Theta_13 and Quark-Neutrino 4-Color Symmetry Violation behind Flavor Mixing

Transcription

1 1 Theta_13 and Quark-Neutrino 4-Color Symmetry Violation behind Flavor Mixing E. M. Lipmanov 40 Wallingford Road # 272, Brighton MA 02135, USA Abstract Guided by idea that the main cause of opposite mixing patterns of quarks and neutrinos in weak interactions of the SM is the fundamental difference of these particles by color degree of freedom, and stimulated by new T2K data on theta_13 angle, one primary quark-neutrino 4-color symmetric positive definite mixing angle equation is suggested in this paper. A minimal model of realistic particle mixing angles (free parameters in the SM) based on that equation and one small empirical universal epsilon-parameter is considered. Basic in the model benchmark particle flavor mixing pattern that includes two united bimaximal neutrino and zero quark patterns follows from the primary equation without free parameters by partial spontaneous violation of mixing-angle and quarkneutrino 4-color symmetry and hiding the quark primary color indexes in redefined mixing quantities. Realistic small, not zero, quark mixing angles and two large, not maximal, and one small, not zero, neutrino mixing angles are just a little deviated from the benchmark values by epsilon-parameterization. An interesting fundamental physics result of the studied model is equal 3 quark color and flavor numbers. It follows from the primary equation and empirical condition of respectively large and small neutrino and quark flavor mixing angles. 1. Introduction. Quark-neutrino 4-color symmetric mixing-angle equation Without well established flavor theory, new empirical quantitative quark and lepton flavor relations cannot be excluded and may be discovered, sometimes by serendipity. Semi-empirical flavor mixing phenomenology is a system of empirical regularities, and pertinent generalizations, between factual neutrino and quark flavor mixing quantities.

2 2 Though this approach is different from the ongoing major symmetry-quest for flavor theory, it is other fields of physics research that modestly follows the long time traditions of problem solving in frontier physics as experimental science. Flavor physics seems so fundamental and not complete that it reminds the early history of quantum mechanics 1. Considered in this paper semi-empirical phenomenology of the free in the SM particle mixing angles is based on a new physics positive-definite quadratic quark-neutrino (N+1)-color 3 mixing-angle symmetric equation without nontrivial parameters cos 2 2θ k 12 + cos 2 2θ k 23 + cos 2 2θ k 13 = 1, (1) and one small related to the fine structure constant parameter. Superscript index k in (1) is denoting (N+1) particle colors: the 1 is for neutrinos and 2 (N+1) are for N quark colors. It should be noticed, at least for mnemonic purposes that in respect to mixing angles Eq. (1) has geometric form for direction angles of a vector in a 3-dimensional euclidean space ([1], v2). The explicit symmetry of Eq. (1) is two-fold i) between mixing angles (symmetry under permutation of the three lower indexes 12, 23 and 13) and ii) between neutrino and N quark colors. It is a combined quark-neutrino color-flavor symmetry. There is only one solution of Eq. (1) that is universal and completely symmetric under permutation of lower mixing-angle indexes ij and upper neutrino and quark color indexes k, cos 2 2θ k i j = 1/3, θ k i j 27.4 o, ij = 12, 23, 13, k = 1... (N+1). (2) Solution (2) is determined only by the number of mixing angles 2 in (1), but is independent of the number N of quark colors. Well known experimental data on particle mixing angles [2] show that solution (2) is in sharp disagreement with both neutrino and quark mixing angles at low energies. Although (2) looks a nonphysical solution, it should be useful in the research 3 since it unites color quark and neutrino mixing angles and displays the full underlying symmetry of Eq. (1). The neutrino equation, k = 1, cos 2 2θ ν 12 + cos 2 2θ ν 23 + cos 2 2θ ν 13 = 1, (3) 1 Plank constant based semi-empirical phenomenology preceded the new paradigm of quantum theory by Heisenberg, Dirac, Schrödinger and Born. 2 The double angels of solution (2) are equal those of a diagonal in a cube. 3 See e. g. (8) and (20).

3 3 was proposed in [1] for semi-empirical explanation of new T2K data [3] on theta_13 angle by its relation to empirically known two large solar and atmospheric angles. Eq. (1) is factually a generalization of neutrino Eq. (3). In contrast to neutrinos, equation (1) for color quarks is definitely in strong disagreement with experimental data. This is considered an indication on violation of the quark-neutrino color symmetry and can be achieved by regrouping of quark color equations in (1) and redefinition of mixing angles to produce one color-symmetric quark mixing-angle equation. At N = 3, the result is given by cos 2 2θ q 12 + cos 2 2θ q 23 + cos 2 2θ q 13 = 3. (4) Quark colors are hidden in the color-symmetric quantities cos 2 (2θ q i j). Eq. (4) means zero quark mixing angles in reasonable approximate agreement with CKM data [2]. Generated by Eq. (1), equations (3) and (4) define the concept of benchmark particle mixing pattern without free parameters that include united bimaximal neutrino and zero quark mixing patterns. It is the benchmark which gives meaning to neutrino and quark realistic flavor mixing angles as deviations from primary basic level by emergence of one small, probably dynamical, universal empirical parameter. The united quark-neutrino benchmark mixing pattern is considered zero approximation of small empirical epsilon-parameter ε exp(-2.5). (5) This parameter is close (~ 4%) to the dimensionless-made elemental electric charge e = α (6) Both parameters (5) and (6) are independently used below for data fitting with close results 4. The main inferences from the present research are: 1) quark-neutrino 4-color symmetry is a useful background for realistic particle mixing patterns, 2) unique and united benchmark neutrino and quark mixing patterns follow from Eq. (1) without empirical parameters, 3) quark benchmark Eq. (4) follows from the primary symmetric Eq.(1) only at N = 3 by new definition of realistic quark mixing angles, 4) widely discussed in the literature two empirical flavor-mixing rules of large neutrino mixing angles versus small quark ones and quark-lepton complementarity QLC [4] are 4 The preference is for the epsilon-parameter [6].

4 4 explained mainly by different numbers of neutrino and quark colors (1 and 3) and small ε-deviation from benchmark, 5) two large realistic solar and atmospheric neutrino mixing angles determine small reactor theta_13 11 o mixing angle by Eq. (3); in reverse, by data small θ ν 13 angle determines large θ ν 12 and θ ν 23 angles by that Eq. (3). Not equal zero small quark mixing angles are inferences from Eq. (4) and ε- parameterizations, 6) correctly defined in Sec.2 ε-parameterization is especially suitable for description of small deviations of the realistic quark and neutrino flavor mixing angles from the bimaximal neutrino and zero quark benchmark mixing angles. In Sec. 2, neutrino mixing angles are obtained by symmetry violation of Eq. (3). In Sec. 3, Eq. (4) is derived from Eq. (1) and the realistic small quark mixing angles are obtained. In Sec. 4, explanation of the discussed two empirical flavor rules is summarized. Sec. 5 contains discussions of some results. 2. Neutrino mixing a) Neutrino part of benchmark mixing pattern A symmetric set of asymmetric mixing-angle solutions of Eq. (3) without nontrivial parameters is given by cos 2 2θ ν 12 = 0, cos 2 2θ ν 23 = 0, cos 2 2θ ν 13 = 1, cos 2 2θ ν 12 = 0, cos 2 2θ ν 23 = 1, cos 2 2θ ν 13 = 0, cos 2 2θ ν 12 = 1, cos 2 2θ ν 23 = 0, cos 2 2θ ν 13 = 0. (7) This set is symmetric until the mixing angles are physically identified by experimental data. Though every solution (7) of Eq. (3) is not symmetric, the superposition of all three must be a symmetric solution 5. The result 3cos 2 2θ ν ij = 1, ij = 12, 23, 13 (8) coincides with the universal symmetric solution (2). Physical identification of mixing angles by known experimental data [2] singles out the upper line solution in the set (7), cos 2 (2θ ν 12) = 0, cos 2 (2θ ν 23) = 0, cos 2 (2θ ν 13) = 1; θ ν 12 = θ ν 23 = π/4, θ ν 13= 0. (9) 5 Equations (1) and (3) are linear with respect to the quantities cos 2 2θ ν ij.

5 5 It has physical meaning of two maximal and one zero mixing angles of realistic benchmark neutrino mixing pattern. This singling out of solution (9) by condition of approximate agreement with data is a spontaneous violation 6 of Eq. (3), or set (7), symmetry. Unitary neutrino mixing matrix with angles (9) is the bimaximal matrix, 1/ 2 1/ 2 0-1/2 1/2 1/ 2 (10) 1/2-1/2 1/ 2 ν. This widely discussed in the literature neutrino mixing matrix approximately describes empirical neutrino mixing data [5]. Benchmark neutrino mixing pattern (9), (10) resulted from the primary mixing angle neutrino equation (3) by data suggested partial spontaneous symmetry violation of the symmetric solution-set (7) with no involvement of empirical parameters, and appears a pertinent level for realistic neutrino mixing angles as small deviations from it by epsilon-parameterization. b) Realistic neutrino mixing pattern Bimaximal neutrino mixing is considered a benchmark for accurate neutrino mixing angles via small empirical ε-parameter (5) and introduced earlier [6] exponential universal flavor function f(y), f(y) = y exp(y), (11) with y a power function of the ε-parameter. This combination of two conditions (5) and (11) is the content of the term epsilon-parameterization. Symmetry violating solution of Eq. (3) that is singled out by reasonably good agreement with known neutrino mixing experimental data analyses for the two largest angles [7, 8, 9], and is only a little deviated from the benchmark bimaximal solution (9) is given by accurate ε-parameterization [1] cos 2 (2θ ν 12) = f(-2ε), cos 2 (2θ ν 23) = f(ε 2 ), sin 2 (2θ ν 13) = f( 2ε) +f(ε 2 ), (12) it coincides with solution (9) at ε = 0, and contains only two independent mixing angles. 6 By the original meaning of the term spontaneous symmetry violation.

6 6 It should be noticed that replacement of directly empirically indicated ε-powers (2ε), (ε 2 ) at right sides of the first two equations (12) by exponential functions (11) (as it is done in (12)) remarkably increases the accuracy of all considered flavor-mixing quantities. Realistic asymmetric solution (12) of Eq. (3) is factually singled out from a fully symmetric set of six solutions of that equation, cos 2 (2θ ν 12) = f(-2ε), cos 2 (2θ ν 23) = f(ε 2 ), sin 2 (2θ ν 13) = f( 2ε) +f(ε 2 ), cos 2 (2θ ν 12) = f(-2ε), cos 2 (2θ ν 13) = f(ε 2 ), sin 2 (2θ ν 23) = f( 2ε) +f(ε 2 ), cos 2 (2θ ν 23) = f(-2ε), cos 2 (2θ ν 12) = f(ε 2 ), sin 2 (2θ ν 13) = f( 2ε) +f(ε 2 ), cos 2 (2θ ν 23) = f(-2ε), cos 2 (2θ ν 13) = f(ε 2 ), sin 2 (2θ ν 12) = f( 2ε) +f(ε 2 ), cos 2 (2θ ν 13) = f(-2ε), cos 2 (2θ ν 12) = f(ε 2 ), sin 2 (2θ ν 23) = f( 2ε) +f(ε 2 ), cos 2 (2θ ν 13) = f(-2ε), cos 2 (2θ ν 23) = f(ε 2 ), sin 2 (2θ ν 12) = f ( 2ε) +f(ε 2 ). (13) It is only a little deviated from the benchmark set (7) and coincides with (7) at ε = 0. This symmetric set of solutions includes all permutations of the three indexes 12, 23 and 13. Singling out the realistic solution (12) from the set (13) (upper line) is an indicated by data phenomenological spontaneous symmetry violation. The ε-parameterization in (12) breaks the residual symmetry of the bimaximal solution (9) and ensures agreement with data. Realistic neutrino mixing angles from solution (12) are given by θ ν o, θ ν o, θ ν o. (14) From comparison with experimental data analysis, e. g. [7], θ ν 12 = (33.6 ± 1.0) o, θ ν 23 = (40.4 ± 3.2) o, (14exp) agreement with predictions (14) for θ ν 12 and θ ν 23 angles is good [7-9]. Solution for the θ ν 13 angle in (14) is compatible with data indications [3, 10, 11] and recent new Daya Bay [12] results. Interestingly, at linear ε-approximation the reactor angle θ 13 in (12) is complementary to the solar mixing angle, sin 2 2θ ν 13 cos 2 2θ sol., sin 2 2θ ν 13 2ε, θ ν o. (15)

7 7 In terms of elemental electric charge (6), as alternative parameter instead of ε, realistic neutrino mixing angles are given by cos 2 2θ sol = f( 2e), cos 2 2θ atm = f(e 2 ); θ sol 33.9 o, θ atm 42.5 o, sin 2 2θ ν 13 = f( 2e), + f(e 2 ); θ ν o. (16) So, the elemental electric charge (6) as small parameter is almost as good as the ε- parameter for describing spontaneous symmetry violation solution of Eq. (3) and realistic neutrino mixing angles. 3. Quark mixing a) Quark part of particle benchmark mixing pattern Summing up the N color quark equations from the primary ones in Eq. (1) leads to c (cos 2 2θ c 12 + cos 2 2θ c 23 + cos 2 2θ c 13) = N. (17) It should be underlined that (17) is the only one possible quadratic relation that is simultaneously symmetric under flavor mixing angles and color quark quantities, which can be obtained from the primary Eq. (1). Since Eq. (4) is supported by data, let us define new quark mixing angles with superscript q by relations cos 2 2θ q ij c (cos 2 2θ c ij). (18) The new quark mixing angles θ q ij are physical ones, color white angles. The new quantity (18) hides primary quark color indexes and, in conjunction with (17), determines physical mixing-angle equation cos 2 2θ q 12 + cos 2 2θ q 23 + cos 2 2θ q 13 = N. (19) Note the relevance of the real meaning of quark colors. In an imagined world without strong color interactions the quark colors would be identical, cos 2 2θ q ij = Ncos 2 2θ c ij, and Eq. (17) would coincide not with quark Eq. (4), but with neutrino Eq. (3). Positive-definite Eq. (19) is a restriction on the number of colors N 3 and leaves only a few choices for the number of quark colors N = 0, 1, 2 or 3. From known data on CKM quark mixing angles [2] three values N = 0, 1, 2 are excluded and only one left N = 3. Then Eq. (19) coincides with Eq. (4). Another derivation of Eq. (4) is by using the unphysical (at low energies) universal solution (2) of Eq. (1). Summation over 3 colors results in relation

8 8 cos 2 2θ q i j = c (cos 2 2θ c i j) = c (1/3) = N/3.. (20) As mentioned above, it is in agreement with data only at N = 3. For completeness, consider a third derivation of Eq. (4) that underlined the relation between quark and neutrino solutions of Eq. (1). Each of the three color quark equations in (1) has evidently a symmetric set of three asymmetric solution of the neutrino type (7): cos 2 2θ r,g,b 12 = 0, cos 2 2θ r,g,b 23 = 0, cos 2 2θ r,g,b 13 = 1, cos 2 2θ r,g,b 12 = 0, cos 2 2θ r,g,b 23 = 1, cos 2 2θ r,g,b 13 = 0, cos 2 2θ r,g,b 12 = 1, cos 2 2θ r,g,b 23 = 0, cos 2 2θ r,g,b 13 = 0. (21) The superscript indexes denote three quark colors red (r), green (g) and blue (b). There are 9 mixing angle asymmetric solutions of Eq. (1) in (21). Summing all 27 relations in Eq. (21) and using the definition (18) with N = 3 results in Eq.(4) for realistic benchmark quark mixing. An important result of this derivation of Eq. (4) follows: experimental data on quark mixing angles in considered phenomenology definitely require equal numbers of quark colors and mixing angles and so equal numbers of quark colors and flavors 7. Thus 3 quark colors are necessary to establish experimental data indicated opposite quark and neutrino flavor mixing patterns - in agreement with SU(3) c QCD paradigm. Eq. (4) has only one zero mixing angle solution, cos 2 2θ q 12 = cos 2 2 θ q 23 = cos 2 2 θ q 13 = 1, sin 2 2θ q 12 = sin 2 2 θ q 23 = sin 2 2 θ q 13 = 0. (22) Unitary quark mixing matrix with angles (22) is the unit matrix (23) q. It describes benchmark quark mixing angles (zero ε-approximation) that approximately reproduce the small realistic CKM mixing angles [2]. To conclude, important benchmark quark mixing pattern is a unique result of Eq. (4). This equation follows from the original symmetric Eq. (1) without free parameters by 7 The numbers of flavors n f and mixing angles are equal only at n f = 3. At n f = 4 the number of mixing angles would be 6 and six quark colors would be needed to obtain the equivalent of benchmark Eq. (4) with zero mixing angles in form cos 2 2θ q i j = 1.

9 9 violation of symmetry between color quarks and neutrinos via formation of new, physical at low energies, quark mixing quantities and hiding there the primary color indexes. b) Realistic quark mixing pattern Zero quark mixing pattern is the benchmark level for evaluation of accurate quark mixing angles. Symmetry violating realistic quark mixing angles, which are in reasonably good quantitative agreement with experimental CKM data [2], should be described by the following ε- parameterization of Eq. (4), sin 2 (2θ q 12) + sin 2 2 θ q 23 + sin 2 2 θ q 13 = f(2ε) + f(ε 2 ) + f(ε 4 ). (24) It is a small deviation from the benchmark system (22) by ε 0. A completely symmetric set of six asymmetric solutions (compare neutrino set (13)) of Eq. (24) is given by sin 2 2θ q 12 = f(2ε), sin 2 2θ q 23 = f(ε 2 ), sin 2 2θ q 13 = f(ε 4 ), sin 2 θ q 12 = f(2ε), sin 2 2θ q 13 = f(ε 2 ), sin 2 2θ q 23 = f(ε 4 ), sin 2 2θ q 23 = f(2ε), sin 2 2θ q 12 = f(ε 2 ), sin 2 2θ q 13 = f(ε 4 ), sin 2 2θ q 23 = f(2ε), sin 2 2θ q 13 = f(ε 2 ), sin 2 2θ q 12 = f(ε 4 ), sin 2 2θ q 13 = f(2ε), sin 2 2θ q 12 = f(ε 2 ), sin 2 2θ q 23 = f(ε 4 ), sin 2 2θ q 13 = f(2ε), sin 2 2θ q 23 = f(ε 2 ), sin 2 2θ q 12 = f(ε 4 ). (25) This symmetric set of solutions includes all permutations of the three lower indexes 12, 23 and 13. Realistic solution for quark mixing angles is singled out from the set (25) (upper line), sin 2 2θ q 12 = f(2ε), sin 2 2θ q 23 = f(ε 2 ), sin 2 2θ q 13 = f(ε 4 ), (26) and means spontaneous mixing-angle symmetry violation suggested by experimental CKM data [2]. Note that the right sides in relations (26) for the two largest angles are different 8 from the neutrino ones in Eq. (12) only by the sign of the ε-parameter. Equations (26) determine three realistic quark mixing angles 8 As discussed in [6], probably more accurate realistic neutrino mixing angles can be obtained if the original geometric QLC [4] is supplemented by change of the ε-parameter sign ( combined QLC ) at transition from quark to neutrino angles, as it is already done in (12)-(13) and (24)-(26).

10 10 θ q o, θ q o, θ q o. (27) By comparison with PDG data [2], θ q 12 = (13.02 ± 0.04) o, θ q 23 = (2.35 ± 0.05) o, θ q 13 = (0.20 ± 0.01) o, (27 exp) the agreement with predictions (27) for all three angles is remarkably good. In terms of elemental electric charge (6), as alternative parameter, realistic quark mixing angles are given by sin 2 2θ q 12 = f(2e), sin 2 2θ q 23 = f(e 2 ), sin 2 2θ q 13 = f(e 4 ), (28) θ o, θ o, θ o. (29) They should be compared with (27). 4.Empirical flavor rules from benchmark mixing and small ε-parameterization The main results of the considered above phenomenology are reasonably accurate realistic neutrino and quark mixing patterns just a little deviated from benchmark mixing patterns via complete spontaneous violation of mixing-angle and quark-neutrino color symmetry of Eq. (1) and hiding the three quark colors in white mixing quantities. These results reveal two emphasized flavor mixing rules. Neutrino Eq. (3) is a part of the symmetric Eq. (1), and has a symmetric set of solutions (7). The white quark mixing angle Eq. (4) has only one zero mixing angle solution (20), also symmetric. The first step of spontaneous symmetry violation leads from these symmetric sets of solutions to benchmark mixing patterns with unit quark and bimaximal neutrino mixing matrices. The second step of spontaneous symmetry violation is from benchmark patterns to reasonably accurate realistic mixing patterns by complete spontaneous symmetry violation that resulted in only small deviations from benchmark, and so reveals the first flavor mixing rule large neutrino mixing angles versus small quark ones. Second flavor-mixing rule, geometric QLC [4] for the two largest quark and neutrino mixing angles, directly follows from the trivial in benchmark case relations for zero quark and maximal neutrino mixing angles sin 2 2θ q 12 = cos 2 2θ ν 12 and sin 2 2θ q 23 = cos 2 2θ ν 23, (0 o + 45 o = 45 o ). Since realistic deviations from benchmark neutrino and

11 11 quark mixing angles are respectively equal in magnitude and opposite in sign and so preserve the two benchmark mixing-angle relations, exact geometric QLC rule immediately follows. Above in text, modified combined QLC is implemented with the complementarity relation sin 2 2θ q 12 = cos 2 2θ ν 12 for θ 12 quark and neutrino angles violated by different signs of ε-parameter, comp. (12) and (24) and footnote eight. Nevertheless, exact QLC is approximately preserved for both θ 12 and θ 23 quark and neutrino angles at linear ε-approximation, comp. (15), and the small deviation from QLC for the pair of solar-cabibbo angles appears in encouraging agreement with data. Finally, an important question should be answered of how are found the accurate formulas for realistic quark (26) and neutrino (12) mixing angles. The answer is unexpectedly simple. All low energy dimensionless flavor quantities as small deviations from benchmark quark and neutrino ones are expressed through the epsilon-parameter via one universal function f[y i (ε)] = y i (ε) expy i (ε), (11); y i (ε) are power functions of ε that approximately fit empirical neutrino and quark data mixing angles. So, the problem is reduced to finding five arguments y i (ε) for three quark and two neutrino mixing angles. Luckily, data indications appear here surprisingly helpful; instead of five different functions y i (ε), i = 1 5, we need only the easy to find by simple data-fitting three ε- power ones: y 1 (ε) = 2ε for quark sin 2 2θ q 12 in (24) and y 1 (ε) = ( 2ε) for neutrino cos 2 2θ ν 12 in (12); y 2 (ε) = ε 2 for both sin 2 2θ q 23 in (24) and cos 2 2θ ν 23 in (12); and sin 2 2θ q 13 = ε 4 for (24). The important points are the testified by experimental data fitting qualities of small universal ε-parameter (5) and f-function (11) if benchmark flavor mixing patterns are bimaximal neutrino and zero quark ones. 5. Conclusions Quark color involvement in flavor mixing is interesting since it is in spirit of unity of three elementary particle forces. Guided by idea that one of the main causes of opposite mixing patterns of quarks and leptons in the weak interactions of SM is the fundamental difference of these particles by color degree of freedom, and stimulated by new T2K data,

12 12 one completely symmetric quadratic and positive definite mixing angle Eq. (1) for quark and neutrino four colors is investigated. Though the origin of this primary equation is beyond the semi-empirical flavor-mixing phenomenology, it appears a useful phenomenological source of appropriate low energy neutrino and quark benchmark mixing patterns and related ε-parameterization. On the one hand, Eq. (1) is a generalization of Eq. (3) that is considered in [1] for prediction a relatively large theta_13 in response to new T2K experimental indications [3]. On the other hand, the data supported extension to quark color mixing angles by Eq. (1) is an additional justification of the neutrino Eq. (3) and so the inference for theta_13 angle. Basic difference between the benchmark particle flavor patterns and accurate realistic ones is that the former follow from Eq. (1) without empirical parameters, whereas the latter are determined as small deviations from benchmark by ε-parameterization. It seems that the benchmark neutrino and quark mixing patterns are determined by symmetry of Eq. (1) and its spontaneous violation, while the small realistic deviations of mixing angles from benchmark values are determined by new dynamics probably represented in the semi-empirical phenomenology by epsilon-parameterization 9. Small ε-parameterization as deviation from benchmark mixing clearly explains on phenomenological grounds the considered above two known quantitative empirical quark-neutrino realistic flavor mixing rules. Two large, not maximal, neutrino mixing angles in contrast to small quark mixing ones are necessary because the neutrino mixing is described by only two independent mixing angles via Eq. (3), and from data indications there is one small neutrino mixing angle. In reverse, the neutrino theta_13 angle is small since there are two large neutrino angles. In detail, the reasons of why the neutrino mixing angle theta_13 is predicted as relatively large are the empirically not very small deviations from maximal values of the two large neutrino mixing angles, most importantly the solar one in Eq. (3). 9 By order of magnitude epsilon-parameter may be simple connected with the value of the fine structure constant at the grand unification scale [6].

13 13 It should be noticed that recently published new results of the Daya Bay reactor ν e - bar disappearance experiment [12] established non-zero value of the theta_13 angle with significance of 5.2 σ, sin 2 2θ ν 13 = ± 0.016(Stat) ± 0.005(Syst). (30) This result agrees with prediction (14) for theta_13 angle at 3σ. In the Standard Model quark QCD color and particle flavor physical quantities are independent. In the present semi-empirical phenomenology an attractive synergistic effect of quark color and flavor quantities in the weak interactions is considered. The following three new interesting phenomenological results are obtained from primary Eq. (1) by partial spontaneous symmetry violation without involvement of the ε- parameter, or the other parameter, 1) Strong interacting quark QCD colors as the fundamental physical distinction between quarks and leptons are also substantial in the appearance of large difference between quark and lepton flavor mixing in weak interactions. 2) The basic benchmark particle flavor mixing patterns - united bimaximal neutrino and zero quark ones - uniquely follow from the primary equation and data guidance. 3) Equal numbers 10 of quark colors and flavors follow from the primary equation and data grounded quark and neutrino small and large flavor mixing angles. Some experimental tests of the discussed semi-empirical phenomenology could be by new accurate data on the full set of neutrino and quark mixing angles, especially on the scarcely known neutrino theta_13 angle. References [1] E. M. Lipmanov, arxiv: [2] Particle Data Group, K. Nakamura et al., J. Phys. G37, (2010). [3] K. Abe et al, Phys. Rev. Lett., 107, (2011). [4] H. Minakata and A. Yu. Smirnov, Phys. Rev., D70: (2004); M. Raidal, Phys. 10 Equal 3 numbers of both quark colors and particle flavors is one of mysterious traits of the SM.

14 14 Rev. Lett. 93, (2004). [5] e. g. Howard Georgi, S. L. Glashow, Phys. Rev. D61: (2000). [6] E. M. Lipmanov, arxiv: [7] L. Fogli, E. Lisi, A. Marone, A. Palazzo, A. M. Rotunno, Phys. Rev. D 84:053007(2011). [8] T. Schwetz, M.A. Tortola, J.W.F. Valle, New J. Phys. 13, , [9] M. C. Gonzalez-Garcia, M. Maltoni, J. Salvado, JHEP 04, 056 (2010). [10] P. Adamson et al. (MINOS Collab.), Phys. Rev. Lett. 107, (2011). [11] Y. Abe et al., arxiv: [12] Daya-Bay Collaboration, F. P. An et al, arxiv: