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 √ 2G F N e E, where N e is the electron density in matter and E is the neutrino energy. We present simple analytical approximations to these 'running' parameters. We show that for the moderately large value of θ 13 , as discovered by the reactor experiments, the running of the mixing angle θ 23 and the CP violating phase δ can be neglected. It simplifies the analysis of the resulting expressions for the oscillation probabilities considerably. Approaches which attempt to directly provide approximate analytical expressions for the oscillation probabilities in matter suffer in accuracy due to their reliance on expansion in θ 13 , or in simplicity when higher order terms in θ 13 are included. We demonstrate the accuracy of our method by comparing it to the exact numerical result, as well as the direct approximations of Cervera et al., Akhmedov et al., Asano and Minakata, and Freund. We also discuss the utility of our approach in figuring out the required baseline lengths and neutrino energies for the oscillation probabilities to exhibit certain desirable features.

New physics beyond the Standard Model can lead to extra matter effects on neutrino oscillation if the new interactions distinguish among the three flavors of neutrino. In Ref. 1, we argued that a long-baseline neutrino oscillation experiment in which the Fermilab-NUMI beam in its high-energy mode 2 is aimed at the planned Hyper-Kamiokande detector 3 would be capable of constraining the size of those extra matter effects, provided the vacuum value of sin 2 2θ 23 is not too close to one. In this talk, we discuss how such a constraint would translate into limits on the coupling constants and masses of new particles in models such as topcolor assisted technicolor. 4

In this article we unravel the role of matter effect in neutrino oscillation in the presence of lepton-flavor-conserving, non-universal non-standard interactions (NSI's) of the neutrino. Employing the Jacobi method, we derive approximate analytical expressions for the effective mass-squared differences and mixing angles in matter. It is shown that, within the effective mixing matrix, the Standard Model (SM) W -exchange interaction only affects θ 12 and θ 13 , while the flavor-diagonal NSI's only affect θ 23 . The CP-violating phase δ remains unaffected. Using our simple and compact analytical approximation, we study the impact of the flavor-diagonal NSI's on the neutrino oscillation probabilities for various appearance and disappearance channels. At higher energies and longer baselines, it is found that the impact of the NSI's can be significant in the ν µ → ν µ channel, which can probed in future atmospheric neutrino experiments, if the NSI's are of the order of their current upper bounds. Our analysis also enables us to explore the possible degeneracy between the octant of θ 23 and the sign of the NSI parameter for a given choice of mass hierarchy in a simple manner.

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