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.
Highlights
After Wolfenstein showed that neutrino oscillations are altered in matter, [1] exact analytic solutions for three flavors were calculated under the assumption of uniform matter density [2,3]
When expanding around sin θ13 1⁄4 0, two of the eigenvalues cross at an energy around E ∼ 10 GeV for Earth density, a perturbative expansion will not converge near the atmospheric resonance
We have significantly improved the accuracy and understanding of the recent perturbative framework for neutrino propagations in uniform matter in [14]. This has been achieved by performing additional rotations which diagonalize the sectors with leading order off-diagonal elements of the Hamiltonian
Summary
After Wolfenstein showed that neutrino oscillations are altered in matter, [1] exact analytic solutions for three flavors were calculated under the assumption of uniform matter density [2,3]. This is the atmospheric Δm2 measured in a νe disappearance experiment [15,16] After both the (1-3) and (1-2) rotations, given in [14], the expansion parameter for the perturbing Hamiltonian is ε0 ≡ ε sinðθ13 − θ13Þ sin θ12 cos θ12; where ε ≡ Δm221=Δm2ee ≃ 0.03; ð2Þ. The magnitude of the expansion parameter is never larger than 0.015 and vanishes in vacuum After these two twoflavor rotations, the perturbative expansion is well behaved for all values of the matter potential and zeroth, first and second order perturbative results are all given in [14]. In principle, performing additional rotations can be chosen to be equivalent to any order of the perturbation expansion, unnecessary for the expected precision of any future oscillation experiment. All other remarks and supplementary materials we believe necessary can be found in the Appendices
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
