Rotations Versus Perturbative Expansions for Calculating Neutrino Oscillation Probabilities in Matter

Abstract

We further develop a simple and compact technique for calculating the three flavor neutrino oscillation probabilities in uniform matter density. By performing additional rotations instead of implementing a perturbative expansion we significantly decrease the scale of the perturbing Hamiltonian and therefore improve the accuracy of zeroth order. We explore the relationship between implementing additional rotations and that of performing a perturbative expansion. Based on our analysis, independent of the size of the matter potential, we find that the first order perturbation expansion can be replaced by two additional rotations and a second order perturbative expansion can be replaced by one more rotation. Numerical tests have been applied and all the exceptional features of our analysis have been verified.

arXiv comment15 pages, 4 figures, 1 table; Matches version published in PRD

References in corpus (20)

• Observation of Reactor Electron Antineutrino Disappearance in the RENO Experiment
• The T2K Experiment
• Golden measurements at a neutrino factory
• Global fit to three neutrino mixing: critical look at present precision
• Analytic Approximations for Three Neutrino Oscillation Parameters and Probabilities in Matter
• Series expansions for three-flavor neutrino oscillation probabilities in matter
• Physics Potential of a Long Baseline Neutrino Oscillation Experiment Using J-PARC Neutrino Beam and Hyper-Kamiokande
• Another possible way to determine the Neutrino Mass Hierarchy
• CP and T violation test in neutrino oscillation
• Exact Formulas and Simple CP dependence of Neutrino Oscillation Probabilities in Matter with Constant Density
• Neutrino Propagation in Matter
• The NOvA Experiment: Status and Outlook
• CP and T Violation in Neutrino Oscillations and Invariance of Jarlskog's Determinant to Matter Effects
• Compact Perturbative Expressions For Neutrino Oscillations in Matter
• Large-Theta(13) Perturbation Theory of Neutrino Oscillation for Long-Baseline Experiments
• Simple and Compact Expressions for Neutrino Oscillation Probabilities in Matter
• New measurement of ${\theta }_{13}$ via neutron capture on hydrogen at Daya Bay
• What is $\Delta m_{ee}^2$ ?
• Matter Density Profile Shape Effects at DUNE
• Compact Perturbative Expressions for Neutrino Oscillations in Matter: II

Cited by in corpus (17)

• CP-Violating Neutrino Non-Standard Interactions in Long-Baseline-Accelerator Data
• Neutrino oscillation probabilities through the looking glass
• Eigenvalues: the Rosetta Stone for Neutrino Oscillations in Matter
• Analytical solutions to renormalization-group equations of effective neutrino masses and mixing parameters in matter
• Parameter symmetries of neutrino oscillations in vacuum, matter, and approximation schemes
• Compact Perturbative Expressions for Oscillations with Sterile Neutrinos in Matter
• Neutrino Oscillation in Dense Matter
• Sum rules and asymptotic behaviors of neutrino mixing in dense matter
• The Effective $\Delta m_{ee}^2$ in Matter
• Fibonacci Fast Convergence for Neutrino Oscillations in Matter
• Toward diagnosing neutrino non-unitarity through CP phase correlations
• The Smallness of Matter Effects in Long-Baseline Muon Neutrino Disappearance
• From ray to spray: augmenting amplitudes and taming fast oscillations in fully numerical neutrino codes
• Radiative corrections to the lepton flavor mixing in dense matter
• Neutrino Oscillations in the Three Flavor Paradigm
• Novel matter effects on neutrino oscillations observables
• The case for adopting the sequential Jacobi's diagonalization algorithm in neutrino oscillation physics