206 research outputs found
The Effective in Matter
In this paper we generalize the concept of an effective for
disappearance experiments, which has been extensively used
by the short baseline reactor experiments, to include the effects of
propagation through matter for longer baseline
disappearance experiments. This generalization is a trivial, linear combination
of the neutrino mass squared eigenvalues in matter and thus is not a simple
extension of the usually vacuum expression, although, as it must, it reduces to
the correct expression in the vacuum limit. We also demonstrated that the
effective in matter is very useful conceptually and
numerically for understanding the form of the neutrino mass squared eigenstates
in matter and hence for calculating the matter oscillation probabilities.
Finally we analytically estimate the precision of this two-flavor approach and
numerically verify that it is precise at the sub-percent level.Comment: 9 pages, 6 figures, 1 table, comments welcom
Neutrino oscillation probabilities through the looking glass
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.Comment: 32 pages, 6 figure
Rotations versus perturbative expansions for calculating neutrino oscillation probabilities in matter
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.Comment: 15 pages, 4 figures, 1 table; Matches version published in PR
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