Leptonic CP Phase Research Articles

Running neutrino masses, mixings and CP phases: analytical results and phenomenological consequences

We derive simple analytical formulae for the renormalization group running of neutrino masses, leptonic mixing angles and CP phases, which allow an easy understanding of the running. Particularly for a small angle θ 13 the expressions become very compact, even when non-vanishing CP phases are present. Using these equations we investigate: (i) the influence of Dirac and Majorana phases on the evolution of all parameters, (ii) the implications of running neutrino parameters for leptogenesis, (iii) changes of the mass bounds from WMAP and neutrinoless double β decay experiments, relevant for high-energy mass models, (iv) the size of radiative corrections to θ 13 and θ 23 and implications for future precision measurements.

Terrestrial neutrino experiments and the search for leptonic CP violation

Terrestrial neutrino experiments could be the ideal tool to investigate CP violation in the leptonic sector if the θ13 angle of the PMNS matrix is sufficiently high. This condition will be tested by several future long-baseline detectors (Phase I experiments). We discuss the interplay among these experiments and possible synergies. It is shown that, without a dedicated $\bar{\nu}$ run, Phase I experiments cannot reach a sensitivity able to ground (or discourage in a definitive manner) the building of the Phase II projects that are aimed at the determination of the leptonic CP phase. In fact, this capability is almost saturated by high energy beams like CNGS, especially for high values of the ratio Δ m221/|Δ m231|. Moreover, we discuss the interplay between on-peak and off-peak experiments and the constraints to the PMNS matrix in case of early evidence for ν μ → ν e oscillations at the athmospheric scale (high θ13). PACS: 14.60.Pq Neutrino mass and mixing

Reactor neutrino experiments compared to superbeams

We present a detailed quantitative discussion of the measurement of the leptonic mixing angle sin 22 θ 13 with a future reactor neutrino oscillation experiment consisting of a near and far detector. We perform a thorough analysis of the impact of various systematical errors and compare the resulting physics potential to the one of planned first-generation superbeam experiments. Furthermore, we investigate the complementarity of both types of experiments. We find that, under realistic assumptions, a determination of sin 22 θ 13 down to 10 −2 is possible with reactor experiments. They are thus highly competitive to first-generation superbeams and may be able to test sin 22 θ 13 on shorter timescales. In addition, we find that the combination of a KamLAND-size reactor experiment with one or two superbeams could substantially improve the ability to access the neutrino mass hierarchy or the leptonic CP phase.

Superbeams vs. neutrino factories

We compare the physics potential of planned superbeams with the one of neutrino factories. Therefore, the experimental setups as well as the most relevant uncertainties and errors are considered on the same footing as much as possible. We use an improved analysis including the full parameter correlations, as well as statistical, systematical, and degeneracy errors. Especially, degeneracies have so far not been taken into account in a numerical analysis. We furthermore include external input, such as improved knowledge of the solar oscillation parameters from the KamLAND experiment. This allows us to determine the limiting uncertainties in all cases. For a specific comparison, we choose two representatives of each class: for the superbeam, we take the first conceivable setup, namely, the JHF to SuperKamiokande experiment, as well as, on a longer time scale, the JHF to HyperKamiokande experiment. For the neutrino factory, we choose an initially conceivable setup and an advanced machine. We determine the potential to measure the small mixing angle sin 22 θ 13, the sign of Δm 2 31, and the leptonic CP phase δ CP, which also implies that we compare the limitations of the different setups. We find interesting results, such as the complete loss of the sensitivity to the sign of Δm 2 31 due to degeneracies in many cases.

Neutrino mixing and leptonic CP phase in neutrino oscillations

Oscillations of the Dirac neutrinos of three generations in vacuum are considered with allowance made for the effect of the CP-violating leptonic phase (analogue of the quark CP phase) in the lepton mixing matrix. The general formulas for the probabilities of neutrino transition from one sort to another in oscillations are obtained as functions of three mixing angles and the CP phase. It is found that the leptonic CP phase can, in principle, be reconstructed by measuring the oscillation-averaged probabilities of neutrino transition from one sort to another. The manifestation of the CP phase as a deviation of the probabilities of direct processes from those of inverse processes is an effect that is practically unobservable as yet.

Neutrino mass operator renormalization in two Higgs doublet models and the MSSM

In a recent re-analysis of the Standard Model (SM) beta-function for the effective neutrino mass operator, we found that the previous results were not entirely correct. Therefore, we consider the analogous dimension five operators in a class of Two Higgs Doublet Models (2HDM's) and the Minimal Supersymmetric Standard Model (MSSM). Deriving the renormalization group equations for these effective operators, we confirm the existing result in the case of the MSSM. Some of our 2HDM results are new, while others differ from earlier calculations. This leads to modifications in the renormalization group evolution of leptonic mixing angles and CP phases in the 2HDM's.

Neutrino mass operator renormalization revisited

We re-derive the renormalization group equation for the effective coupling of the dimension five operator which corresponds to a Majorana mass matrix for the Standard Model neutrinos. We find a result which differs somewhat from earlier calculations, leading to modifications in the evolution of leptonic mixing angles and CP phases. We also present a general method for calculating beta-functions from counterterms in MS-like renormalization schemes, which works for tensorial quantities.

Neutrino mixing and leptonic CP phase in neutrino oscillations

Oscillations of the Dirac neutrinos of three generations in vacuum are considered with allowance made for the effect of the CP-violating leptonic phase (analogue of the quark CP phase) in the lepton mixing matrix. The general formulas for the probabilities of neutrino transition from one sort to another in oscillations are obtained as functions of three mixing angles and the CP phase. It is found that the leptonic CP phase can, in principle, be reconstructed by measuring the oscillation-averaged probabilities of neutrino transition from one sort to another. The manifestation of the CP phase as a deviation of the probabilities of direct processes from those of inverse processes is an effect that is practically unobservable as yet.

Neutrino oscillation physics with a neutrino factory

We review some of the results of the works presented in [1] and [2] concerning the measurement of leptonic mixing angles and CP phases in the context of the neutrino beam emanating from a neutrino factory: the straight sections of a muon storage ring. We emphasize the importance of charge identification. The appearance of wrong sign muons in a long baseline experiment may provide a powerful test of neutrino oscillations in the mass-difference range indicated by atmospheric-neutrino observations.

Mass and CKM matrices of quarks and leptons, the leptonic CP-phase in neutrino oscillations

A general approach for construction of quark and lepton mass matrices is formulated. The hierarchy of quarks and charged leptons (“electrons”) is large, it leads using the experimental values of mixing angles to the hierarchical mass matrix slightly deviating from the ones suggested earlier by Stech and including naturally the CP-phase. The same method based on the rotation of generation numbers in the diagonal mass matrix is used in the electron–neutrino sector of theory, where neutrino mass matrix is determined by the Majorano see-saw approach. The hierarchy of neutrino masses, much smaller than for quarks, was used including all existing (even preliminary) experimental data on neutrino mixing. The leptonic mass matrix found in this way includes the unknown value of the leptonic CP-phase. It leads to large ν μ ν τ oscillations and suppresses the ν e ν τ and also ν e ν μ oscillations. The explicit expressions for the probabilities of neutrino oscillation were obtained in order to specify the role of leptonic CP-phase. The value of time reversal effect (proportional to sin δ′ ) was found to be small ∼1%. However, a dependence of the values of ν e ν μ , ν e ν τ transition probabilities, averaged over oscillations, on the leptonic CP-phase has found to be not small – of order of ten percent.