Hidden symmetry of the CKM and neutrino-mapping matrices

We propose that the smallness of the light quark masses is related to the smallness of the T (i.e. CP) violation in hadronic weak interactions. Accordingly, for each of the two quark sectors (“upper” and “lower”) we construct a 3 × 3 mass matrix in a bases of unobserved quark states, such that the “upper” and “lower” basis states correspond exactly via the W^± transitions in the weak interaction. In the zeroth approximation of our formulation, we assume T conservation by making all matrix elements real. In addition, we impose a “hidden symmetry” (invariance under simultaneous translations of all three basis quark states in each sector), which ensures a zero mass eigenstate in each sector.Next, we simultaneously break the hidden symmetry and T invariance by introducing a phase factor e^iχ in the interaction for each sector. The Jarlskog invariant J_CKM, as well as the light quark masses are evaluated in terms of the parameters of the model. Comparing formulas, we find that most unknown factors drop out, resulting in a simple relation with , to leading order in χ and m_s/m_b, with A, λ the Wolfenstein parameters. (Because of the large top quark mass, the contribution from upper quark sector can be neglected.) Setting J_CKM = 3.08 × 10⁻⁵, m_b = 4.7 GeV (1s mass), m_s = 95 MeV, A = 0.818, and λ = 0.227, we find , consistent with the accepted value m_d = 3 − 7 MeV.We make a parallel proposal for the lepton sectors. With the hidden symmetry and in the approximation of T invariance, both the masses of e and ν₁ are zero. The neutrino-mapping matrix V_ν is shown to be of the same Harrison-Perkins-Scott form which is in agreement with experiments. We also examine the correction due to T violation, and evaluate the corresponding Jarlskog invariant J_ν.     

Realistic neutrinogenesis with radiative vertex correction

We propose a new model for naturally realizing light Dirac neutrinos and explaining the baryon asymmetry of the universe through neutrinogenesis. To achieve these, we present a minimal construction which extends the Standard Model with a real singlet scalar, a heavy singlet Dirac fermion and a heavy doublet scalar besides three right-handed neutrinos, respecting lepton number conservation and a Z₂$Z_2$ symmetry. The neutrinos acquire small Dirac masses due to the suppression of weak scale over a heavy mass scale. As a key feature of our construction, once the heavy Dirac fermion and doublet scalar go out of equilibrium, their decays induce the CP asymmetry from the interference of tree-level processes with the radiative vertex corrections (rather than the self-energy corrections). Although there is no lepton number violation, an equal and opposite amount of CP asymmetry is generated in the left-handed and the right-handed neutrinos. The left-handed lepton asymmetry would then be converted to the baryon asymmetry in the presence of the sphalerons, while the right-handed lepton asymmetry remains unaffected.     

Testing non-standard CP violation in neutrino propagation

Non-standard physics which can be described by effective four fermion interactions may be an additional source of CP violation in the neutrino propagation. We discuss the detectability of such a CP violation at a neutrino factory. We assume the current baseline setup of the international design study of a neutrino factory (IDS-NF) for the simulation. We find that the CP violation from certain non-standard interactions is, in principle, detectable significantly below their current bounds – even if there is no CP violation in the standard oscillation framework. Therefore, a new physics effect might be mis-interpreted as the canonical Dirac CP violation, and a possibly even more exciting effect might be missed.     

Possible new interactions of neutrino and the KATRIN experiment

We analyse the possible role of new interactions of neutrino in the forthcoming tritium beta decay experiment KATRIN aimed at detecting the neutrino mass with the sensitivity of 0.3–0.2 eV. It is shown that under certain circumstances the standard procedure of data analysis would have to be modified by the introduction of an extra parameter describing the strength of the new interactions. Our model simulations show that the modified procedure may improve the quality of the fit compared with the standard case. Ignoring the possibility of new interactions may lead to a systematic error in the neutrino mass determination.     

Fourier analysis of the parametric resonance in neutrino oscillations

Parametric enhancement of the appearance probability of the neutrino oscillation under the inhomogeneous matter is studied. Fourier expansion of the matter density profile leads to a simple resonance condition and manifests that each Fourier mode modifies the energy spectrum of oscillation probability at around the corresponding energy; below the MSW resonance energy, a large-scale variation modifies the spectrum in high energies while a small-scale one does in low energies. In contrast to the simple parametric resonance, the enhancement of the oscillation probability is itself an slow oscillation as demonstrated by a numerical analysis with a single Fourier mode of the matter density. We derive an analytic solution to the evolution equation on the resonance energy, including the expression of frequency of the slow oscillation.     

A4-based tri-bimaximal mixing within inverse and linear seesaw schemes

We consider tri-bimaximal lepton mixing within low-scale seesaw schemes where light neutrino masses arise from TeV scale physics, potentially accessible at the Large Hadron Collider (LHC). Two examples are considered, based on the A₄$A_4$ flavor symmetry realized within the inverse or the linear seesaw mechanisms. Both are highly predictive so that in both the light neutrino sector effectively depends only on three mass parameters and one Majorana phase, with no CP violation in neutrino oscillations. We find that the linear seesaw leads to a lower bound for neutrinoless double beta decay while the inverse seesaw does not. The models also lead to potentially sizeable decay rates for lepton flavor violating processes, tightly related by the assumed flavor symmetry.     

Neutrino Oscillation Induced by Chiral Phase Transition

Electric charge neutrality provides a relationship between chiral dynamics and neutrino propagation in compact stars. Due to the sudden drop of the electron density at the first-order chiral phase transition, the oscillation for low energy neutrinos is significant and can be regarded as a signature of chiral symmetry restoration in the core of compact stars.     

Non-cyclic phases for neutrino oscillations in quantum field theory

We show the presence of non-cyclic phases for oscillating neutrinos in the context of quantum field theory. Such phases carry information about the non-perturbative vacuum structure associated with the field mixing. By subtracting the condensate contribution of the flavor vacuum, the previously studied quantum mechanics geometric phase is recovered.     

Multiple seesaw mechanisms of neutrino masses at the TeV scale

In pursuit of a balance between theoretical naturalness and experimental testability, we propose two classes of multiple seesaw mechanisms at the TeV scale to understand the origin of tiny neutrino masses. They are novel extensions of the canonical and double seesaw mechanisms, respectively, by introducing even and odd numbers of gauge-singlet fermions and scalars. It is thanks to a proper implementation of the global U(1)×Z_2N$\mathrm{U}(1)\times {\mathbb{Z}}_{2N}$ symmetry that the overall neutrino mass matrix in either class has a suggestive nearest-neighbor-interaction pattern. We briefly discuss possible consequences of these TeV-scale seesaw scenarios, which can hopefully be explored in the upcoming Large Hadron Collider and precision neutrino experiments, and present a simple but instructive example of model building.     

Quantum mechanics in space-time: The Feynman path amplitude description of physical optics, de Broglie matter waves and quark and neutrino flavour oscillations

Feynman’s laws of quantum dynamics are concisely stated, discussed in comparison with other formulations of quantum mechanics and applied to selected problems in the physical optics of photons and massive particles as well as flavour oscillations. The classical wave theory of light is derived from these laws for the case in which temporal variation of path amplitudes may be neglected, whereas specific experiments, sensitive to the temporal properties of path amplitudes, are suggested. The reflection coefficient of light from the surface of a transparent medium is found to be markedly different to that predicted by the classical Fresnel formula. Except for neutrino oscillations, good agreement is otherwise found with previous calculations of spatially dependent quantum interference effects.     

The mass hierarchy with atmospheric neutrinos at INO

We study the neutrino mass hierarchy at the magnetized Iron CALorimeter (ICAL) detector at India-based Neutrino Observatory with atmospheric neutrino events generated by the Monte Carlo event generator Nuance. We judicially choose the observables so that the possible systematic uncertainties can be reduced. The resolution as a function of both energy and zenith angle simultaneously is obtained for neutrinos and anti-neutrinos separately from thousand years un-oscillated atmospheric neutrino events at ICAL to migrate number of events from neutrino energy and zenith angle bins to muon energy and zenith angle bins. The resonance ranges in terms of directly measurable quantities like muon energy and zenith angle are found using this resolution function at different input values of θ₁₃${\theta }_{13}$. Then, the marginalized χ²s${\chi }^2\mathrm{s}$ are studied for different input values of θ₁₃${\theta }_{13}$ with its resonance ranges taking input data in muon energy and zenith angle bins. Finally, we find that the mass hierarchy can be explored up to a lower value of θ₁₃≈5°${\theta }_{13}\approx 5°$ with confidence level >95% in this set up.     

The flavor problem and discrete symmetries

In this Letter we propose a multi-Higgs extension of the standard model with Abelian and non-Abelian discrete symmetries in which the mass matrices of the charged fermions obtained from renormalizable interactions are diagonal. However, non-diagonal contributions, that are important for obtaining the CKM matrix in the quark sector, arise from non-renormalizable dimension five interactions. Active neutrinos acquire mass only from non-renormalizable interactions, the non-diagonal entries arising through dimension five operators, while the diagonal entries comes from dimension six operators. Realistic mixing matrices in the neutrino and the quarks sectors are obtained.     

Parameterization for Neutrino Mixing Matrix with Deviated Unitarity

Neutrino oscillation experiments provide the first evidence on non-zero neutrino masses and indicate new physics beyond the standard model. With Majorana neutrinos introduced to acquire tiny neutrino masses, it leads to the existence of more than three neutrino species, implying that the ordinary neutrino mixing matrix is only a part of the whole extended unitary mixing matrix and thus no longer unitary. We give a parameterization for a non-unitary neutrino mixing matrix under seesaw framework and further present a method to test the unitarity of the ordinary neutrino mixing matrix.     

Emission and absorption of photons and the black-body spectrum in Lorentz-odd electrodynamics

We study emission and absorption of radiation by non-relativistic electrons within the framework of a Lorentz-breaking electrodynamics in (3+1)$(3+1)$ dimensions. We have realised that Planck-type law acquires extra terms proportional to the violating parameters: For the CPT-odd model, the leading extra terms appear to be linear or quadratic in these violating parameters according to the background vector is parallel or perpendicular to the photon wave-vector. In the CPT-even case a linear correction shows up. Besides these deviations in the black-body spectra, those violations may be also probed through a difference in the photon mean occupation number for the two modes. Our results also indicate that such violations are better probed at very low temperatures, where their effects on the thermal spectra are largely enhanced.     

A comment on the topological phase for anti-particles in a Lorentz-violating environment

Recently, a scheme to analyse topological phases in quantum mechanics by means of the non-relativistic limit of fermions non-minimally coupled to a Lorentz-breaking background has been proposed. In this Letter, we show that the fixed background, responsible for the Lorentz-symmetry violation, may induce opposite Aharonov–Casher phases for a particle and its corresponding anti-particle. We then argue that such a difference may be used to investigate the asymmetry for particle/anti-particle as well as to propose bounds on the associated Lorentz-symmetry violating parameters.