Dirac CP-violating Phase Research Articles

Families from supergroups and predictions for leptonic CP violation

As was shown in 1984 by Caneschi, Farrar, and Schwimmer, decomposing representations of the supergroup SU(M |N ), can give interesting anomaly-free sets of fermion representations of SU(M ) × SU(N ) × U(1). It is shown here that such groups can be used to construct realistic grand unified models with non-abelian gauged family symmetries. A particularly simple three-family example based on SU(5) × SU(2) × U(1) is studied. The forms of the mass matrices, including that of the right-handed neutrinos, are determined in terms of SU(2) Clebsch coefficients; and the model is able to fit the lepton sector and predict the Dirac CP-violating phase of the neutrinos. Models of this type would have a rich phenomenology if part of the family symmetry is broken near the electroweak scale.

Impact of CP-violation on neutrino lepton number asymmetries revisited

We revisit the effect of the (Dirac) CP-violating phase on neutrino lepton number asymmetries in both mass- and flavor-basis. We found that, even if there are sizable effects on muon- and tau-neutrino asymmetries, the effect on the asymmetry of electron-neutrinos is at most similar to the upper bound set by BBN for initial neutrino degeneracy parameters smaller than order unity. We also found that, for the asymmetries in mass-basis, the changes caused by CP-violation is of sub-\% level which is unlikely to be accesible neither in the current nor in the forthcoming experiments.

Neutrino mixing model based on anA4×Z3×Z4flavor symmetry

A model of a neutrino mixing with an $A_4\times Z_3\times Z_4$ flavour symmetry is suggested. In addition to the standard model fields, the present model contains six new fields which transform under different representations of $A_4\times Z_3\times Z_4$. The model is constructed to slightly deviate from a tri-bi-maximal model in agreement with the current experimental data, thus, all analysis can be done in the base of the perturbation method. Within this model, as an application, a relation between the mixing angles ($\theta_{12}, \theta_{23}, \theta_{13}$) and the Dirac CP-violation phase ($\delta_{CP}$) is established. This relation allows a prediction of $\delta_{CP}$ and the Jarlskog parameter ($J_{CP}$). The predicted value $\delta_{CP}$ is in the 1$\sigma$ region of the global fit for both the normal- and inverse neutrino mass ordering and gives $J_{CP}$ to be within the bound $|J_{CP}|\leq 0.04$. For an illustration, the model is checked numerically and gives values of the neutrino masses (of the order of 0.1 eV) and the mixing angle $\theta_{13}$ (about $9^\circ$) very close to the current experimental data.

Fermion masses and mixings in the 3-3-1 model with right-handed neutrinos based on the $$S_3$$ S 3 flavor symmetry

We propose a 3-3-1 model where the $${SU}(3)_{C}\otimes {SU}(3)_{L}\otimes U(1)_{X}$$ symmetry is extended by $$S_{3}\otimes Z_{3}\otimes Z_{3}^{\prime }\otimes Z_{8}\otimes Z_{16}$$ and the scalar spectrum is enlarged by extra $$ {SU}(3)_{L}$$ singlet scalar fields. The model successfully describes the observed SM fermion mass and mixing pattern. In this framework, the light active neutrino masses arise via an inverse seesaw mechanism and the observed charged fermion mass and quark mixing hierarchy is a consequence of the $$Z_{3}\otimes Z_{3}^{\prime }\otimes Z_{8}\otimes Z_{16}$$ symmetry breaking at very high energy. The obtained physical observables for both quark and lepton sectors are compatible with their experimental values. The model predicts the effective Majorana neutrino mass parameter of neutrinoless double beta decay to be $$m_{\beta \beta }=$$ 4 and 48 meV for the normal and the inverted neutrino spectra, respectively. Furthermore, we found a leptonic Dirac CP-violating phase close to $$\frac{\pi }{2}$$ and a Jarlskog invariant close to about $$3\times 10^{-2}$$ for both normal and inverted neutrino mass hierarchy.

Renormalisation group corrections to neutrino mixing sum rules

Neutrino mixing sum rules are common to a large class of models based on the (discrete) symmetry approach to lepton flavour. In this approach the neutrino mixing matrix $U$ is assumed to have an underlying approximate symmetry form $\tilde{U}_{\nu}$, which is dictated by, or associated with, the employed (discrete) symmetry. In such a setup the cosine of the Dirac CP-violating phase $\delta$ can be related to the three neutrino mixing angles in terms of a sum rule which depends on the symmetry form of $\tilde{U}_{\nu}$. We consider five extensively discussed possible symmetry forms of $\tilde{U}_{\nu}$: i) bimaximal (BM) and ii) tri-bimaximal (TBM) forms, the forms corresponding to iii) golden ratio type A (GRA) mixing, iv) golden ratio type B (GRB) mixing, and v) hexagonal (HG) mixing. For each of these forms we investigate the renormalisation group corrections to the sum rule predictions for $\delta$ in the cases of neutrino Majorana mass term generated by the Weinberg (dimension 5) operator added to i) the Standard Model, and ii) the minimal SUSY extension of the Standard Model.

A combined study of source, detector and matter non-standard neutrino interactions at DUNE

We simultaneously investigate source, detector and matter non-standard neutrino interactions at the proposed DUNE experiment. Our analysis is performed using a Markov Chain Monte Carlo exploring the full parameter space. We find that the sensitivity of DUNE to the standard oscillation parameters is worsened due to the presence of non-standard neutrino interactions. In particular, there are degenerate solutions in the leptonic mixing angle $\theta_{23}$ and the Dirac CP-violating phase $\delta$. We also compute the expected sensitivities at DUNE to the non-standard interaction parameters. We find that the sensitivities to the matter non-standard interaction parameters are substantially stronger than the current bounds (up to a factor of about 15). Furthermore, we discuss correlations between the source/detector and matter non-standard interaction parameters and find a degenerate solution in $\theta_{23}$. Finally, we explore the effect of statistics on our results.

Double Froggatt–Nielsen mechanism

We present a doubly parametric extension of the standard Froggatt--Nielsen (FN) mechanism. As is well known, mass matrices of the up- and down-type quark sectors and the charged lepton sector in the standard model can be parametrized well by a parameter $\lambda$ which is usually taken to be the sine of the Cabibbo angle ($\lambda = \sin\theta_\text{C} \simeq 0.225$). However, in the neutrino sector, there is still room to realize the two neutrino mass squared differences $\Delta m_\text{sol}^2$ and $\Delta m_\text{atm}^2$, two large mixing angles $\theta _{12}$ and $\theta _{23}$, and non-zero $\theta _{13}$. Then we consider an extension with an additional parameter $\rho$ in addition to $\lambda$. Taking the relevant FN charges for a power of $\lambda~(=0.225)$ and additional FN charges for a power of $\rho$, which we assume to be less than one, we can reproduce the ratio of the two neutrino mass squared differences and three mixing angles. In the normal neutrino mass hierarchy, we show several patterns for taking relevant FN charges and the magnitude of $\rho$. We find that if $\sin \theta_{23}$ is measured more precisely, we can distinguish each pattern. This is testable in the near future, for example in neutrino oscillation experiments. In addition, we predict the Dirac CP-violating phase for each pattern.

Radiative corrections to the solar lepton mixing sum rule

The simple correlation among three lepton flavor mixing angles $(\theta^{}_{12}, \theta^{}_{13}, \theta^{}_{23})$ and the leptonic Dirac CP-violating phase $\delta$ is conventionally called a sum rule of lepton flavor mixing, which may be derived from a class of neutrino mass models with flavor symmetries. In this paper, we consider the solar lepton mixing sum rule $\theta^{}_{12} \approx \theta^{\nu}_{12} + \theta^{}_{13} \cos \delta$, where $\theta^\nu_{12}$ stems from a constant mixing pattern in the neutrino sector and takes the value of $\theta^\nu_{12} = 45^\circ$ for the bi-maximal mixing (BM), $\theta^\nu_{12} = \tan^{-1}(1/\sqrt{2}) \approx 35.3^\circ$ for the tri-bimaximal mixing (TBM) or $\theta^\nu_{12} = \tan^{-1}\left[2/(\sqrt{5} + 1)\right] \approx 31.7^\circ$ for the golden-ratio mixing (GR), and investigate the renormalization-group (RG) running effects on lepton flavor mixing parameters when this sum rule is assumed at a superhigh-energy scale. For illustration, we work within the framework of the minimal supersymmetric standard model (MSSM), and implement the Bayesian approach to explore the posterior distribution of $\delta$ at the low-energy scale, which becomes quite broad when the RG running effects are significant. Moreover, we also discuss the compatibility of the above three mixing scenarios with current neutrino oscillation data, and observe that radiative corrections can increase such a compatibility for the BM scenario, resulting in a weaker preference for the TBM and GR ones.

On the CP Violation Phase in a Neutrino Mixing Model with an A4 Flavor Symmetry

Neutrino masses and mixing in an extended standard model acquiring an A4 flavour symmetry are considered. The corresponding three-neutrino mixing matrix obtained via a pertur- bative method allows us to determine the Dirac CP violation phase (\delta_{CP}) as a function of the mixing angles (\theta_{12}, \theta_{23}, \theta_{13}). Then, numerical values and distributions of \delta_{CP} are given. The latter values are quite close to the global fits of the experimental data for both the normal ordering and inverse ordering of the neutrino masses.

SUSY SU(5)×S 4 GUT flavor model for fermion masses and mixings with adjoint, large θ 13 PMNS

We propose an $S_{4}$ flavor model based on supersymmetric (SUSY) SU(5) GUT. The first and third generations of \textbf{10} dimensional representations in SU(5) are all assigned to be $1_{1}$ of $S_{4}$. The second generation of \textbf{10} is to be $1_{2}$ of $S_{4}$. Right-handed neutrinos of singlet \textbf{1} and three generations of $\bar{\textbf{5}}$ are all assigned to be $3_{1}$ of $S_{4}$. The VEVs of two sets of flavon fields are allowed a moderate hierarchy, that is $\langle\Phi^{\nu}\rangle \sim \lambda_{c}\langle\Phi^{e}\rangle$. Tri-Bimaximal (TBM) mixing can be produced at both leading order (LO) and next to next to leading order (NNLO) in neutrino sector. All the masses of up-type quarks are obtained at LO. We also get the bottom-tau unification $m_{\tau}=m_{b}$ and the popular Georgi-Jarlskog relation $m_{\mu}=3m_{s}$ as well as a new mass relation $m_{e}=\frac{8}{27}m_{d}$ in which the novel Clebsch-Gordan (CG) factor arises from the adjoint field $H_{24}$. The GUT relation leads to a sizable mixing angle $\theta^{e}_{12} \sim \theta_{c}$ and the correct quark mixing matrix $V_{CKM}$ can also be realised in the model. The resulting CKM-like mixing matrix of charged leptons modifies the vanishing $\theta^{\nu}_{13}$ in TBM mixing to a large $\theta^{PMNS}_{13}\simeq\theta_{c}/\sqrt{2}$, in excellent agreement with experimental results. A Dirac CP violation phase $\phi_{12}\simeq\pm\pi/2$ is required to make the deviation from $\theta^{\nu}_{12}$ small. We also present some phenomenological numerical results predicted by the model.

The role of flavon cross couplings in leptonic flavour mixing

In models with discrete flavour symmetries, flavons are critical to realise specific flavour structures. Leptonic flavour mixing originates from the misalignment of flavon vacuum expectation values which respect different residual symmetries in the charged lepton and neutrino sectors. Flavon cross couplings are usually forbidden, in order to protect these symmetries. Contrary to this approach, we show that cross couplings can play a key role and give raise to necessary corrections to flavour-mixing patterns, including a non-zero value for the reactor angle and CP violation. For definiteness, we present two models based on $A_4$. In the first model, all flavons are assumed to be real or pseudo-real, with 7 real degrees of freedom in the flavon sector in total. A sizable reactor angle associated with nearly maximal CP violation is achieved, and, as both originate from the same cross coupling, a sum rule results with a precise prediction for the value of the Dirac CP-violating phase. In the second model, the flavons are taken to be complex scalars, which can be connected with supersymmetric models and multi-Higgs models. The complexity properties of flavons provide new sources for generating the reactor angle. Models in this new approach introduce very few degrees of freedom beyond the Standard Model and can be more economical than those in the framework of extra dimension or supersymmetry.

The leptonic Dirac CP-violating phase from sum rules

In the reference 3-neutrino mixing scheme with three light massive neutrinos, CP-violating effects in neutrino oscillations can be caused by the Dirac CP-violating phase δ present in the unitary neutrino mixing matrix U. Using the fact that U = U†eUv, where Ue and Uv are unitary matrices arising from the diagonalisation, respectively, of the charged lepton and neutrino mass matrices, we consider in a systematic way forms of Ue and Uv allowing us to express δ as a function of the neutrino mixing angles present in U and the angles contained in Uv. After obtaining sum rules for cos δ, we consider several forms of Uv dictated by, or associated with, symmetries, such as tri-bimaximal, bimaximal, etc., for which the angles in Uv are fixed. For each of these forms and forms of Ue allowing to reproduce the measured values of the neutrino mixing angles, we construct the likelihood function for cos δ, using the prospective uncertainties in the determination of the mixing angles. Our results show that the measurement of δ along with improvement of the precision on the neutrino mixing angles can provide unique information about the possible existence of a new fundamental symmetry in the lepton sector.

Theory prospective on leptonic CP violation

The phenomenology of 3-neutrino mixing, the current status of our knowledge about the 3-neutrino mixing parameters, including the absolute neutrino mass scale, and of the Dirac and Majorana CP violation in the lepton sector are reviewed. The problems of CP violation in neutrino oscillations and of determining the nature – Dirac or Majorana – of massive neutrinos are discussed. The seesaw mechanism of neutrino mass generation and the related leptogenesis scenario of generation of the baryon asymmetry of the Universe are considered. The results showing that the CP violation necessary for the generation of the baryon asymmetry of the Universe in leptogenesis can be due exclusively to the Dirac and/or Majorana CP-violating phase(s) in the neutrino mixing matrix U are briefly reviewed. The discrete symmetry approach to understanding the observed pattern of neutrino mixing and the related predictions for the leptonic Dirac CP violation are also reviewed.

Warped flavor symmetry predictions for neutrino physics

A realistic five-dimensional warped scenario with all standard model fields propagating in the bulk is proposed. Mass hierarchies would in principle be accounted for by judicious choices of the bulk mass parameters, while fermion mixing angles are restricted by a $\Delta(27)$ flavor symmetry broken on the branes by flavon fields. The latter gives stringent predictions for the neutrino mixing parameters, and the Dirac CP violation phase, all described in terms of only two independent parameters at leading order. The scheme also gives an adequate CKM fit and should be testable within upcoming oscillation experiments.

Non-Standard Neutrino Interactions in T2K and Daya Bay

We show that the relatively large best fit value of sin2⁡2θ13=0.14(0.17) measured in the T2K experiment for fixed values of i) the Dirac CP violation phase δ=0, and ii) the atmospheric neutrino mixing parameters θ23=π/4, |Δm322|=2.4×10−3 eV2, can be reconciled with the Daya Bay result sin2⁡2θ13=0.090±0.009 if the effects of non-standard neutrino interactions (NSI) in the relevant ν‾e→ν‾e and νμ→νe oscillation probabilities are taken into account.

ESSnuSB: a Project for Leptonic CP Violation Discovery based on the European Spallation Source Linac

Very intense neutrino beams and large neutrino detectors will be needed in order to discover of CP violation in the leptonic sector. The proton driver of the European Spallation Source (ESS) currently under construction in Lund, Sweden, could provide, in parallel with the spallation neutron production, a very intense, cost effective and high performance neutrino beam. The ESS linac will be fully operational at 5 MW average power by 2022. The proposal presented here is to upgrade the linac to give another 5 MW to produce neutrinos i.e. 10 MW average power, in total. The high current required in the pulsed neutrino horn, requires proton pulses compressed from 2.86 ms to a few μs in an accumulator ring. A long baseline experiment using this Super Beam and a megaton underground Water Cherenkov detector located in existing mines 300–600 km from Lund, will enable precision measurements at the second νμ→νe neutrino oscillation maximum and thereby discover leptonic CP violation at 5 σ significance level in more than 50% of the leptonic Dirac CP-violating phase range. The detector would also be used to measure the proton lifetime, detect cosmological neutrinos and neutrinos from supernova explosions. The presentation will describe the proposed facility and the physics possible with this experiment.

Neutrino mixing with nonzero θ13 and CP violation in the 3-3-1 model based on A4 flavor symmetry

We propose a 3-3-1 model with neutral fermions based on [Formula: see text] flavor symmetry responsible for fermion masses and mixings with nonzero [Formula: see text]. To get realistic neutrino mixing, we just add a new [Formula: see text] triplet being in [Formula: see text] under [Formula: see text]. The neutrinos get small masses from two [Formula: see text] antisextets and one [Formula: see text] triplet. The model can fit the present data on neutrino masses and mixing as well as the effective mass governing neutrinoless double beta decay. Our results show that the neutrino masses are naturally small and a little deviation from the tri-bimaximal neutrino mixing form can be realized. The Dirac CP violation phase [Formula: see text] is predicted to either [Formula: see text] or [Formula: see text] with [Formula: see text].

Predictions for the leptonic Dirac CP violation phase: a systematic phenomenological analysis.

We derive predictions for the Dirac phase delta present in the 3times 3 unitary neutrino mixing matrix U = U_e^{dagger } , U_{nu }, where U_e and U_{nu } are 3times 3 unitary matrices which arise from the diagonalisation, respectively, of the charged lepton and the neutrino mass matrices. We consider forms of U_e and U_{nu } allowing us to express delta as a function of three neutrino mixing angles, present in U, and the angles contained in U_{nu }. We consider several forms of U_{nu } determined by, or associated with, symmetries, tri-bimaximal, bimaximal, etc., for which the angles in U_{nu } are fixed. For each of these forms and forms of U_e allowing one to reproduce the measured values of the neutrino mixing angles, we construct the likelihood function for cos delta , using (i) the latest results of the global fit analysis of neutrino oscillation data, and (ii) the prospective sensitivities on the neutrino mixing angles. Our results, in particular, confirm the conclusion, reached in earlier similar studies, that the measurement of the Dirac phase in the neutrino mixing matrix, together with an improvement of the precision on the mixing angles, can provide unique information as regards the possible existence of symmetry in the lepton sector.

Neutrino mixing with nonzero θ13 and CP violation in the 3-3-1 model based on S4 flavor symmetry

The 3-3-1 model proposed in 2011 based on discrete symmetry [Formula: see text] responsible for the neutrino and quark masses is updated, in which the nonzero [Formula: see text] is focused. Neutrino masses and mixings are consistent with the most recent data on neutrino oscillations without perturbation. The new feature is adding a new [Formula: see text] anti-sextet lying in doublet under [Formula: see text] which can result the nonzero [Formula: see text] without perturbation, and consequently, the number of Higgs multiplets required is less than those of other models based on non-Abelian discrete symmetries and the 3-3-1 models. The exact tribimaximal form obtained with the breaking [Formula: see text] in charged lepton sector and [Formula: see text] in neutrino sector. If both breakings [Formula: see text] and [Formula: see text] are taken place in neutrino sector, the realistic neutrino spectrum is obtained without perturbation. The upper bound on neutrino mass and the effective mass governing neutrinoless double beta decay at the tree level are presented. The model predicts the Dirac CP violation phase [Formula: see text] in the normal spectrum (with [Formula: see text]) and [Formula: see text] in the inverted spectrum.

Predictions for the Dirac CP violation phase in the neutrino mixing matrix

Using the fact that the neutrino mixing matrix [Formula: see text], where Ue and Uν result from the diagonalization of the charged lepton and neutrino mass matrices, we analyze the predictions based on the sum rules which the Dirac phase δ present in U satisfies when Uν has a form dictated by, or associated with, discrete flavor symmetries and Ue has a "minimal" form (in terms of angles and phases it contains) that can provide the requisite corrections to Uν, so that the reactor, atmospheric and solar neutrino mixing angles θ13, θ23 and θ12 have values compatible with the current data.