Related papers: Looking into Analytical Approximations for Three-f…
We argue that the neutrino oscillation probabilities in matter are best understood by allowing the mixing angles and mass-squared differences in the standard parametrization to `run' with the matter effect parameter $a=2\sqrt{2}G_F N_e E$,…
We construct a new perturbative framework to describe neutrino oscillation in matter with the unique expansion parameter \epsilon, which is defined as \Delta m^2_{21} / \Delta m^2_{ren} with the renormalized atmospheric \Delta m^2_{ren}…
We summarize our recent paper on neutrino oscillation probabilities in matter, explaining the importance, relevance and need for simple, highly accurate approximations to the neutrino oscillation probabilities in matter. Simple expressions…
We reformulate perturbation theory for neutrino oscillations in matter with an expansion parameter related to the ratio of the solar to the atmospheric $\Delta m^2$ scales. Unlike previous works, we use a renormalized basis in which certain…
We present a number of complete sets of series expansion formulas for neutrino oscillation probabilities in matter of constant density for three flavors. In particular, we study expansions in the mass hierarchy parameter $\alpha \equiv…
Neutrino oscillations are now a well-stablished and deeply studied phenomena. Their mixing parameters, except for the CP phase, are measured with good accuracy. The three-neutrino oscillation picture in matter is currently of great interest…
Neutrino oscillations are one of the most studied and successful phenomena since the establishment of the solar neutrino problem in late 1960's. In this work we discuss the exact expressions for the probability P_{\alpha\beta} in a constant…
It is known in vacuum that the three-flavor neutrino survival probability can be approximated by the effective two-flavor form to first orders in $\epsilon \equiv \Delta m^2_{21} / \Delta m^2_{31}$, with introduction of the effective…
A simple closed-form analytic expression for the probability of two-flavour neutrino oscillations in a matter with an arbitrary density profile is derived. Our formula is based on a perturbative expansion and allows an easy calculation of…
We present, both exactly and approximately, a complete set of mappings between the vacuum (or fundamental) leptonic mixing parameters and the effective ones in matter with non-standard neutrino interaction (NSI) effects included. Within the…
We extend a simple and compact method for calculating the three flavor neutrino oscillation probabilities in uniform matter density to schemes with sterile neutrinos, with favorable features inherited. The only constraint of the extended…
Neutrino oscillation is the new physics beyond standard model. In this paper we have revisited the issue of neutrino oscillation in simple and delicate manner. Starting from the fundamental quantum mechanical treatment for the neutrinos, we…
Analytic formulas are presented for three flavor neutrino oscillations in matter in the plane wave approximation. We calculate in particular the time evolution operator in both mass and flavor bases. We also find the transition…
We perform an updated global analysis of the known and unknown parameters of the standard $3\nu$ framework as of 2025. The known oscillation parameters include three mixing angles $(\theta_{12},\,\theta_{23},\,\theta_{13})$ and two squared…
We investigate the effective case of two-flavor neutrino oscillations in infinitely dense matter by using a perturbative approach. We begin by briefly summarizing the conditions for the three-flavor neutrino oscillation probabilities to…
The conventional approximate formula for neutrino oscillation in matter which is obtained from the expansion in terms of the ratio of mass square differences $\alpha=\Delta m_{21}^{2}/\Delta m_{31}^{2}\approx0.03$, first proposed by…
As the increasing of neutrino energy or matter density, the neutrino oscillation in matter may undergo "vacuum-dominated", "resonance" and "matter-dominated" three different stages successively. Neutrinos endure very different matter…
In this article, we point out that the effective Hamiltonian for neutrino oscillations in matter is invariant under the transformation of the mixing angle $\theta^{}_{12} \to \theta^{}_{12} - \pi/2$ and the exchange of first two neutrino…
We study neutrino oscillation within the framework of three generations in matter. We propose a simple method to approximate the coefficients A, B and C which do not depend on the CP phase \delta in the oscillation probability P(\nu_e \to…
We further develop and extend a recent perturbative framework for neutrino oscillations in uniform matter density so that the resulting oscillation probabilities are accurate for the complete matter potential versus baseline divided by…