KamLAND has measured the flux of nu;(e)'s from distant nuclear reactors. We find fewer nu;(e) events than expected from standard assumptions about nu;(e) propagation at the 99.95% C.L. In a 162 ton.yr exposure the ratio of the observed inverse beta-decay events to the expected number without nu;(e) disappearance is 0.611+/-0.085(stat)+/-0.041(syst) for nu;(e) energies >3.4 MeV. In the context of two-flavor neutrino oscillations with CPT invariance, all solutions to the solar neutrino problem except for the "large mixing angle" region are excluded.

First Results from KamLAND: Evidence for Reactor Anti-Neutrino Disappearance

The K2K experiment observes indications of neutrino oscillation: a reduction of nu(mu) flux together with a distortion of the energy spectrum. Fifty-six beam neutrino events are observed in Super-Kamiokande (SK), 250 km from the neutrino production point, with an expectation of 80.1(+6.2)(-5.4). Twenty-nine one ring mu-like events are used to reconstruct the neutrino energy spectrum, which is better matched to the expected spectrum with neutrino oscillation than without. The probability that the observed flux at SK is explained by statistical fluctuation without neutrino oscillation is less than 1%.

Indications of Neutrino Oscillation in a 250 km Long-Baseline Experiment

Behind the observed pattern of lepton flavor mixing is a partial or approximate mu-tau flavor symmetry --- a milestone on our road to the true origin of neutrino masses and flavor structures. In this review article we first describe the features of mu-tau permutation and reflection symmetries, and then explore their various consequences on model building and neutrino phenomenology. We pay particular attention to soft mu-tau symmetry breaking, which is crucial for our deeper understanding of the fine effects of flavor mixing and CP violation.

A review of mu-tau flavor symmetry in neutrino physics

Flavor structures of charged fermions and massive neutrinos

S(3) symmetry and tri-bimaximal mixing

μ–τ symmetry and maximal CP violation

Determination of neutrino mass texture for maximal CP violation

The requirement of the {mu}-{tau} symmetry in the neutrino sector that yields the maximal atmospheric neutrino mixing is shown to yield either sin{theta}{sub 13}=0 (referred to as C1)) or sin{theta}{sub 12}=0 (referred to as C2)), where {theta}{sub 12(13)} stands for the solar (reactor) neutrino mixing angle. We study general properties possessed by approximately {mu}-{tau} symmetric textures. It is argued that the tiny {mu}-{tau} symmetry breaking generally leads to cos2{theta}{sub 23}{approx}sin{theta}{sub 13} for C1) and cos2{theta}{sub 23}{approx}{delta}m{sub {center_dot}}{sup 2}/{delta}m{sub atm}{sup 2}({identical_to}R) for C2), which indicates that the smallness of cos2{theta}{sub 23} is a good measure of the {mu}-{tau} symmetry breaking, where {delta}m{sub atm}{sup 2} ({delta}m{sub {center_dot}}{sup 2}) stands for the square mass difference of atmospheric (solar) neutrinos. We further find that the relation R{approx}sin{sup 2}{theta}{sub 13} arises from contributions of O(sin{sup 2}{theta}{sub 13}) in the estimation of the neutrino masses (m{sub 1,2,3}) for C1), and that possible forms of textures are strongly restricted to realize sin{sup 2}2{theta}{sub 12}=O(1) for C2). To satisfy R{approx}sin{sup 2}{theta}{sub 13} for C1), neutrinos exhibit the inverted mass hierarchy, or the quasi degenerate mass pattern with |m{sub 1,2,3}|{approx}O({radical}({delta}m{sub atm}{sup 2})), and, to realize sin{sup 2}2{theta}{sub 12}=O(1) for C2), there should be an additional small parameter {eta} whosemore » size is comparable to that of the {mu}-{tau} symmetry breaking parameter {epsilon}, giving tan2{theta}{sub 12}{approx}{epsilon}/{eta} with {eta}{approx}{epsilon} to be compatible with the observed large mixing.« less

What does μ-τ symmetry imply about neutrino mixings?

The requirement of the mu-tau symmetry in the neutrino sector that yields the maximal atmospheric neutrino mixing is shown to yield either sin(\theta_{13})=0 (referred to as C1)) or sin(\theta_{12})=0 (referred to as C2)), where \theta_{12(13)} stands for the solar (reactor) neutrino mixing angle. We study general properties possessed by approximately mu-tau symmetric textures. It is argued that the tiny mu-tau symmetry breaking generally leads to cos(2\theta_{23}) \simsin(\theta_{13}) for C1) and cos(2\theta_{23}) \sim \Delta m^2_\odot/\Delta m^2_{atm}(\equiv R) for C2), which indicates that the smallness of cos(2\theta_{23}) is a good measure of the mu-tau symmetry breaking, where \Delta m^2_{atm} (\Delta m^2_\odot) stands for the square mass differences of atmospheric (solar) neutrinos. We further find that the relation R \sim sin^2(\theta_{13}) arises from contributions of O(sin^2(\theta_{13})) in the estimation of the neutrino masses (m_{1,2,3}) for C1), and that possible forms of textures are strongly restricted to realize sin^2(2\theta_{12})=O(1) for C2). To satisfy R \sim sin^2(\theta_{13}) for C1), neutrinos exhibit the inverted mass hierarchy, or the quasi degenerate mass pattern with | m_{1,2,3}| \sim O(\sqrt{\Delta m^2_{atm}}), and, to realize sin^2(2\theta_{12})=O(1) for C2), there should be an additional small parameter \eta whose size is comparable to that of the mu-tau symmetry breaking parameter \epsilon, giving tan(2\theta_{12}) \sim \epsilon/\eta with \eta \sim \epsilon to be compatible with the observed large mixing.

What does mu-tau symmetry imply in neutrino mixings?

We show three types of neutrino mass textures, which give maximal $CP$ violation as well as maximal atmospheric neutrino mixing. These textures are described by six real mass parameters: one specified by two complex flavor neutrino masses and two constrained ones and the others specified by three complex flavor neutrino masses. In each texture, we calculate mixing angles and masses, which are consistent with observed data, as well as Majorana $CP$ phases.

Masaki Yasuè

Papers

μ–τ symmetry and maximal CP violation

Determination of neutrino mass texture for maximal CP violation

What does μ-τ symmetry imply about neutrino mixings?

What does mu-tau symmetry imply in neutrino mixings?

Neutrino mass textures with maximal CP violation