Neutrino Mass-squared Differences Research Articles

Distortion of neutrino oscillations by dark photon dark matter

A weakly coupled and light dark photon coupling to lepton charges ${L}_{\ensuremath{\mu}}\ensuremath{-}{L}_{\ensuremath{\tau}}$ is an intriguing dark matter candidate whose coherent oscillations alter the dispersion relations of leptons. We study how this effect modifies the dynamics of neutrino flavor conversions, focusing on long baseline and solar oscillations. We analyze data from the T2K, SNO, and Super-Kamiokande experiments in order to obtain world-leading limits on the dark photon gauge coupling for masses below $\ensuremath{\sim}{10}^{\ensuremath{-}11}\text{ }\text{ }\mathrm{eV}$. Degeneracies between shifts in the neutrino mass-squared differences and mixing angles and the new physics effect significantly relax the current constraints on the neutrino vacuum oscillation parameters.

Diffuse supernova neutrino background as a probe of late-time neutrino mass generation

The relic neutrinos from old supernova explosions are among the most ancient neutrino fluxes within experimental reach. Thus, the diffuse supernova neutrino background (DSNB) could teach us if neutrino masses were different in the past (redshifts $z\ensuremath{\lesssim}5$). Oscillations inside the supernova depend strongly on the neutrino mass-squared differences and the values of the mixing angles, rendering the DSNB energy spectrum sensitive to variations of these parameters. Considering a purely phenomenological parametrization of the neutrino masses as a function of redshift, we compute the expected local DSNB spectrum here on Earth. Given the current knowledge of neutrino oscillation parameters, especially the fact that $|{U}_{e3}{|}^{2}$ is small, we find that the ${\ensuremath{\nu}}_{e}$ spectrum could be significantly different from standard expectations if neutrinos were effectively massless at $z\ensuremath{\gtrsim}1$ as long as the neutrino mass ordering is normal. On the other hand, the ${\overline{\ensuremath{\nu}}}_{e}$ flux is not expected to be significantly impacted. Hence, a measurement of both the neutrino and antineutrino components of the DSNB should allow one to test the possibility of recent neutrino mass generation.

$$\text {TM}_1$$ neutrino mixing with $$\sin \theta _{13}=\frac{1}{\sqrt{3}}\sin \frac{\pi }{12}$$

We construct a neutrino model using the flavour group \(S_4\times C_4 \times C_3{ \times C_2}\) under the type 1 seesaw mechanism. The vacuum alignments of the flavons in the model lead to \(\text {TM}_1\) mixing with \(\sin \theta _{13}=\frac{1}{\sqrt{3}}\sin \frac{\pi }{12}\). The mixing also exhibits \(\mu \text {-}\tau \) reflection symmetry. By fitting the eigenvalues of the effective seesaw mass matrix with the observed neutrino mass-squared differences, we predict the individual light neutrino masses. The vacuum alignment of the \(S_4\) triplet appearing in the Majorana mass term plays a key role in obtaining the aforementioned \(\text {TM}_1\) scenario. Since the symmetries of the flavour group are not sufficient to define this alignment, we apply the recently proposed framework of the auxiliary group in our model. Using this framework, the \(S_4\) triplet is obtained by coupling together several irreducible multiplets that transform under an expanded flavour group consisting of the original flavour group as well as an auxiliary group. The vacuum alignment of each of these multiplets is uniquely defined in terms of its residual symmetries under the expanded flavour group. As a result, the \(S_4\) triplet constructed from these multiplets also becomes uniquely defined.

Sum rules and asymptotic behaviors of neutrino mixing and oscillations in matter

Similar to the case in vacuum, it is straightforward to describe neutrino oscillations in matter with the effective lepton flavor mixing matrix and neutrino mass-squared differences (i, j = 1, 2, 3). By calculating two sets of sum rules of and , we have derived exact expressions of and (for α, β = e, μ, τ and i = 1, 2, 3) and discussed the asymptotic behaviors of and and in very dense matter (i.e., in the limit of the matter parameter approaching infinity).

Towards the meV limit of the effective neutrino mass in neutrinoless double-beta decays * * This work was supported in part by the National Key R&D Program of China (2018YFA0404100), the Strategic Priority Research Program of the Chinese Academy of Sciences (XDA10010100), the National Natural Science Foundation of China (11605081, 11775231, 11775232, 11835013, 11820101005) and the CAS Center for Excellence

We emphasize that it is extremely important for future neutrinoless double-beta ( ) decay experiments to reach the sensitivity to the effective neutrino mass . With such a sensitivity, it is highly possible to discover the signals of decays. If no signal is observed at this sensitivity level, then either neutrinos are Dirac particles or stringent constraints can be placed on their Majorana masses. In this paper, assuming the sensitivity of for future decay experiments and the precisions on neutrino oscillation parameters after the JUNO experiment, we fully explore the constrained regions of the lightest neutrino mass and two Majorana-type CP-violating phases . Several important conclusions in the case of normal neutrino mass ordering can be made. First, the lightest neutrino mass is severely constrained to a narrow range , which together with the precision measurements of neutrino mass-squared differences from oscillation experiments completely determines the neutrino mass spectrum and . Second, one of the two Majorana CP-violating phases is limited to , which cannot be obtained from any other realistic experiments. Third, the sum of three neutrino masses is found to be , while the effective neutrino mass for beta decays turns out to be . These observations clearly set up the roadmap for future non-oscillation neutrino experiments aiming to solve the fundamental problems in neutrino physics.

Fitting neutrino masses in a realistic intersecting D-braneworld

The correct quark and charged lepton mass matrices along with a nearly correct CKM matrix may be naturally accommodated in a Pati-Salam model constructed from intersecting D6 branes on a $T^6/(\Z_2 \times \Z_2)$ orientifold. Furthermore, near-tribimaximal mixing for neutrinos may arise naturally due to the structure of the Yukawa matrices. Consistency with the quark and charged lepton mass matrices in combination with obtaining near-tribimaximal mixing fixes the Dirac neutrino mass matrix completely. Then, applying the seesaw mechanism for different choices of right-handed neutrino masses and running the obtained neutrino parameters down to the electroweak scale via the RGEs, we are able to make predictions for the neutrino masses and mixing angles. We obtain lepton mixing angles which are close to the observed values, $\theta_{12} =33.8^{\circ}\pm1.2^{\circ}$, $\theta_{23}=46.9^{\circ}\pm0.9^{\circ}$, and $\theta_{13}=8.56^{\circ}\pm0.20^{\circ}$. In addition, the neutrino mass-squared differences are found to be $\Delta m^2_{32} = 0.0025\pm0.0001$~eV$^2$ and $\Delta m^2_{21} = 0.000075\pm0.000003$~eV with $m_1=0.0150\pm0.0002$~eV, $m_2=0.0173\pm0.0002$~eV, and $m_3=0.053\pm 0.002$~eV so that $\sum_i m_i = 0.085\pm0.002$~eV, consistent with experimental observations.

On the properties of the effective Jarlskog invariant for three-flavor neutrino oscillations in matter

In this paper, we show that the ratio of the effective Jarlskog invariant J˜ for leptonic CP violation in three-flavor neutrino oscillations in matter to its counterpart J in vacuum J˜/J≈1/(Cˆ12Cˆ13) holds as an excellent approximation, where Cˆ12≡1−2Aˆ⁎cos⁡2θ12+Aˆ⁎2 with Aˆ⁎≡acos2⁡θ13/Δ21 and Cˆ13≡1−2Accos⁡2θ13+Ac2 with Ac≡a/Δc. Here Δij≡mi2−mj2 (for ij=21,31,32) stand for the neutrino mass-squared differences in vacuum and θij (for ij=12,13,23) are the neutrino mixing angles in vacuum, while Δc≡Δ31cos2⁡θ12+Δ32sin2⁡θ12 and the matter parameter a≡22GFNeE are defined. This result has been explicitly derived by improving the previous analytical solutions to the renormalization-group equations of effective neutrino masses and mixing parameters in matter. Furthermore, as a practical application, such a simple analytical formula has been implemented to understand the existence and location of the extrema of J˜.

All fermion masses and mixings in an intersecting D-brane world

It is shown that neutrino mixing angles which are consistent with current experimental observations may be naturally obtained in a Pati-Salam model constructed from intersecting D6 branes on a T6/(Z2×Z2) orientifold. The Dirac mass matrices in the model are naturally the same as those which are obtained by imposing a Δ(27) flavor symmetry, which allows for near-tribimaximal mixing in the neutrino sector. In addition, it is possible to obtain the correct mass matrices for quarks and charged leptons, as well as nearly the correct CKM matrix. An RGE analysis of the neutrino mass parameters, including the seesaw mechanism assuming a specific form for the right-handed neutrino mass matrix is performed, and it is found that the neutrino mixing angles at the electroweak scale are θ12=35.0°, θ23=47.1°, and θ13=8.27°. In addition, the neutrino mass-squared differences are found to be Δm322=0.00252 eV2 and Δm212=0.0000739 eV2 with m1=0.0146 eV, m2=0.0170 eV, m3=0.0530 eV, and Σmi=0.0846 eV. These results depend slightly upon the scale at which the RGE running goes from being that of the MSSM to that of the SM, which we interpret to be the lightest stop mass. The best agreement with experimental data is for m˜t1≈4.28 TeV. This suggests that the superpartners which produce the strongest signal in a hadron collider are just out of reach at the LHC.

Sum rules and asymptotic behaviors of neutrino mixing in dense matter

It has proved convenient to define the effective lepton flavor mixing matrix U˜ and neutrino mass-squared differences Δ˜ji≡m˜j2−m˜i2 (for i,j=1,2,3) to describe the phenomena of neutrino mixing and flavor oscillations in a medium, but the prerequisite is to establish direct and transparent relations between these effective quantities and their fundamental counterparts in vacuum. With the help of two sets of sum rules for U˜ and Δ˜ji, we derive new and exact formulas for moduli of the nine elements of U˜ and the sides of its three Dirac unitarity triangles in the complex plane. The asymptotic behaviors of |U˜αi|2 and Δ˜ji (for α=e,μ,τ and i,j=1,2,3) in very dense matter (namely, allowing the matter parameter A=22GFNeE to mathematically approach infinity) are analytically unraveled for the first time, and in this connection the confusion associated with the parameter redundancy of θ˜12, θ˜13, θ˜23 and δ˜ in the standard parametrization of U˜ is clarified.

Modular S4 models of lepton masses and mixing

We investigate models of charged lepton and neutrino masses and lepton mixing based on broken modular symmetry. The matter fields in these models are assumed to transform in irreducible representations of the finite modular group Γ4 ≃ S4. We analyse the minimal scenario in which the only source of symmetry breaking is the vacuum expectation value of the modulus field. In this scenario there is no need to introduce flavon fields. Using the basis for the lowest weight modular forms found earlier, we build minimal phenomenologically viable models in which the neutrino masses are generated via the type I seesaw mechanism. While successfully accommodating charged lepton masses, neutrino mixing angles and mass-squared differences, these models predict the values of the lightest neutrino mass (i.e., the absolute neutrino mass scale), of the Dirac and Majorana CP violation (CPV) phases, as well as specific correlations between the values of the atmospheric neutrino mixing parameter sin2θ23 and i) the Dirac CPV phase δ, ii) the sum of the neutrino masses, and iii) the effective Majorana mass in neutrinoless double beta decay. We consider also the case of residual symmetries ℤ3ST and ℤ2S respectively in the charged lepton and neutrino sectors, corresponding to specific vacuum expectation values of the modulus.

Neutrino Mass and the Higgs Portal Dark Matter in the ESSFSM

We extend the standard model with three right-handed singlet neutrinos and a real singlet scalar. We impose two Z2 and Z2′ symmetries. We explain the tiny neutrino mass-squared differences with two Z2- and Z2′-even right-handed neutrinos using type I seesaw mechanism. The Z2-odd fermion and the Z2′-odd scalar can both serve as viable dark matter candidates. We identify new regions in the parameter space which are consistent with relic density of the dark matter from recent direct search experiments LUX-2016 and XENON1T-2017 and LHC data.

Broken S3L×S3R flavor symmetry and leptonic CP violation**Supported by NNSFC (11325525), National Recruitment Program for Young Professionals and CAS Center for Excellence in Particle Physics (CCEPP)

In the framework of the canonical seesaw model, we present a simple but viable scenario to explicitly break an S3L×S3R flavor symmetry in the leptonic sector. It turns out that the leptonic flavor mixing matrix is completely determined by the mass ratios of the charged leptons (i.e., me/mμ and mμ/mτ) and those of light neutrinos (i.e., m1/m2 and m2/m3). The latest global-fit results of the three neutrino mixing angles {θ12, θ13, θ23} and two neutrino mass-squared differences at the 3σ level are used to constrain the parameter space of {m1/m2,m2/m3}. The predictions for the mass spectrum and flavor mixing are highlighted: (1) the neutrino mass spectrum shows a hierarchical pattern and a normal ordering, e.g., m1≈2.2 meV, m2≈8.8 meV and m3≈52.7 meV; (2) only the first octant of θ23 is allowed, namely, 41.8°≲θ23≲43.3°; (3) the Dirac CP-violating phase δ≈−22° deviates significantly from the maximal value −90°. All these predictions are ready to be tested in ongoing and forthcoming neutrino oscillation experiments. Moreover, we demonstrate that the cosmological matter-antimatter asymmetry can be explained via resonant leptogenesis, including the individual lepton-flavor effects. In our scenario, leptonic CP violation at low- and high-energy scales is closely connected.

Recent Results from the Daya Bay Experiment

The Daya Bay reactor neutrino experiment was designed to precisely measure the neutrino oscillation parameter θ13 via the relative comparison of neutrino rates and spectra at different baselines. Eight identically designed detectors were deployed in two near experimental halls and a far hall. Six 2.9 GWth nuclear power reactors served as intense sources. Since Dec. 2011, the experiment has been running stably. The latest neutrino oscillation results were based on 1230 days of data. Analysis using a three-flavor oscillation model yielded sin22θ13 = 0.0841 ± 0.0027(stat.) ± 0.0019(syst.), and effective neutrino mass-squared difference . Besides, results from the absolute measurement of reactor flux and energy spectrum, and a search for a light sterile neutrino are also presented.

Nonstandard interactions in solar neutrino oscillations with Hyper-Kamiokande and JUNO

Measurements of the solar neutrino mass-squared difference from KamLAND and solar neutrino data are somewhat discrepant, perhaps due to nonstandard neutrino interactions in matter. We show that the zenith angle distribution of solar neutrinos at Hyper-Kamiokande and the energy spectrum of reactor antineutrinos at JUNO can conclusively confirm the discrepancy and detect new neutrino interactions.

Measurement of electron antineutrino oscillation based on 1230 days of operation of the Daya Bay experiment

A measurement of electron antineutrino oscillation by the Daya Bay Reactor Neutrino Experiment is described in detail. Six 2.9-GW$_{\rm th}$ nuclear power reactors of the Daya Bay and Ling Ao nuclear power facilities served as intense sources of $\overline{\nu}_{e}$'s. Comparison of the $\overline{\nu}_{e}$ rate and energy spectrum measured by antineutrino detectors far from the nuclear reactors ($\sim$1500-1950 m) relative to detectors near the reactors ($\sim$350-600 m) allowed a precise measurement of $\overline{\nu}_{e}$ disappearance. More than 2.5 million $\overline{\nu}_{e}$ inverse beta decay interactions were observed, based on the combination of 217 days of operation of six antineutrino detectors (Dec. 2011--Jul. 2012) with a subsequent 1013 days using the complete configuration of eight detectors (Oct. 2012--Jul. 2015). The $\overline{\nu}_{e}$ rate observed at the far detectors relative to the near detectors showed a significant deficit, $R=0.949 \pm 0.002(\mathrm{stat.}) \pm 0.002(\mathrm{syst.})$. The energy dependence of $\overline{\nu}_{e}$ disappearance showed the distinct variation predicted by neutrino oscillation. Analysis using an approximation for the three-flavor oscillation probability yielded the flavor-mixing angle $\sin^22\theta_{13}=0.0841 \pm 0.0027(\mathrm{stat.}) \pm 0.0019(\mathrm{syst.})$ and the effective neutrino mass-squared difference of $\left|{\Delta}m^2_{\mathrm{ee}}\right|=(2.50 \pm 0.06(\mathrm{stat.}) \pm 0.06(\mathrm{syst.})) \times 10^{-3}\ {\rm eV}^2$. Analysis using the exact three-flavor probability found ${\Delta}m^2_{32}=(2.45 \pm 0.06(\mathrm{stat.}) \pm 0.06(\mathrm{syst.})) \times 10^{-3}\ {\rm eV}^2$ assuming the normal neutrino mass hierarchy and ${\Delta}m^2_{32}=(-2.56 \pm 0.06(\mathrm{stat.}) \pm 0.06(\mathrm{syst.})) \times 10^{-3}\ {\rm eV}^2$ for the inverted hierarchy.

Symmetric formulation of neutrino oscillations in matter and its intrinsic connection to renormalization-group equations

In this article, we point out that the effective Hamiltonian for neutrino oscillations in matter is invariant under the transformation of the mixing angle and the exchange of first two neutrino masses , if the standard parametrization of lepton flavor mixing matrix is adopted. To maintain this symmetry in perturbative calculations, we present a symmetric formulation of the effective Hamiltonian by introducing an η-gauge neutrino mass-squared difference for , where for , and show that only , or is allowed. Furthermore, we prove that is the best choice to derive more accurate and compact neutrino oscillation probabilities, by implementing the approach of renromalization-group equations. The validity of this approach becomes transparent when an analogy is made between the parameter η herein and the renormalization scale μ in relativistic quantum field theories.

Looking into analytical approximations for three-flavor neutrino oscillation probabilities in matter

Motivated by tremendous progress in neutrino oscillation experiments, we derive a new set of simple and compact formulas for three-flavor neutrino oscillation probabilities in matter of a constant density. A useful definition of the $\eta$-gauge neutrino mass-squared difference $\Delta^{}_* \equiv \eta \Delta^{}_{31} + (1-\eta) \Delta^{}_{32}$ is introduced, where $\Delta^{}_{ji} \equiv m^2_j - m^2_i$ for $ji = 21, 31, 32$ are the ordinary neutrino mass-squared differences and $0 \leq \eta \leq 1$ is a real and positive parameter. Expanding neutrino oscillation probabilities in terms of $\alpha \equiv \Delta^{}_{21}/\Delta^{}_*$, we demonstrate that the analytical formulas can be remarkably simplified for $\eta = \cos^2 \theta^{}_{12}$, with $\theta_{12}^{}$ being the solar mixing angle. As a by-product, the mapping from neutrino oscillation parameters in vacuum to their counterparts in matter is obtained at the order of ${\cal O}(\alpha^2)$. Finally, we show that our approximate formulas are not only valid for an arbitrary neutrino energy and any baseline length, but also still maintaining a high level of accuracy.

Terrestrial matter effects on reactor antineutrino oscillations at JUNO or RENO-50: how small is small?**Supported by National Natural Science Foundation of China (11135009, 11305193), the Strategic Priority Research Program of the Chinese Academy of Sciences (XDA10010100) and the CAS Center for Excellence in Particle Physics

We have carefully examined, in both analytical and numerical ways, how small the terrestrial matter effects can be in a given medium-baseline reactor antineutrino oscillation experiment like JUNO or RENO-50. Taking the forthcoming JUNO experiment as an example, we show that the inclusion of terrestrial matter effects may reduce the sensitivity of the neutrino mass ordering measurement by and a neglect of such effects may shift the best-fit values of the flavor mixing angle θ12 and the neutrino mass-squared difference Δ21 by about 1σ to 2σ in the future data analysis. In addition, a preliminary estimate indicates that a 2σ sensitivity of establishing the terrestrial matter effects can be achieved for about 10 years of data taking at JUNO with the help of a suitable near detector implementation.

Some comments on high precision study of neutrino oscillations

I discuss here some problems connected with the high precision study of neutrino oscillations. In the general case of n-neutrino mixing I derive a convenient expression for transition probability in which only independent terms (and mass-squared differences) enter. For three-neutrino mixing I discuss a problem of a definition of a large (atmospheric) neutrino mass-squared difference. I comment also possibilities to reveal the character of neutrino mass spectrum in future reactor neutrino experiments.

Abelian realization of phenomenological two-zero neutrino textures

In an attempt at explaining the observed neutrino mass-squared differences and leptonic mixing, lepton mass matrices with zero textures have been widely studied. In the weak basis where the charged lepton mass matrix is diagonal, various neutrino mass matrices with two zeros have been shown to be consistent with the current experimental data. Using the canonical and Smith normal form methods, we construct the minimal Abelian symmetry realizations of these phenomenological two-zero neutrino textures. The implementation of these symmetries in the context of the seesaw mechanism for Majorana neutrino masses is also discussed.