Semi-Empirical Neutrino and Quark Mixing Angle Broken 4-Color Geometric Symmetry

Two semi-empirical ideas are guiding the present research: 1) one neutrino and N color quark triple mixing angles have second physical meaning of vector direction angles in euclidean 3-space, and 2) the difference between neutrino and quark mixing in the SM weak interactions is mostly conditioned by known fundamental difference of these particles by numbers of color degree of freedom. As main physical inference, the elementary particle mixing angles obey a novel phenomenological quark-neutrino (N+1)-color and 3 mixing angle symmetric positive definite quadratic Pythagorean equation in terms of double mixing angles. This equation predicts immediately that two large solar and atmospheric angles must be accompanied by one small not zero theta-13 neutrino angle in convincing agreement with recent new theta-13 experimental data. Benchmark flavor mixing pattern - united bimaximal neutrino and zero quark ones - follows from solutions of the primary equation without free parameters. Agreement with known experimental data follows only when the number of quark colors is equal to the number of particle flavors, N = 3. Together with closely related to the fine structure constant one empirical small parameter, that benchmark pattern determines realistic quark and neutrino mixing angles in good agreement with data and especially accurate for quark Cabibbo and neutrino solar angles. Coming accurate neutrino mixing angle data are important for testing the Pythagorean equation.Comment: 12 page

Precise match for the new experimental fine structure constant value

In this note I point out a highly accurate relation - to within 0.2 ppb - between the recently discovered accurate experimental value of the fine structure constant (1/a)_exp =137.035999710(96) and the precise solution (1/a)= 137.035999737 of a nonlinear equation for the fine structure constant generated by the earlier suggested new universal flavor-electroweak phenomenological constant a_o = exp(-5) as a source and hints from the new experimental data. This perfect match for the experimental value (1/a)_exp lends additional support to the basic notion of a new universal physical constant a_o.Comment: 6 pages; comments on substance and references adde

Complementary Quark and Lepton Deviation from Mass-Degeneracy Hierarchies

Near magnitudes of Dirac particle mass-ratios, mixing hierarchy-quantities and electroweak charges against the background of highly successful flavor-universal one-generation EW theory is a puzzle in need of diverse inclusive research. In this paper I study the problem in proper terms of lepton and quark Deviation-from-Mass-Degeneracy (DMD) hierarchies at tree EW approximation. As primary are considered not discrete flavor symmetry but rather the deviations from mass-degeneracy-symmetry without inventing exact particular symmetry. Empirically suggested benchmark flavor patterns (zero approximation) and deviations from benchmarks caused by emergence of a small related to EW charges parameter are considered two sources of realistic flavor quantities. Physically interesting mass and mixing flavor quantities are obtained as solutions of linear and quadratic DMD-hierarchy equation-pairs with complementary patterns of quark and lepton DMD-hierarchies. Dual relations between DMD-quantities of quarks and charged leptons (Dirac particles), on the one hand, and neutrinos (likely Majorana particles), on the other hand, are inferences. Considered in the literature approximate quark-neutrino mixing angle complementarity appears naturally from the violation of benchmark patterns by the emergent small parameter.Comment: 21 pages. Some notations and quantitative estimations change

Small Q-D neutrino masses from a generic lepton mass hierarchy

Exponential lepton mass ratios are studied in a low energy phenomenology. In view of the known data, the mass patterns of the charged leptons and widely discussed quasi-degenerate neutrinos are related to one another by two different traits - opposite mass ratios with large versus small exponents, and probably conformable mass-degeneracy-deviation hierarchies. The solar-atmospheric hierarchy parameter should have a special physical meaning in the Q-D neutrino scenario. A general generic hierarchy equation with two opposite solutions respectively for the charged lepton and neutrino mass ratios is considered. It determines a small upper bound on the Q-D neutrino mass scale, with estimations: m = 0.30 eV at 90% C.L., and m = 0.18 eV at best-fit mass-squared differences.Comment: 8 pages, no figures. Revised version. Results unchange

Combined Quark-Lepton-Complementarity via United by One-Parameter Particle Mixing Angles

On the level of phenomenology unification-type idea of a basic connection between dimensionless mass and charge quantities requires particle mass copies and therefore is interesting as raison d'etre for particle flavor (degree of freedom). Particle mass ratios and mixing angles expressed in terms of related to the fine structure constant e-parameter are particular examples of mass-matrix -- charge unification. In this paper small violations of quark-lepton-complementarity (QLC) come from an accurate system of three quark mixing angles in terms of the e-parameter. Two patterns of small QLC-violations, 'combined' and 'universal', are considered. The first pattern predicts solar mixing angle {\theta}sol= 34.04o as ~7% violation of QLC, and atmospheric mixing angle {\theta}atm= 42.64o that is in agreement with QLC. The 'universal' pattern predicts the same magnitude of solar angle, while the atmospheric one violates QLC by ~1%, {\theta}atm= 43.0o. Quantitative tests of both QLC-violation patterns and choice between them can be made at accurate neutrino oscillation experiments.Comment: 5 pages, (B-L)-assertion excluded, title and abstract changed, results unchange

Advanced One-Parameter CKM Mixing Matrix and Universal Deviation from Exact Quark-Lepton Complementarity

In this paper, realistic CPT-symmetric united at substance quark and neutrino mixing matrices are studied by the idea that they are shifted from respectively unit and bimaximal benchmark matrices by one new small universal empirical e-parameter. At leading finite e-approximation quark-lepton complementarity (QLC) is an exact regularity. Equal solar and atmospheric deviations from exact QLC constitute one of the main inferences at next to leading approximation. That universal violation of exact QLC advances the status of the QLC idea; and the more so, as that deviation from QLC is quantitatively estimated and used for accurate calculations of lepton mixing angles. Quark and neutrino Dirac CP-violating phases are determined by the considered quadratic hierarchy paradigm in flavor phenomenology. Inferences are partly supported by quark heavy flavor unitarity triangle angles and testable at B-factory and LHC b experiments. Estimated magnitude of the unitarity triangle gamma-angle concurs with the quark CP-violating phase to within ~5x10-4. The final quark CKM mixing matrix in terms of the e-parameter is in excellent quantitative agreement with world data and suggests a fitting form of neutrino PMNS mixing matrix. The e-constant implications in flavor phenomenology are considered.Comment: 20 pages; e-constant implications in flavor phenomenology are considered in new Sec.

On lepton flavor mass-degeneracy-deviation hierarchies and QD-neutrino mass

Two guiding new phenomenological flavor and flavor-electroweak ideas are expounded in this paper: (I) Oppositeness relation between neutrino and Charged Lepton Mass-Degeneracy-Deviation quantities. With inputs from the mass and neutrino oscillation data, it enables two independent estimations of the neutrino masses m =(0.11-0.30)eV and m =(0.11-0.16) eV. Small value of the neutrino oscillation hierarchy parameter is a consistency condition. (II) Essential connection between lepton mass hierarchies and low energy electroweak coupling constants. It enables an independent estimation of the QD-neutrino mass m = (0.11-0.14) eV, and renders three sequential charged lepton copies into one flavor system with the elementary charge encoded in the three-flavor mass hierarchy. An exact relation between the fine structure constant at Q2=0 and the experimental charged lepton mass-ratio parameter exp(-5) is observed. Experimental evidence is suggesting that this parameter has physical meaning of a dimensionless universal parameter that links flavor and electroweak quantities in accord with the guiding idea (II).Comment: 29 pages, footnote corrected, some phrases correcte

Neutrino Flavor Tagging in a Four-Neutrino Mixing and Oscillation Model

A neutrino mass dominance quantity is introduced for tagging the neutrino flavor in the phenomenological two-parameter four neutrino mixing matrix with two neutrino mass doublets and thorough maximal neutrino doublet mixing. While there is no hierarchy of the neutrino masses in the neutrino flavor eigenstates of this model, it may rather be a special hierarchy of the mass dominance ratios in these eigenstates. A neutrino flavor hierarchy condition is suggested: a direct link between the neutrino flavor and the flavor of the charged leptons which interconnects the two mixing angles, theta and phi, via the charged lepton mass ratios, with the net result tg^2 phi = (tg^2 theta)^gamma, gamma ~ 2.06. It leads to distinct inferences testable at SNO and Super-K.Comment: 3 pages; A remark added on the meaning of the auxiliary neutrino fields in the limit of mass-degenerate neutrino doublet

Top-Quark Mass Data and the Sum of Quasi-Degenerate Neutrino Masses (One small electroweak-bound e-parameter organizes elementary particle 3-flavor phenomenology)

The absolute neutrino masses and type of neutrino mass hierarchy are among the main problems in neutrino physics. Top-quark mass is another topical problem in particle physics. These problems extend the old puzzle of electron-muon mass ratio close to the fine structure constant, which is still not solved by known theory. Here I continue the search for a general flavor pattern that may incorporate these problems. Relations between neutrino/electron and electron/top-quark pole mass ratios are obtained from supposition that realistic elementary particle dimensionless bare flavor quantities are small deviated (measured by universal parameter e) from the values of a stated flavor pattern (at e=0) and experimental data hints. With the world average t-quark mass data the sum of QD-neutrino masses is estimated (0.50 +- 0.003)eV in agreement with cosmological constraints and known QD-neutrino mass estimations from experimental data on neutrino oscillation mass-squared differences.Comment: 23 pages. Arguments for a deeper physical meaning of the neutrino oscillation solar-atmospheric hierarchy parameter are added to Sec.

Accurate Quark CKM Mixing Matrix in terms of one universal parameter

The quark Cabibbo-Kobayashi-Maskawa mixing matrix is a fundamental part of the Standard Model accurately determined to fit world data analysis. In this paper the CKM matrix elements are high accurately rendered via simple compact parameterization by one small dimensionless parameter. Unique value of the KM CP-violating phase -65.53 deg is derived in agreement with fitting the data Wolfenstein parameterization. With the three mixing angles and CP-violating phase quantitatively determined, the complete content of the CKM global fit in the SM is accurately reproduced within the small relative 1 S.D. ranges in the form of a united system. Parameterization of the neutrino Pontecorvo-Maki-Nakagava-Sakata mixing matrix by the same parameter in agreement with available data is related to the quark CKM one by the idea of quark-neutrino mixing angle complementarity extended to the relation between Dirac CP-violating phases.Comment: 10 pages. Title and text partially reorganized. Appendix adde