Neutrino oscillations: Quantum mechanics vs. quantum field theory

A consistent description of neutrino oscillations requires either the quantum-mechanical (QM) wave packet approach or a quantum field theoretic (QFT) treatment. We compare these two approaches to neutrino oscillations and discuss the correspondence between them. In particular, we derive expressions for the QM neutrino wave packets from QFT and relate the free parameters of the QM framework, in particular the effective momentum uncertainty of the neutrino state, to the more fundamental parameters of the QFT approach. We include in our discussion the possibilities that some of the neutrino's interaction partners are not detected, that the neutrino is produced in the decay of an unstable parent particle, and that the overlap of the wave packets of the particles involved in the neutrino production (or detection) process is not maximal. Finally, we demonstrate how the properly normalized oscillation probabilities can be obtained in the QFT framework without an ad hoc normalization procedure employed in the QM approach.Comment: LaTeX, 42 pages, 1 figure; v2: minor clarifications, matches published version; v3: Corrected the discussion of the conditions under which an oscillation probability can be sensibly defined in the QFT approach (sec. 5.2.4

Quantum field theoretic approach to neutrino oscillations in matter

We consider neutrino oscillations in non-uniform matter in a quantum field theoretic (QFT) approach, in which neutrino production, propagation and detection are considered as a single process. We find the conditions under which the oscillation probability can be sensibly defined and demonstrate how the properly normalized oscillation probability can be obtained in the QFT framework. We derive the evolution equation for the oscillation amplitude and discuss the conditions under which it reduces to the standard Schr\"odinger-like evolution equation. It is shown that, contrary to the common usage, the Schr\"odinger-like evolution equation is not applicable in certain cases, such as oscillations of neutrinos produced in decays of free pions provided that sterile neutrinos with $\Delta m^2\gtrsim 1$ eV$^2$ exist.Comment: LaTeX, 24 pages + 16 pages of appendices, 1 figure. V2: typos correcte

The Physics of Core-Collapse Supernovae

Supernovae are nature's grandest explosions and an astrophysical laboratory in which unique conditions exist that are not achievable on Earth. They are also the furnaces in which most of the elements heavier than carbon have been forged. Scientists have argued for decades about the physical mechanism responsible for these explosions. It is clear that the ultimate energy source is gravity, but the relative roles of neutrinos, fluid instabilities, rotation and magnetic fields continue to be debated.Comment: Review article; 17 pages, 5 figure

Limits on active-sterile neutrino mixing and the primordial deuterium abundance.

Studies of limits on active-sterile neutrino mixing derived from big bang nucleosynthesis (BBN) considerations are extended to consider the dependence of these constraints on the primordial deuterium abundance. This study is motivated by recent measurements of D/H in quasar absorption systems, which at present yield discordant results. Limits on active-sterile mixing are somewhat relaxed for high D/H (≈2×[Formula presented]). For low D/H (≈2×[Formula presented]), no active-sterile neutrino mixing is allowed by currently popular upper limits on the primordial [Formula presented] abundance [Formula presented]. For such low primordial D/H values, the observational inference of active-sterile neutrino mixing by upcoming solar neutrino experiments would imply that [Formula presented] has been systematically underestimated, unless there is new physics not included in standard BBN. © 1996 The American Physical Society

Neutrino oscillations in curved spacetime: A heuristic treatment

We discuss neutrino oscillations in curved spacetime. Our heuristic approach can accommodate matter effects and gravitational contributions to neutrino spin precession in the presence of a magnetic field. By way of illustration, we perform explicit calculations in the Schwarzschild geometry. In this case, gravitational effects on neutrino oscillations are intimately related to the redshift. We discuss how spacetime curvature could affect the resonance position and adiabaticity of matter-enhanced neutrino flavor conversion. © 1997 The American Physical Society

The Deuteron confronts big bang nucleosynthesis

Recent determinations of the deuterium abundance, 2H/H, in high redshift Lyman limit hydrogen clouds challenge the usual picture of primordial nucleosynthesis based on "concordance" of the calculated light element (2H, 3He, 4He, 7Li) nucleosynthesis yields with the observationally-inferred abundances of these species. Concordance implies that all light element yields can be made to agree with the observationally-inferred abundances (within errors) for single global specifications of the baryon-to-photon ratio, η; lepton number; neutron lifetime; and expansion rate (or equivalently, effective number of light neutrino degrees of freedom Nv). Though one group studying Lyman limit systems obtains a high value of 2H/H (∼ 2 × 10-4), another group finds consistently low values (∼ 2 × 10-5). In the former case, concordance for Nv = 3 is readily attained for the current observationally-inferred abundances of 4He and 7Li. But if the latter case represents the primordial deuterium abundance, then concordance for any Nv is impossible unless the primordial value of 7Li/H is considerably larger than the abundance of lithium as measured in old, hot Pop II halo stars. Furthermore, concordance with Nv = 3 is possible for low 2H/H only if either (1) the primordial 4He abundance has been significantly underestimated, or (2) new neutrino sector physics is invoked. We argue that systematic underestimation of both the 7Li and 4He primordial abundances is the likely resolution of this problem, a conclusion which is strengthened by new results on 4He

Neutrino oscillations in curved spacetime: A heuristic treatment

We discuss neutrino oscillations in curved spacetime. Our heuristic approach can accommodate matter effects and gravitational contributions to neutrino spin precession in the presence of a magnetic field. By way of illustration, we perform explicit calculations in the Schwarzschild geometry. In this case, gravitational effects on neutrino oscillations are intimately related to the redshift. We discuss how spacetime curvature could affect the resonance position and adiabaticity of matter-enhanced neutrino flavor conversion. © 1997 The American Physical Society

Three-generation neutrino mixing and LSND dark matter neutrinos

The reported signal at the LSND experiment, when interpreted as neutrino mixing with δm2 = 6 eV2, provides evidence for neutrinos with a cosmologically significant mass. However, attempts to reconcile this interpretation of the experiment with other hints about neutrino properties require a (sterile) fourth neutrino and/or an "inverted" neutrino mass hierarchy. An interpretation of the LSND experiment employing δm2 = 0.3 eV2, with three-generation mixing and a "normal" neutrino mass hierarchy, can just barely be reconciled with the negative results of other laboratory neutrino oscillation experiments and the positive hints of neutrino oscillation from the solar and atmospheric neutrino problems. Though subject to test by by future experiments, such a solution allows (but does not demand) neutrino masses relevant for dark matter