Predictions for the Dirac CP Violation Phase in the Neutrino Mixing Matrix
I. Girardi, S. T. Petcov, A. V. Titov
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10 pages, 3 figures, one table; to be published in the Proceedings of the International Conference on Massive Neutrinos, Nanyang Technological University, Singapore, 9-13 February, 2015
Using the fact that the neutrino mixing matrix $U = U^\dagger_{e}U_ν$, where $U_{e}$ and $U_ν$ result from the diagonalisation of the charged lepton and neutrino mass matrices, we analyse the predictions based on the sum rules which the Dirac phase $δ$ present in $U$ satisfies when $U_ν$ has a form dictated by, or associated with, discrete flavour symmetries and $U_e$ has a "minimal" form (in terms of angles and phases it contains) that can provide the requisite corrections to $U_ν$, so that the reactor, atmospheric and solar neutrino mixing angles $θ_{13}$, $θ_{23}$ and $θ_{12}$ have values compatible with the current data.
Non-zero leptonic CP phases in the neutrino sector are clear evidence for physics beyond the Standard Model and have many implications in particle physics and cosmology. Some clues to maximal Dirac CP violation $δ_{CP}=3π/2$ are reviewed. An approach to connect the Dirac CP violation phase and the neutrino mass hierarchy in terms of the measurement of CP asymmetry is proposed. Under appropriate requirements for baseline distance and beam energy, the problem of neutrino mass hierarchy can be revealed at maximal Dirac CP violation. General allowed parameter spaces are investigated, within which …
The seesaw mechanism explains the exclusive smallness of neutrino masses by the presence of very heavy Majorana masses and leads to the appearance of Majorana particles and to the direct lepton number violation. The author proposes a seesaw scenario that produces only Dirac neutrinos with the same violation. This scenario appears possible for heavy neutrinos with non-perturbative Higgs boson H couplings. Such a scenario could be accomplished in the model describing the structure of weak mixing matrices for quarks and leptons through the existence of very heavy mirror analogs of Standard Model …
If neutrinos are Dirac, the conditions for cobimaximal mixing, i.e. $θ_{23}=π/4$ and $δ_{CP}=\pm π/2$ in the $3 \times 3$ neutrino mixing matrix, are derived. One example with $A_4$ symmetry and radiative Dirac neutrino masses is presented.
In this review, the $X^{0}-\bar{X}^{0}$\ mixing ($% X^{0}=B^{0},B_{s}^{0},K^{0}$) and its implication for CP\ violation in the standard model are discussed. Both direct and mixing induced CP\ violation for $K^{0}(\bar{K}^{0})$, $B^{0}(\bar{B}^{0})$\ and $B_{s}^{0}(% \bar{B}_{s}^{0})$\ are reviewed.
Predictive spontaneous CP violation is possible if it is obtained geometrically through a non-Abelian discrete symmetry. I propose such a model of neutrino mass and mixing based on Delta(27).
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Dirac leptogenesis (or Dirac neutrinogenesis), in which neutrinos are purely Dirac particles, is an interesting alternative to the standard leptogenesis scenario. In its supersymmetric version, the modified form of the superpotential required for successful baryogenesis contributes new, generically non-flavor-diagonal terms to the slepton and sneutrino mass matrices. In this work, we examine how current experimental bounds on flavor-changing effects in the lepton sector (and particularly the bound on Mu -> e Gamma) constrain Dirac leptogenesis and we find that it is capable of succeeding with …
Recent developments for mixing and CP violation in the D0 and Bs systems are reviewed, including (i) the recently emerging evidence for D0-D0bar mixing and the interpretations of the measurements; (ii) the theoretical status of the calculations of Delta(Gamma_D) and Delta(m_D); (iii) some implications of the measurement of Bs mixing for new physics.
Suppose the geometrical explaination to the weak CP phase in quark sector is also valid for neutrinos, the mixing and CP violation in neutrino system are discussed. We find a larger $J_{CP}$ than $3\times 10^{-3}$ implys the large-mixing solution for solar neutrino problem. In case of bi-maximal mixing, we predict relative large CP violation with $J_{CP}$ larger than $10^{-3}$ in neutrino system, except the third mixing angle approachs to 0 or $π/2$ very closely.
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Flavor mixing and the quark mass spectrum are intimately related. In view of the observed strong hierarchy of the quark and lepton masses and of the flavor mixing angles it is argued that the description of flavor mixing must take this into account. One particular interesting way to describe the flavor mixing emerges, which is particularly suited for models of quark mass matrices based on flavor symmetries. We conclude that the unitarity triangle important for $B$ physics should be close to or identical to a rectangular triangle. $CP$ violation is maximal in this sense.
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We propose a democratic-type neutrino mass matrix based on $Z_3$ symmetry. This mass matrix predicts the CP violation phase, $δ=π/2$, and the mixing angle between the mass eigenstates $ν_2$ and $ν_3$, $\sin^2 θ_{23}= \cos^2 θ_{23}=1/2$ which is essential for the large atmospheric neutrino mixing, between $ν_μ$ and $ν_τ$. In this model, the large CP violation effect may be expected.
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We discuss unstable particle mixing in CP-violating weak decays. It is shown that for a completely degenerate system unstable particle mixing does not introduce a CP-violating partial rate difference, and that when the mixings are small only the off-diagonal mixings are relevant. Also, in the absence of mixing, unstable particle wave function renormalization does not introduce any additional effect. An illustrative example is given to heavy scalar decays with arbitrary mixing.
The phenomenology of flavor mixing of heavy Majorana neutrinos is studied. The physical degrees of freedom, which propagate like free particles until they decay in the presence of flavor mixing, are identified by diagonalizing the resummed propagator. It is shown that they should be interpreted as quasiparticles which lose Majorana nature.
The CP violation required in leptogenesis may have different origin, but in an effective theory they all are related to the rephasing invariant CP violating measure in the mixing matrix of the leptonic sector. We point out that the maximum amount of CP violation in some models can be estimated with our present knowledge of the neutrino mixing angles, which can help us understand the CP violation in the generation of the lepton asymmetry of the universe. For example, the possibility of leptogenesis may be ruled out in some models from an knowledge of the effective neutrino mass matrix.
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Following the anomalous like-sign dimuon charge asymmetry measured by the D0 collaboration at the Tevatron collider we discuss the implications of large CP violation in $B_{d,s}$ mixing for Supersymmetric (SUSY) Standard Models, focussing on those models which allow a family symmetry and unification. For the Minimal Supersymmetric Standard Model (MSSM) we show that it is only possible to account for $B_{s}$ mixing and CP violation at the expense of large squark mixing which would require a new approach to family symmetry models. In order to describe both $B_{s}$ and $B_{d}$ mixing and CP viola…
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If massive neutrinos are Majorana particles, then the lepton number should be violated and neutrino-antineutrino oscillations will take place. In this talk, we present the properties of CP violation in neutrino-antineutrino oscillations with a non-unitary leptonic flavor mixing matrix, which naturally arises in the type-I seesaw model due to the mixing between light and heavy Majorana neutrinos. Taking into account current experimental bounds on the leptonic unitarity violation, we show that the CP asymmetries induced by the non-unitary mixing parameters can significantly deviate from those in…
Implications of recently measured leptonic mixing angle $θ_{13}$ as well as the other two mixing angles have been examined for Fritzsch-like mass matrices with minimal texture for Dirac neutrinos. Interestingly, the existing data seems to rule out this texture specific case of Dirac neutrinos for normal, inverted hierarchy as well as degenerate scenario of masses.
We study effects of CP violation in a modified bipair neutrino mixing scheme predicting $\sin^2θ_{23}$ near both 0.4 and 0.6 currently consistent with experimentally allowed values. The source of CP violation is supplied by charged lepton mixing accompanied by a single phase, whose mixing size is assumed to be less than that of the Wolfenstein parameter for the quark mixing. Including results of leptogenesis, which is based on the minimal seesaw model, we obtain the allowed region of CP-violating Dirac and Majorana phases, which provides the observed baryon asymmetry of the universe in the cas…
We construct for the first time a flavor model, based on the smallest discrete symmetry Delta(27) that implements spontaneous CP violation with a complex phase of geometric origin, which can actually reproduce all quark masses and mixing data. We show that its scalar sector has exotic properties that can be tested at the LHC.
The motivation most often cited in searches for D0-anti-D0 mixing and CP-violation in charm system lies with the possibility of observing a signal from new physics which dominates that from the Standard Model. We review recent theoretical predictions and experimental constraints on D0-anti-D0 mixing parameters. We also discuss the current status of searches for CP-violation in charmed meson transitions, as well as some recent theoretical ideas.
We examine certain extensions of the standard model in which $CP$ violation is spontaneous and the strong $CP$ problem is resolved. In these models, the $3 \times 3$ quark mixing matrix is neither real nor unitary. However, to a precision of 0.1%, it is real and orthogonal. There are no readily observable $CP$-violating effects besides those in the neutral kaon system.
Both BaBar and Belle have found evidence for a non-zero width difference in the $D^0$-$\bar D^0$ system. Although there is no direct experimental evidence for CP-violation in $D$ mixing (yet), we show that the measured values of the width difference $y\sim ΔΓ$ already imply constraints on the CP-violating phase in $D$ mixing, which, if significantly different from zero, would be an unambiguous signal of new physics.
The exponential parameterization of Pontecorvo-Maki-Nakagawa-Sakata mixing matrix for neutrino is used for comparative analysis of different neutrino mixing data. The UPMNS matrix is considered as the element of the SU(3) group and the second order matrix polynomial is constructed for it. The inverse problem of constructing the logarithm of the mixing matrix is addressed. In this way the standard parameterization is related to the exponential parameterization exactly. The exponential form allows easy factorization and separate analysis of the rotation and the CP violation. With the most recent…
The 2-neutrino exchange potential is a Standard Model weak potential arising from the exchange of virtual neutrino-antineutrino pairs which must include all neutrino properties, including the number of flavors, their masses, fermionic nature (Dirac or Majorana), and CP violation. We describe a new approach for calculating the spin-independent 2-neutrino exchange potential, including the mixing of three neutrino mass states and CP violation.
The Standard Model predictions for $D^0$-$\bar{D}^0$ mixing and CP violation in $D$ decays are revised. The emphasis is put on obtaining the order of magnitude of the effects. In the case of mixing, the different approaches to the long distance contributions are carefully discussed. The size of CP asymmetries is discussed in general and some specific calculations are reviewed. The possibility of using kinematic signals is briefly described.}}
A large number of observables can be constructed from differential decay rate based on the polarization of final state while considering decay of a neutral meson $(P^0 \text{ or } \bar P^0)$ to two vector particles. But all of these observables are not independent to each other since there are only a few independent theoretical parameters controlling the whole dynamics and therefore various relations among observables emerge. In this paper, we have studied the behaviour of observables for neutral meson decaying to two vectors in presence of T and CPT violations in mixing accompanied by both di…
Brief overview of the present status on mixing and CP violation in kaons and B mesons is given by means of the unitarity triangle. Theoretical predictions on epsilon'/epsilon are confronted with experimental results. The prospects of detecting CP violation at high-energy p pbar, p p, e- e+ and mu- mu+ colliders are discussed in resonant scatterings involving top quarks and/or heavy scalars. The relevance of the latter for baryogenesis is briefly outlined.
We perform a general analytic study of feasibility of obtaining a combined explanation for the deficits in the solar and the atmospheric neutrino fluxes with two large mixing angles in supersymmetric model with bilinear R parity violations. The required hierarchy among the solar and atmospheric neutrino mass scales follows in this framework in the presence of an approximate Higgs - slepton universality at the weak scale. The solar mixing angle is shown to be related to non-universality in slepton mass terms specifically to differences in soft parameters of the first two leptonic generations. I…
The Daya Bay Collaboration has recently reported the precise measurement of $θ_{13}\simeq 8.8^\circ \pm 0.8^\circ $ or $θ_{13} \neq 0$ at 5.2 σlevel. The observed non-zero $θ_{13}$ can be accommodated by some general modifications to the Democratic mixing matrix. Using such matrices we study the possibility of observing non-zero CP violation in the leptonic sector.
The observed hierarchy of the quark masses is interpreted as a signal for an underlying ``subnuclear democracy'' as the relevant symmetry of the quark mass terms. A simple breaking of the symmetry leads to a mixing between the second and the third family, in agreement with observation. Introducing the mixing between the first and the second family, one finds an interesting pattern of maximal CP--violation as well as a complete determination of the elements of the CKM matrix and of the unitarity triangle.
We propose a scheme of lepton mixing in which the unitary matrix that diagonalizes the neutrino mass matrix is bimaximal and the deviation from bimaximal of the lepton mixing matrix is due to the unitary matrix that diagonalizes the charged-lepton mass matrix. This matrix is assumed to be hierarchical, like the quark mixing matrix. It is shown that in general it is possible to have a sizable value for |U_{e3}| together with an effective two-neutrino maximal mixing in solar neutrino experiments. If the effective mixing in solar neutrino experiments is less than maximal, as indicated by current …
When a neutral meson $(P^0 \text{ or } \bar P^0)$ decays to two vector particles, a large number of observables can be constructed from differential decay rate based on the polarization of final state. But, theoretically, all of them are not independent to each other and hence, some relations among observables emerge. These relations have been well studied in the scenario with no $T$ and $CPT$ violation in neutral meson mixing and no direct $CP$ violation as well. In this paper, we have studied the relations among observables in the presence of $T$, $CP$ and $CPT$ violating effects in mixing o…
We review the historical developments leading to the Cabibbo-Kobayashi-Maskawa (CKM) quark mixing matrix. Present status of the CKM matrix from direct measurements is summarized, giving also the present profile of the unitarity triangle. CP Violation in the $K^0$ - $\bar{K^0}$ complex and in $B$-meson decays are discussed in the context of the CKM matrix.
We discuss the implications of CP violation as well as final state interaction phases in the experimental search for $D^0-\bar{D}^0$ mixing. At the present level of sensitivity, these are not yet a significant systematic experimental limitation.
Maximal CP violation hypothesis is applied to a simple lepton mixing matrix form U=V_{CKM}^\dagger U_{TB}, which has recently been speculated under an ansatz that U becomes an exact tribimaximal mixing U_{TB} in a limit of the quark mixing matrix V_{CKM} \to {\bf 1}. The prediction \tan^2 θ_{12} =1/2 in the case of the exact tribimaximal mixing U=U_{TB} is onsiderably spoiled in the speculated mixing U=V_{CKM}^\dagger U_{TB}. However, the application of the hypothesis to the lepton sector can again recover the spoiled value to \tan^2 θ_{12} \simeq 1/2 if the original Kobayashi-Maskawa phase co…
We present a systematic approach to solve analytically for the right-handed quark mixings in the minimal left-right symmetric model which generally has both explicit and spontaneous CP violations. The leading-order result has the same hierarchical structure as the left-handed CKM mixing, but with additional CP phases originating from a spontaneous CP-violating phase in the Higgs vev. We explore the phenomenology entailed by the new right-handed mixing matrix, particularly the bounds on the mass of $W_R$ and the CP phase of the Higgs vev.
We show that in a recently proposed $S_3$ model for tri-bimaximal mixing pattern for neutrinos, CP violating phases in neutrino mixings are directly responsible for lepton asymmetry $ε_\ell$. In the exact tri-bimaximal limit, $ε_\ell$ is proportional to one of the Majorana phases whereas in the presence of small deviations from tri-bimaximal pattern, there are two contributions, one being proportional to the Dirac phase and the other to one of the two Majorana phases. In the second case, $θ_{13}$ is nonzero and correlated with the deviation from maximal atmospheric mixing.
The connection between B_s mixing phase and lepton flavor violation is studied in SU(5) GUT. The O(1) phase, preferring a non-vanishing squark mixing, generically implies tau -> (e + mu) gamma and mu -> e gamma. In addition to the facts already well-known, stresses are put on the role of gaugino to scalar mass ratio at the GUT scale and the possible modifications due to Planck-suppressed non-renormalizable operators.
The measurement of the charged-current 8B solar neutrino reaction on deuterium at the Sudbury Neutrino Observatory confirms the neutrino oscillation hypothesis for the solar neutrino problem, and the result favours the solution with large neutrino mixing angles. We demonstrate that the current neutrino oscillation data (including atmospheric and reactor neutrinos) are sufficient to construct the lepton flavour mixing matrix with a reasonable accuracy. We also infer the maximum size of CP violation effects consistent with the current neutrino oscillation experiments.
Neutral meson mixing and $CP$ violation are very well known weak processes that involve decays to meson states that are, in general, a superposition of flavor eigenstates. This paper describes a mathematical interpretation of the time-dependent mixing amplitudes as a complex hyperbolic rotation of the time evolution of those amplitudes without mixing, which involves a Lie group $SO(1,1,\mathbb{C})$. This allows a geometric interpretation of mixing as a curve into the $SO(1,1,\mathbb{C})$ manifold, parameterized with the proper decay time, where $CP$ violation is the image of this curve at $t =…
I begin by commenting on the most recent experimental compilation of D^0 mixing data, emphasizing the so-called 'strong phase' issue. This is followed by a review of the theory underlying charm mixing, both Standard Model and New Physics. The mechanism of R_p-violation is used to illustrate the methodology for New Physics contributions and the relation of this to rare D^0 decays is pointed out. Finally, I address the subject of CP-violating asymmetries by describing some suggestions for future experimental studies and a recent theoretical analysis of New Physics contributions.
