Explicit seesaw with nearly bimaximal neutrino mixing and no LSND effect

An explicit model of neutrino texture is presented, where in the 6 times 6 mass matrix the Majorana lefthanded component is zero, the Majorana righthanded component - diagonal with equal entries, and the Dirac component gets a hierarchical structure, deformed by nearly bimaximal mixing. If the Majorana righthanded component dominates over the Dirac component, the familiar seesaw mechanism leads effectively to the popular, nearly bimaximal oscillations of active neutrinos. The Dirac component, before its deformation, may be similar in shape to the charged-lepton and quark mass matrices. Then, parameters for solar and atmospheric neutrinos may be related to each other, predicting from the SuperKamiokande value of Delta m_{32}^2 a tiny Delta m_{21}^2, typical for MSW LOW solar solution (rather than for MSW Large Mixing Angle solution).Comment: Some improvements introduce

A satisfactory empirical mass sum rule for charged leptons

In the framework of a mass formula proposed previously (transforming in a specific way three free parameters into three masses), a simple empirical sum rule for three charged-lepton masses is found, predicting m_\tau = 1776.9926 MeV, when the experimental values of m_e and m_\mu are used as an input. The experimental value to be compared with is m_\tau = 1776.99^{+0.29}_{-0.26} MeV. This satisfactory sum rule (equivalent to a simple parameter constraint in the mass formula) is linear in masses and involves integers as its coefficients. The author believes that such a simple and precise mass sum rule for charged leptons may help in the process of developing realistic models for mass spectra of fundamental fermions. In the second part of the paper, another equivalent parametrization of the charged-lepton mass formula is described, corresponding to an oscillatory picture of their mass matrix, where two matrices appear playing the role of annihilation and creation operators in the generation space.Comment: 11 page

Option of three pseudo--Dirac neutrinos

As an alternative for popular see-saw mechanism, the option of three pseudo% -Dirac neutrinos is discussed, where ${1/2}(m^{(L)} + m^{(R)}) \ll m^{(D)}$ for their Majorana and Dirac masses. The actual neutrino mass matrix is assumed in the form of tensor product M^{(\nu)} \otimes {(\{array} {cc} \lambda^{(L)} & 1 1 & \lambda^{(R)} \{array})}, where $M^{(\nu)}$ is a neutrino family mass matrix ($M^{(\nu) \dagger} = M^{(\nu)}$) and $\lambda^{(L,R)} \equiv m^{(L,R)}/m^{(D)}$ with $m^{(L)}$, $m^{(R)}$ and $m^{(D)}$ being taken as universal for three neutrino families. It is shown that three neutrino effects (deficits of solar $\nu_e$'s and atmospheric $\nu_\mu$'s as well as the possible LSND excess of $\nu_e$'s in accelerator $\nu_\mu$ beam) can be nicely described by the corresponding neutrino oscillations, though the LSND effect may, alternatively, be eliminated (by a parameter choice). Atmospheric $\nu_\mu$'s oscillate dominantly into $\nu_\tau$'s, while solar $\nu_e$'s - into (existing here automatically) Majorana sterile counterparts of $\nu_e$'s. A phenomenological texture for neutrinos, compatible with the proposed description, is briefly presented.Comment: LaTeX, 10 page

The four-group Z_2 x Z_2 as a discrete invariance group of effective neutrino mass matrix

Two sets of four 3x3 matrices 1^(3), varphi_1, varphi_2, varphi_3 and 1^(3), mu_1, mu_2, mu_3 are constructed, forming two unitarily isomorphic reducible representations 3 of the group Z_2 x Z_2 called often the four-group. They are related to each other through the effective neutrino mixing matrix U with s_{13} = 0, and generate four discrete transformations of flavor and mass active neutrinos, respectively. If and only if s_{13} = 0, the generic form of effective neutrino mass matrix M becomes invariant under the subgroup Z_2 of Z_2 x Z_2 represented by the matrices 1^(3) and varphi_3. In the approximation of m_1 = m_2, the matrix M becomes invariant under the whole Z_2 x Z_2 represented by the matrices 1^(3), varphi_1, varphi_2, varphi_3. The effective neutrino mixing matrix U with s_{13} = 0 is always invariant under the whole Z_2 x Z_2 represented in two ways, by the matrices 1^(3), varphi_1, varphi_2, varphi_3 and 1^(3), mu_1, mu_2, mu_3.Comment: LaTeX, 1+10 pages. The term "irreducible" applied to the considered doublet representations of the four-group is replaced by the correct term "not reduced

Photonic portal to hidden sector and a parity-preserving option

In the case of previously proposed idea of photonic portal to hidden sector, the parity in this sector may be violated. We discuss here two new options within our model, where the parity is preserved. The first of them is not satisfactory, as not diplaying a full relativistic covariance. The second seems to be satisfactory.Comment: 9 page

Constructing the off-diagonal part of active-neutrino mass matrix from annihilation and creation matrices in neutrino-generation space

The off-diagonal part of the active-neutrino mass matrix is constructed from two $3\times 3$ matrices playing the role of annihilation and creation matrices acting in the neutrino-generation space of $\nu_e, \nu_\mu, \nu_\tau$. The construction leads to a new relation, $M_{\mu \tau} = 4\sqrt{3} M_{e \mu}$, which predicts in the case of tribimaximal neutrino mixing that $m_3 - m_1 = \eta (m_2 - m_1)$ with $\eta = 5.28547$. Then, the maximal possible value of ${\Delta m^2_{32}}/{\Delta m^2_{21}}$ is equal to $\eta^2 -1 = 26.9362$ and gives $m_1 = 0$. With the experimental estimate ${\Delta m^2_{21}}\sim 8.0\times 10^{-5} {\rm eV}^2$, this maximal value, if realized, predicts $\Delta m^2_{32} \sim 2.2\times 10^{-3} {\rm eV}^2$, near to the popular experimental estimation $\Delta m^2_{32} \sim 2.4\times 10^{-3} {\rm eV}^2$.Comment: 9 page

Oscillations of the mixed pseudo--Dirac neutrinos

Oscillations of three pseudo--Dirac flavor neutrinos $\nu_e, \nu_\mu, \nu_\tau$ are considered: $0 < m^{(L)} = m^{(R)} \ll m^{(D)}$ for their Majorana and Dirac masses taken as universal before family mixing. The actual neutrino mass matrix is assumed to be the tensor product $M^{(\nu)} \otimes {(\begin{array}{cc} \lambda^{(L)} & 1 1 & \lambda^{(R)} \end{array})}$, where $M^{(\nu)}$ is a neutrino family mass matrix ($M^{(\nu) \dagger} = M^{(\nu)}$) and $\lambda^{(L,R)} = m^{(L,R)}/m^{(D)}$. The $M^{(\nu)}$ is tried in a form proposed previously for charged leptons $e, \mu, \tau$ for which it gives $m_\tau = 1776.80$ MeV versus $m^{exp}_\tau = 1777.05^{+0.29}_{-0.20}$ MeV (with the experimental values of $m_e$ and $m_\mu$ used as inputs). However, in contrast to the charged -lepton case, in the neutrino case its off-diagonal entries dominate over diagonal. Then, it is shown that three neutrino effects (the deficits of solar $\nu_e$'s and atmospheric $\nu_\mu$'s as well as the possible LSND excess of $\nu_e$'s in accelerator $\nu_\mu$ beam) can be explained by neutrino oscillations though, alternatively, the LSND effect may be eliminated (by a parameter choice). Atmospheric $\nu_\mu$'s oscillate dominantly into $\nu_\tau$'s, while solar $\nu_e$'s -- into (automatically existing) Majorana sterile counterparts of $\nu_e$'s.Comment: 1+13 pages (LaTeX

Explicit lepton texture

An explicit form of charged--lepton mass matrix, predicting $m_\tau = 1776.80$~MeV from the experimental values of $m_e$ and $m_\mu$ (in good agreement with the experimental figure $m_\tau = 1777.05^{+0.29}_{-0.26}$ MeV), is applied to three neutrinos $\nu_e$, $\nu_\mu$, $\nu_\tau$ in order to correlate tentatively their masses and mixing parameters. While for charged leptons the off--diagonal mass--matrix elements turn out to be small {\it versus} its diagonal elements, it is suggested that for neutrinos the situation is inverse. Under such a conjecture, the neutrino masses, lepton \CKM matrix and neutrino oscillation probabilities are calculated in the corresponding lowest (and the next to lowest) perturbative order. Then, the nearly maximal mixing of $\nu_\mu$ and $\nu_\tau$ is predicted in consistency with the observed deficit of atmospheric $\nu_\mu$'s. However, the predicted deficit of solar $\nu_e$'s is much too small to explain the observed effect, what suggests the existence of (at least) one sort, $\nu_s$, of sterile neutrinos, whose mixing with $\nu_e$ would be responsible for the observed deficit. In the last Section, promising perspectives for applying the same form of mass matrix to quarks are outlined. Two independent predictions of $|V_{ub}|/|V_{cb}| = 0.0753 \pm 0.0032$ and unitary angle $\gamma \simeq 70^\circ$ are deduced from the experimental values of $|V_{us}|$ and $|V_{cb}|$ (with the use of quark masses $m_s$, $m_c$ and $m_b$).Comment: Latex, 20 page

Overall empirical formula for mass spectra of leptons and quarks

We present an overall empirical formula that, after specification of its free parameters, describes precisely the mass spectrum of charged leptons and is suggested to reproduce correctly also the mass spectra of neutrinos and up and down quarks (together, twelve masses with eight free parameters are presented). Then, it predicts m_tau = 1776.80 MeV, m_{nu_1} -> 0 eV and m_d = 5.0 MeV, $m_s = 102 MeV, respectively, when the remaining lepton and quark masses, m_e, m_mu, Delta m^2_{21} = m^2_{nu_2}-m^2_{nu_1}, Delta m^2_{32} = m^2_{nu_3}-m^2_{nu_2} and m_u, m_c, m_t, m_b, are taken as an input.Comment: 7 page

Sterile neutrino creating a reduced LSND effect

Although the hypothetic sterile neutrino $\nu_s$ is probably not involved significantly in the deficits of solar $\nu_e$'s and atmospheric $\nu_\mu$'s, it may cause the possible LSND effect. In fact, we face such a situation, when the popular nearly bimaximal texture of active neutrinos $\nu_e$, $\nu_\mu$, $\nu_\tau$ is perturbed through a small rotation in the 14 plane, where $\nu_4$ is the extra neutrino mass state induced by the sterile neutrino $\nu_s$. Then, with $m^2_1\simeq m^2_2$ we predict in the simplest case of $s_{13}\to0$ that $\sin^22\theta_{\rm LSND}=s^4_{14}/2$ and $\Delta m^2_{\rm LSND} = |\Delta m^2_{41}|$. However, the negative CHOOZ experiment imposes on $s^4_{14}/2$ the upper bound $1.3\times10^{-3}$, suggesting a reduction of the amplitude of possible LSND effect.Comment: 8 pages, no figure