Orbifold Family Unification in SO(2N) Gauge Theory

We study the possibility of family unification on the basis of SO(2N) gauge theory on the five-dimensional space-time, $M^4\times S^1/Z_2$. Several SO(10), $SU(4) \times SU(2)_L \times SU(2)_R$ or SU(5) multiplets come from a single bulk multiplet of SO(2N) after the orbifold breaking. Other multiplets including brane fields are necessary to compose three families of quarks and leptons.Comment: 28 page

Relation between the neutrino and quark mixing angles and grand unification

We argue that there exists simple relation between the quark and lepton mixings which supports the idea of grand unification and probes the underlying robust bi-maximal fermion mixing structure of still unknown flavor physics. In this framework the quark mixing matrix is a parameter matrix describing the deviation of neutrino mixing from exactly bi-maximal, predicting theta_{sol}+theta_C=pi/4, where theta_C is the Cabibbo angle, theta_{atm}+theta_{23}^{CKM}=pi/4 and theta_{13}^{MNS} ~ theta_{13}^{CKM} ~ O(lambda^3), in a perfect agreement with experimental data. Both non-Abelian and Abelian flavor symmetries are needed for such a prediction to be realistic. An example flavor model capable to explain this flavor mixing pattern, and to induce the measured quark and lepton masses, is outlined.Comment: references added, title changed in journa

Discussions on Stability of Diquarks

Since the birth of the quark model, the diquark which is composed of two quarks has been considered as a substantial structure of color anti-triplet. This is not only a mathematical simplification for dealing with baryons, but also provides a physical picture where the diquark would behave as a whole object. It is natural to ask whether such a structure is sufficiently stable against external disturbance. The mass spectra of the ground states of the scalar and axial-vector diquarks which are composed of two-light (L-L), one-light-one-heavy (H-L) and two-heavy quarks (H-H) respectively have been calculated in terms of the QCD sum rules. We suggest a criterion as the quantitative standard for the stability of the diquark. It is the gap between the masses of the diquark and $\sqrt{s_0}$ where $s_0$ is the threshold of the excited states and continuity, namely the larger the gap is, the more stable the diquark would be. In this work, we calculate the masses of the type H-H to complete the series of the spectra of the ground state diquarks. However, as the criterion being taken, we find that all the gaps for the various diquaks are within a small range, especially the gap for the diquark with two heavy quarks which is believed to be a stable structure, is slightly smaller than that for other two types of diquarks, therefore we conclude that because of the large theoretical uncertainty, we cannot use the numerical results obtained with the QCD sum rules to assess the stability of diquarks, but need to invoke other theoretical framework.Comment: 14 pages, 4 figure

On the Early History of Current Algebra

The history of Current Algebra is reviewed up to the appearance of the Adler-Weisberger sum rule. Particular emphasis is given to the role current algebra played for the historical struggle in strong interaction physics of elementary particles between the S-matrix approach based on dispersion relations and field theory. The question whether there are fundamental particles or all hadrons are bound or resonant states of one another played an important role in this struggle and is thus also regarded.Comment: 17 page

Maximally Entangled Mixed States and Conditional Entropies

The maximally entangled mixed states of Munro, James, White, and Kwiat [Phys. Rev. A {\bf 64} (2001) 030302] are shown to exhibit interesting features vis a vis conditional entropic measures. The same happens with the Ishizaka and Hiroshima states [Phys. Rev. A {\bf 62} 022310 (2000)], whose entanglement-degree can not be increased by acting on them with logic gates. Special types of entangled states that do not violate classical entropic inequalities are seen to exist in the space of two qubits. Special meaning can be assigned to the Munro {\it et al.} special participation ratio of 1.8

A Comprehensive Mechanism Reproducing the Mass and Mixing Parameters of Quarks and Leptons

It is shown that if, from the starting point of a universal rank-one mass matrix long favoured by phenomenologists, one adds the assumption that it rotates (changes its orientation in generation space) with changing scale, one can reproduce, in terms of only 6 real parameters, all the 16 mass ratios and mixing parameters of quarks and leptons. Of these 16 quantities so reproduced, 10 for which data exist for direct comparison (i.e. the CKM elements including the CP-violating phase, the angles $\theta_{12}, \theta_{13}, \theta_{23}$ in $\nu$-oscillation, and the masses $m_c, m_\mu, m_e$) agree well with experiment, mostly to within experimental errors; 4 others ($m_s, m_u, m_d, m_{\nu_2}$), the experimental values for which can only be inferred, agree reasonably well; while 2 others ($m_{\nu_1}, \delta_{CP}$ for leptons), not yet measured experimentally, remain as predictions. In addition, one gets as bonuses, estimates for (i) the right-handed neutrino mass $m_{\nu_R}$ and (ii) the strong CP angle $\theta$ inherent in QCD. One notes in particular that the output value for $\sin^2 2 \theta_{13}$ from the fit agrees very well with recent experiments. By inputting the current experimental value with its error, one obtains further from the fit 2 new testable constraints: (i) that $\theta_{23}$ must depart from its "maximal" value: $\sin^2 2 \theta_{23} \sim 0.935 \pm 0.021$, (ii) that the CP-violating (Dirac) phase in the PMNS would be smaller than in the CKM matrix: of order only $|\sin \delta_{CP}| \leq 0.31$ if not vanishing altogether.Comment: 37 pages, 1 figur