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In this paper we review different expansions for neutrino oscillation probabilities in matter in the context of long-baseline neutrino experiments. We examine the accuracy and computational efficiency of different exact and approximate expressions. We find that many of the expressions used in the literature are not precise enough for the next generation of long-baseline experiments, but several of them are while maintaining comparable simplicity. The results of this paper can be used as guidance to both phenomenologists and experimentalists when implementing the various oscillation expressions into their analysis tools.
Motivated by tremendous progress in neutrino oscillation experiments, we derive a new set of simple and compact formulas for three-flavor neutrino oscillation probabilities in matter of a constant density. A useful definition of the $eta$-gauge neutr
We perform the flavour $SU(3)$ analysis of the recently discovered $Omega(2012)$ hyperon. We find that well known (four star) $Delta(1700)$ resonance with quantum numbers of $J^P=3/2^-$ is a good candidate for the decuplet partner of $Omega(2012)$ if
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} equiv Delta m^2_{
In the work of Mukhin and Varchenko from 2002 there was introduced a Wronskian map from the variety of full flags in a finite dimensional vector space into a product of projective spaces. We establish a precise relationship between this map and the P
One can hardly believe that there is still something to be said about cubic equations. To dodge this doubt, we will instead try and say something about Sylvester. He doubtless found a way to solve cubic equations. As mentioned by Rota, it was the onl