Neutrino Splitting and Density-Dependent Dispersion Relations
arXiv:1112.3551 · doi:10.5402/2012/436580
Abstract
We show that particles can split only when their group velocity exceeds their phase velocity. In this sense the splitting process is the quantum analog of the modulational instability in anomalous dispersive media. In the case of a neutrino whose dispersion relation contains a subdominant Lorentz-violating correction of the form aP^k, the neutrino will decay into two neutrinos and an antineutrino at a rate proportional to a^3G_F^2E^{2+3k}. Unlike the Cohen-Glashow instability, the splitting instability exists even if all particles involved in the interaction have the same dispersion relations at the relevant energy scales. We show that this instability leads to strong constraints even if the energy E is a function of both the momentum P and also of the background density rho, for example we show that it alone would have been sufficient to eliminate any model of the MINOS/OPERA velocity anomaly which modifies the neutrino dispersion relation while leaving those of other particles intact.
23 pages, 1 figure, focus shifted from superluminality to a general treatment of splitting constraints
References in corpus (39)
- Measurement of the neutrino velocity with the OPERA detector in the CNGS beam
- Environmental Dependence of Masses and Coupling Constants
- New Constraints on Neutrino Velocities
- Measurement of the atmospheric neutrino energy spectrum from 100 GeV to 400 TeV with IceCube
- Measurement of neutrino velocity with the MINOS detectors and NuMI neutrino beam
- Constraints and tests of the OPERA superluminal neutrinos
- OPERA-reassessing data on the energy dependence of the speed of neutrinos
- On the Possibility of Superluminal Neutrino Propagation
- Interpreting OPERA results on superluminal neutrino
- On the fate of Lorentz symmetry in relative-locality momentum spaces
- A search for the analogue to Cherenkov radiation by high energy neutrinos at superluminal speeds in ICARUS
- Superluminal Neutrinos at OPERA Confront Pion Decay Kinematics
- Superluminal neutrinos and extra dimensions: constraints from the null energy condition
- Model dependence of the bremsstrahlung effects from the superluminal neutrino at OPERA
- Astrophysical consequences of the OPERA superluminal neutrino
- Relativistic Superluminal Neutrinos
- Price for Environmental Neutrino-Superluminality
- Constraints on Neutrino Velocities Revisited
- Violations of Lorentz invariance in the neutrino sector: an improved analysis of anomalous threshold constraints
- Constraints from Neutrino Decay on Superluminal Velocities
- Neutrino Dispersion Relations from a Dark Energy Model
- Constraints on the interpretation of the superluminal motion of neutrinos at OPERA
- Superluminal neutrino, flavor, and relativity
- Neutrino Shortcuts in Spacetime
- Background Dependent Lorentz Violation from String Theory
- Non-Standard Neutrino Propagation and Pion Decay
- Superluminal Dark Neutrinos
- Apparent faster than light propagation from light sterile neutrinos
- Background Dependent Lorentz Violation: Natural Solutions to the Theoretical Challenges of the OPERA Experiment
- The Superluminal Neutrinos from Deformed Lorentz Invariance
- Replaying neutrino bremsstrahlung with general dispersion relations
- The Price of Neutrino Superluminality continues to rise
- A note on superluminal neutrinos and deformed special relativity
- On the generality of the Cohen and Glashow constraints on the neutrino velocity
- Spontaneously broken Lorentz invariance from the dynamics of a heavy sterile neutrino
- Dispersion Relations Explaining OPERA Data From Deformed Lorentz Transformation
- Testing the Special Relativity Theory with Neutrino interactions
- Fitting to data of superluminal neutrinos with phenomenological scenarios
- Particle-dependent deformations of Lorentz symmetry