Quantum Gravity on Neutrino Oscillation Length

The oscillation length of neutrino oscillation could be discussed in the frame work of quantum gravity. Quantum gravity (Planck scale effects) leads to an effective SU(2) _L ×U(1) invariant dimension-5 Lagrangian involving, neutrino and Higgs fields. On symmetry breaking, this operator gives rise to correction to the neutrino masses and mixing. We compute the neutrino oscillation length due to Planck scale effects. The gravitational interaction (M _X =M _pl ) demands that the element of this perturbation matrix should be independent of flavor indices. In this paper, we study the quantum gravity effects on neutrino oscillation length, namely modified dispersion relation for neutrino oscillation phases.     

Neutrino Oscillation Phase Shift from Quantum Gravity

The phase shift of neutrino oscillation could be discussed in the frame work of quantum gravity. Quantum gravity (Planck scale effects) leads to an effective SU(2) _L ×U(1) invariant dimension-5 Lagrangian involving, neutrino and Higgs fields. On symmetry breaking, this operator gives rise to correction to the neutrino masses and mixing. We compute the neutrino oscillation phase due to Planck scale effects. The gravitational interaction (M _X =M _pl ) demands that the element of this perturbation matrix should be independent of flavor indices. In this paper, we study the quantum gravity effects on neutrino oscillation phases, namely modified dispersion relation for neutrino oscillation phases.     

Effect of Majorana Phases in Neutrino Oscillation

Quantum gravity (Planck scale effects) lead to an effective SU(2) _L ×U(1) invariant dimension-5 Lagrangian involving neutrino and Higgs fields. On symmetry breaking, this operator gives rise to correction to the above masses and mixing. The gravitational interaction M _X =M _pl , we find that for degenerate neutrino mass spectrum, it is shown that the Majorana phase of the neutrino mixing matrix can effects in neutrino oscillation probability.     

Neutrino Mass Hierarchy Above GUT Scale

Quantum gravity (Planck scale effects) lead to an effective SU(2) _L ×U(1) invariant dimension-5 Lagrangian involving neutrino and Higgs fields. On symmetry breaking, this operator gives rise to correction to the above masses and mixing. The gravitational interaction M _X =M _pl , we find that for degenerate neutrino mass spectrum, it is shown that the Majorana phase of the neutrino mixing matrix can effects in neutrino oscillation probability.     

Probing low-scale quantum gravity with high-energy neutrinos

Motivated by the quantum structure of space-time at high scales M _QG, we study the propagation behavior of the high-energy neutrino within the quantum gravity effect. We consider the possible induced dispersive effect and derive the resulting vacuum refraction index η_vac(E _ν) ? 1 + E _ν ² /M _QG ² . Then, by referring to the SN1987A and basing on the recorded neutrino data we approach the corresponding scale M _QG ? 10⁴ GeV.     

Does CP Phase Exist Above the GUT Scale

We consider non-reormalizable interaction term as a perturbation of the conventional neutrino mass matrix. Quantum gravitational (Planck scale )effects lead to an effective SU(2) _L ×U(1) invariant dimension-5 Lagrangian involving neutrino and Higgs fields, which gives rise to additional terms in neutrino mass matrix. There additional term can be considered to be perturbation of the GUT scale bi-maximal neutrino mass matrix. In particular, for the $\theta_{13}'$ range 0.00005–0.28, indicates the existence of CP violating phase above the GUT scale. We assume that the gravitational interaction is flavor blind. In this paper, we further investigate the possibility of CP phase exist from Quantum gravity.     

LETTER: Neutrino Oscillations Induced by Gravitational Recoil Effects

Quantum gravitational fluctuations of the space-time background, described by virtual D branes, may induce the neutrino oscillations if a tiny violation of the Lorentz invariance (or a violation of the equivalence principle) is required. In this approach, the oscillation length of massless neutrinos turns out to be proportional to E ^–2 M, where E is the neutrino energy and M is the mass scale characterizing the topological fluctuations in the vacuum. Such a functional dependence on the energy is the same obtained in the framework of loop quantum gravity.     

Constraining Lorentz invariance violation from the continuous spectra of short gamma-ray bursts

In some quantum gravity theories, a foamy structure of space-time may lead to Lorentz invariance violation(LIV). As the most energetic explosions in the Universe, gamma-ray bursts(GRBs) provide an effect way to probe quantum gravity effects. In this paper, we use the continuous spectra of 20 short GRBs detected by the Swift satellite to give a conservative lower limit of quantum gravity energy scale MQG. Due to the LIV effect, photons with different energy have different velocities. This will lead to the delayed arrival of high energy photons relative to low energy ones. Based on the fact that the LIV-induced time delay cannot be longer than the duration of a GRB,we present the most conservative estimate of the quantum gravity energy scales from 20 short GRBs. The strictest constraint, M_(QG) 5.05 × 10~(14) GeV in the linearly corrected case, is from GRB 140622 A. Our constraint on MQG,although not as tight as previous results, is the safest and most reliable so far.     

Gauge boson masses and lepton mixing inO(4)⊗U(1) gauge model

The Cabibbo angle is introduced as a mixing angle of the gauge bosonsW ^± andX ^± in anO(4)?U(1) gauge model. Masses of gauge bosons are calculated to beM _W=82 (input), \(M_z = \sqrt 2 M_W s\gamma = 130\) (γ is mixing angle, sin² γ=0.21),M _x=666, andM _Y=660, in units GeV. TheW _μ ^± andZ _μ ⁰ couple to the familiar charged and neutral currents, respectively. The effective neutrino oscillation angle is found to be the Cabibbo angle.     

<Emphasis Type="Italic">O</Emphasis>(1) eV sterile neutrino in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) gravity

We refer [1] to the role of an additional O(1) eV sterile neutrino in modified gravity models. We find parameter constraints in particular f(R) gravity model using following up-to-dated cosmological data: measurements of the cosmic microwave background (CMB) anisotropy, the CMB lensing potential, the baryon acoustic oscillations (BAO), the cluster mass function and the Hubble constant. It was obtained for the sterile neutrino mass 0.47 eV < m _ν,sterile < 1 eV (2σ) assuming that the sterile neutrinos are thermalized and the active neutrinos are massless, not significantly larger than in the standard cosmology model within the same data set: 0.45 eV < m _ν,sterile < 0.92 eV (2σ). But, if the mass of sterile neutrino is fixed and equals ≈ 1.5 eV according to various anomalies in neutrino oscillation experiments, f(R) gravity is much more consistent with observation data than the CDM model.     

Threshold and compactification effects in GUTS

We review general results on threshold effects and their implications on GUTs in the context of LEP data. Among the blooming grand-desert models, threshold effects are computed in the presence of a single real scalar ζ (3, 0, 8) with M_ζ?10¹⁰ GeV leading to experimentally testable predictions on the proton lifetimeτ _p in SU (5) and, in addition, small neutrino masses in SO (10) needed for the solar neutrino flux and the dark matter of the universe. The fine structure constant matching at M_Z is ensured by including threshold effects on the unification coupling. In the minimal SUSY SU (5) such effects at the GUT scale modify the prediction of the supersymmetric mass threshold near the TeV scale and the precision measurments of the Standard Model couplings at M_Z probe into the superheavy mass spectrum. Consequences of theorems proved very useful for threshold, compactification and multiloop effects are discussed. It is noted that in a class of GUTs the highest intermediate scale M_I above which G_224P becomes a good symmetry is not affected by the GUT threshold or compactification effects or multiloop contributions in the range M_I-M_U. But spontaneous compatification effects can decrease the intermediate scale drastically in models where parity and SU(2)_R breakings are decoupled. Low mass W_R-bsosns are permitted in models with decoupled parity and SU (2)_R breakings.     

Cosmology of spontaneously broken gauge family symmetry with axion solution of strong CP-problem

TheSU(3) _H model of spontaneously broken local family symmetry is considered as a simplest version of realistic quantum flavourdynamics, giving reasonable explanation of the mass hierarchy and mixing pattern of quarks and leptons. This scheme can naturally possess one or two additional globalU(1) symmetries, which can play the role of Peccei-Quinn symmetry. The model predicts: existence of the neutrino Majorana masses with definite hierarchy, existence of familon being simultaneously invisible axion (or arion) and Majoron, relationship between neutrino lifetimes relative to familon decays. Thereby, the model provides the unified physical ground for all the main types of dark matter, considered in the theory of large scale structure of the universe.     

Deviation from Tetra-Maximal Neutrino Mixing Above the GUT scale

We consider non-renormalizable interaction term as perturbation of the conventional neutrino mass matrix. We assume that the neutrino masses and mixing arise through physics at a scale intermediate between Planck scale and the electroweak breaking scale. We also assume that, just above the electroweak breaking scale, neutrino masses are nearly degenerate and their mixing is tetra-maximal. Quantum gravity (Planck scale effects) lead to an effective SU(2) _L ×U(1) invariant dimension-5 Lagrangian involving neutrino and Higgs fields. On electroweak symmetry breaking, this operator gives rise to correction to the above masses and mixing. These additional term can be consider as a perturbation to the Tetra-maximal mass matrix. The nature of gravitational interaction demands that the element of this perturbation matrix should be independent of flavor indices. We compute the deviation of three neutrino mixing angles due to Planck scale effects. We find that there is no change in θ ₁₃ and θ ₂₃ but change in solar mixing angle θ ₁₂ is suppress by 3.0°.     

Fermion masses and mixing angles in anSU(2) L ×U(1) model with horizontal interactions

AnSU(2) _L ×U(1) horizontal model is presented, in which fermions mass splitting, quark and lepton family mixing is attributed to the presence of the horizontal interactions. In the quark sector, the Cabibbo angle and the Cabibbo-like angles are evaluated. In the lepton sector, the neutrinos mixing angles, which orginate from the charged leptons mixing, are calculated, the scale of the horizontal interactions is related to the neutrino oscillation length.     

An effective lower bound of the solar neutrino flux

If the deficit of the solar neutrino (ν_e) flux is caused by the neutrino oscillation, there exists a lower bound of an effective neutrino flux detectable by electron scattering experiment, since the converted neutrino can also interact with atomic electron via neutral current effect. The effective reduction factor and day-night asymmetry for the ⁸B flux is calculated and plotted in the mixing parameter space, when matter oscillation effects both in the sun and in the earth are included, yielding a lower flux bound, ∼ 14% of the standard value.     

<Emphasis Type="Italic">SU</Emphasis><Subscript><Emphasis Type="Italic">L</Emphasis></Subscript>(4)×<Emphasis Type="Italic">U</Emphasis>(1) model for electroweak unification and sterile neutrinos

Some of the basic problems in neutrino physics, such as new energy scales, the enormous gap between the neutrino masses and the lightest charged fermion mass, and the possible existence of sterile neutrinos in the eV mass range are studied in the local gauge group SU _L (4)×U(1) for electroweak unification, which does not contain fermions with exotic electric charges. It is shown that the neutrino mass spectrum can be decoupled from that of the other fermions. The further normal seesaw mechanism for neutrinos, with right-handed neutrino Majorana masses of order M≫M _weak as well a new eV-scale can be accommodated. The eV-scale seesaw may manifest itself in experiments like the Liquid Scintillation Neutrino Detector (LSND) and MiniBooNE (MB) experimental results and future neutrino experiments.     

Space-Time Fluctuations Induced by D-Branes and Their Effects on Neutrino Oscillations

Neutrino oscillations are analyzed in the Ellis-Mavromatos-Nanopoulos-Volkov (ENMV) model, where the quantum gravitational fluctuations of the space-time background are described by virtual D branes. Such fluctuations may induce neutrino oscillations if a violation of the equivalence principle or a tiny violation of the Lorentz invariance is imposed. In this framework, the oscillation length of neutrinos turns out to be proportional to E ^–2 M, where E is the neutrino energy and M is the energy which is the scale characterizing the topological fluctuations in the vacuum.     

Lepton flavor violation and seesaw symmetries

When the standard model is extended with right-handed neutrinos the symmetries of the resulting Lagrangian are enlarged with a new global U(1) _R Abelian factor. In the context of minimal seesaw models we analyze the implications of a slightly broken U(1) _R symmetry on charged lepton flavor violating decays. We find, depending on the R-charge assignments, models where charged lepton flavor violating rates can be within measurable ranges. In particular, we show that in the resulting models due to the structure of the light neutrino mass matrix muon flavor violating decays are entirely determined by neutrino data (up to a normalization factor) and can be sizable in a wide right-handed neutrino mass range.     

Threshold and compactification effects in GUTS

We review general results on threshold effects and their implications on GUTs in the context of LEP data. Among the blooming grand-desert models, threshold effects are computed in the presence of a single real scalar ζ (3, 0, 8) with M_ζ≃10¹⁰ GeV leading to experimentally testable predictions on the proton lifetimeτ _p in SU (5) and, in addition, small neutrino masses in SO (10) needed for the solar neutrino flux and the dark matter of the universe. The fine structure constant matching at M_Z is ensured by including threshold effects on the unification coupling. In the minimal SUSY SU (5) such effects at the GUT scale modify the prediction of the supersymmetric mass threshold near the TeV scale and the precision measurments of the Standard Model couplings at M_Z probe into the superheavy mass spectrum. Consequences of theorems proved very useful for threshold, compactification and multiloop effects are discussed. It is noted that in a class of GUTs the highest intermediate scale M_I above which G_224P becomes a good symmetry is not affected by the GUT threshold or compactification effects or multiloop contributions in the range M_I-M_U. But spontaneous compatification effects can decrease the intermediate scale drastically in models where parity and SU(2)_R breakings are decoupled. Low mass W_R-bsosns are permitted in models with decoupled parity and SU (2)_R breakings.     

Overview on neutrinos and the Daya Bay experiment

Neutrinos are elementary particles in the Standard Model. Neutrino oscillation is a quantum mechanical phenomenon beyond the Standard Model. Neutrino oscillation can be described by two independent mass-squared differences Δm ₂₁ ² , Δm ₃₁ ² (or Δm ₃₂ ² ) and a 3 × 3 unitary matrix, containing three mixing angles θ ₁₂, θ ₂₃, θ ₁₃, and one charge-parity (CP) phase. θ ₁₂ is about 34° and determined by solar neutrino experiments and the reactor neutrino experiment KamLAND. θ ₂₃ is about 45° and determined by atmospheric neutrino experiments and accelerator neutrino experiments. θ ₁₃ can be measured by either accelerator or reactor neutrino experiments. On Mar. 8, 2012, the Daya Bay Reactor Neutrino Experiment reported the first observation of non-zero θ ₁₃ with 5.2 standard deviations. In June, with 2.5× previous data, Daya Bay improved the measurement of sin²2θ ₁₃ = 0.089 ± 0.010(stat) ± 0.005(syst).