Formulas For Oscillation Probabilities Research Articles

Can oscillating neutrino states be formulated universally?

A standing problem in neutrino physics is the consistent and universal definition of oscillating neutrino states as coherent superpositions of massive neutrino states. This problem is solved in a quantum field theoretical framework of neutrino mixing developed in analogy with the Nambu–Jona–Lasinio model for the dynamical generation of nucleon masses. The massive neutrino states are Bogoliubov quasiparticles and their vacuum is a condensate of “Cooper pairs” of massless flavour neutrinos. Their superpositions as oscillating neutrino states have intrinsic quantum coherence by construction. In this quantization framework, the standard phenomenological flavour neutrino states and oscillation probability formula are validated in the ultrarelativistic approximation.

Experimental study of decoherence effect at Daya Bay

The last unknown neutrino mixing angle has been successfully measured by the Daya Bay, RENO and Double Chooz experiments. The used oscillation probability formula is based on the plane-wave model. A wave-packet model is necessary for a self-consistent description of neutrino oscillations. The oscillation probability formula in the wave-packet model describes effects missing in the plane-wave approximation, such as delocalization, decoherence and dispersion which all depend on a single unknown parameter σp – momentum dispersion of the neutrino wave-packet. The survival probability formula in the wave-packet model was used to fit the Daya Bay data. The high-statistics data set of reactor interactions in the Daya Bay experiment allows us to study the neutrino oscillation in the wave-packet model and provide the first experimental constraint of σp. Some results of our study are reported in this paper.

Perturbation theory of neutrino oscillation with nonstandard neutrino interactions

We discuss various physics aspects of neutrino oscillation with non-standard interactions (NSI). We formulate a perturbative framework by taking \Delta m^2_{21} / \Delta m^2_{31}, s_{13}, and the NSI elements \epsilon_{\alpha \beta} (\alpha, \beta = e, \mu, \tau) as small expansion parameters of the same order \epsilon. Within the \epsilon perturbation theory we obtain the S matrix elements and the neutrino oscillation probability formula to second order (third order in \nu_e related channels) in \epsilon. The formula allows us to estimate size of the contribution of any particular NSI element \epsilon_{\alpha beta} to the oscillation probability in arbitrary channels, and gives a global bird-eye view of the neutrino oscillation phenomena with NSI. Based on the second-order formula we discuss how all the conventional lepton mixing as well as NSI parameters can be determined. Our results shows that while \theta_{13}, \delta, and the NSI elements in \nu_e sector can in principle be determined, complete measurement of the NSI parameters in the \nu_\mu - \nu_\tau sector is not possible by the rate only analysis. The discussion for parameter determination and the analysis based on the matter perturbation theory indicate that the parameter degeneracy prevails with the NSI parameters. In addition, a new solar-atmospheric variable exchange degeneracy is found. Some general properties of neutrino oscillation with and without NSI are also illuminated.

Non-standard interaction effects at reactor neutrino experiments

We study non-standard interactions (NSIs) at reactor neutrino experiments, and in particular, the mimicking effects on θ13. We present generic formulas for oscillation probabilities including NSIs from sources and detectors. Instructive mappings between the fundamental leptonic mixing parameters and the effective leptonic mixing parameters are established. In addition, NSI corrections to the mixing angles θ13 and θ12 are discussed in detailed. Finally, we show that, even for a vanishing θ13, an oscillation phenomenon may still be observed in future short baseline reactor neutrino experiments, such as Double Chooz and Daya Bay, due to the existences of NSIs.

Large non-perturbative effects of small Δm221/Δm231and sin θ13on neutrino oscillation and CP violation in matter

In the framework of three generations, we consider the CP violation in neutrino oscillation with matter effects. At first, we show that the non-perturbative effects of two small parameters, \Delta m_{21}^2/\Delta m_{31}^2 and \sin \theta_{13}, become more than 50% in certain ranges of energy and baseline length. This means that the non-perturbative effects should be considered in detailed analysis in the long baseline experiments. Next, we propose a method to include these effects in approximate formulas for oscillation probabilities. Assuming the two natural conditions, \theta_{23}=45^\circ and the fact that the matter density is symmetric, a set of approximate formulas, which involve the non-perturbative effects, has been derived in all channels.

Dirac spinors and flavor oscillations

In the standard treatment of particle oscillations the mass eigenstates are implicitly assumed to be scalars and, consequently, the spinorial form of neutrino wave functions is not included in the calculations. To analyze this additional effect, we discuss the oscillation probability formula obtained by using the Dirac equation as evolution equation for the neutrino mass eigenstates. The initial localization of the spinor state also implies an interference between positive and negative energy components of mass eigenstate wave packets which modifies the standard oscillation probability.