We discuss various physics aspects of neutrino oscillation with non-standard interactions (NSI). We formulate a perturbative framework by taking ∆m 2 21 /∆m 2 31 , s 13 , and the NSI elements ε αβ (α, β = e, µ, τ ) as small expansion parameters of the same order ǫ. Within the ǫ perturbation theory we obtain the S matrix elements and the neutrino oscillation probability formula to second order (third order in ν e related channels) in ǫ. The formula allows us to estimate size of the contribution of any particular NSI element ε αβ to the oscillation probability in arbitrary channels, and gives a global bird-eye view of the neutrino oscillation phenomena with NSI. Based on the second-order formula we discuss how all the conventional lepton mixing as well as NSI parameters can be determined. Our results shows that while θ 13 , δ, and the NSI elements in ν e sector can in principle be determined, complete measurement of the NSI parameters in the ν µ − ν τ sector is not possible by the rate only analysis. The discussion for parameter determination and the analysis based on the matter perturbation theory indicate that the parameter degeneracy prevails with the NSI parameters. In addition, a new solar-atmospheric variable exchange degeneracy is found. Some general properties of neutrino oscillation with and without NSI are also illuminated.

We discuss the sensitivity reach of a neutrino factory measurement to non-standard neutrino interactions (NSI), which may exist as a low-energy manifestation of physics beyond the Standard Model. We use the muon appearance modes ν e → ν µ /ν e →ν µ and consider two detectors, one at L = 3000 km and the other at L = 7000 km; The latter is nearly at the magic baseline which is known to have a great sensitivity to matter density determination. Assuming the effects of NSI at the production and the detection are negligible, we discuss the sensitivities to NSI and the simultaneous determination of θ 13 and δ by examining the effects in the neutrino propagation of various systems in which two NSI parameters ε αβ are switched on. The sensitivities to offdiagonal ε's are found to be excellent up to small values of θ 13 . At sin 2 2θ 13 = 10 −4 , for example, |ε eτ | a few×10 −3 at 3σ CL for 2 degrees of freedom, whereas the ones for the diagonal ε's are also acceptable, |ε ee |(|ε τ τ |) 0.1(0.2) at the same CL. We demonstrate that the two-detector setting is powerful enough to resolve the θ 13 -NSI confusion problem, a notorious one which is thought to be an obstacle in determining θ 13 and δ. We believe that the results obtained in this paper open the door to the possibility of using neutrino factory as a discovery machine for NSI while keeping its primary function of performing precision measurements of the lepton mixing parameters.

We discuss, in the context of precision measurement of ∆m 2 31 and θ 13 , physics capabilities enabled by the recoilless resonant absorption of monochromatic antineutrino beam enhanced by the Mössbauer effect recently proposed by Raghavan. Under the assumption of small relative systematic error of a few tenth of percent level between measurement at different detector locations, we give analytical and numerical estimates of the sensitivities to ∆m 2 31 and sin 2 2θ 13 . The accuracies of determination of them are enormous; The fractional uncertainty in ∆m 2 31 achievable by 10 point measurement is 0.6% (2.4%) for sin 2 2θ 13 = 0.05, and the uncertainty of sin 2 2θ 13 is 0.002 (0.008) both at 1σ CL with the optimistic (pessimistic) assumption of systematic error of 0.2% (1%). The former opens a new possibility of determining the neutrino mass hierarchy by comparing the measured value of ∆m 2 31 with the one by accelerator experiments, while the latter will help resolving the θ 23 octant degeneracy.

We point out that an accurate in situ determination of the earth matter density ρ is possible in neutrino factory by placing a detector at the magic baseline, L = √ 2π/G F N e where N e denotes electron number density. The accuracy of matter density determination is excellent in a region of relatively large θ 13 with fractional uncertainty δρ/ρ of about 0.43%, 1.3%, and < ∼ 3% at 1σ CL at sin 2 2θ 13 = 0.1, 10 −2 , and 3 × 10 −3 , respectively. At smaller θ 13 the uncertainty depends upon the CP phase δ, but it remains small, 3%-7% in more than 3/4 of the entire region of δ at sin 2 2θ 13 = 10 −4 . The results would allow us to solve the problem of obscured CP violation due to the uncertainty of earth matter density in a wide range of θ 13 and δ. It may provide a test for the geophysical model of the earth, or it may serve as a method for stringent test of the MSW theory of neutrino propagation in matter once an accurate geophysical estimation of the matter density is available.

In neutrino oscillation with non-standard interactions (NSI) the system is enriched with CP violation caused by phases due to NSI in addition to the standard lepton Kobayashi-Maskawa phase δ. In this paper we show that it is possible to disentangle the two CP violating effects by measurement of muon neutrino appearance by a near-far two detector setting in neutrino factory experiments. Prior to the quantitative analysis we investigate in detail the various features of the neutrino oscillations with NSI, but under the assumption that only one of the NSI elements, ε eµ or ε eτ , is present. They include synergy between the near and the far detectors, the characteristic differences between the ε eµ and ε eτ systems, and in particular, the parameter degeneracy. Finally, we use a concrete setting with the muon energy of 50 GeV and magnetized iron detectors at two baselines, one at L = 3000 km and the other at L = 7000 km, each having a fiducial mass of 50 kton to study the discovery potential of NSI and its CP violation effects. We demonstrate, by assuming 4 × 10 21 useful muon decays for both polarities, that one can identify non-standard CP violation down to |ε eµ | ≃ a few × 10 −3 , and |ε eτ | ≃ 10 −2 at 3σ CL for θ 13 down to sin 2 2θ 13 = 10 −4 in most of the region of δ. The impact of the existence of NSI on the measurement of δ and the mass hierarchy is also worked out.