are found to be too small to close the Universe.Comment: 12 pages (no figures), LBL-3459
LHC and lepton flavour violation phenomenology of a left-right extension of the MSSM
We study the phenomenology of a supersymmetric left-right model, assuming
minimal supergravity boundary conditions. Both left-right and (B-L) symmetries
are broken at an energy scale close to, but significantly below the GUT scale.
Neutrino data is explained via a seesaw mechanism. We calculate the RGEs for
superpotential and soft parameters complete at 2-loop order. At low energies
lepton flavour violation (LFV) and small, but potentially measurable mass
splittings in the charged scalar lepton sector appear, due to the RGE running.
Different from the supersymmetric 'pure seesaw' models, both, LFV and slepton
mass splittings, occur not only in the left- but also in the right slepton
sector. Especially, ratios of LFV slepton decays, such as Br()/Br() are sensitive to the
ratio of (B-L) and left-right symmetry breaking scales. Also the model predicts
a polarization asymmetry of the outgoing positrons in the decay , A ~ [0,1], which differs from the pure seesaw 'prediction' A=1$.
Observation of any of these signals allows to distinguish this model from any
of the three standard, pure (mSugra) seesaw setups.Comment: 43 pages, 17 figure
- …