Yang-Mills theory constructed from Cho--Faddeev--Niemi decomposition

We give a new way of looking at the Cho--Faddeev--Niemi (CFN) decomposition of the Yang-Mills theory to answer how the enlarged local gauge symmetry respected by the CFN variables is restricted to obtain another Yang-Mills theory with the same local and global gauge symmetries as the original Yang-Mills theory. This may shed new light on the fundamental issue of the discrepancy between two theories for independent degrees of freedom and the role of the Maximal Abelian gauge in Yang-Mills theory. As a byproduct, this consideration gives new insight into the meaning of the gauge invariance and the observables, e.g., a gauge-invariant mass term and vacuum condensates of mass dimension two. We point out the implications for the Skyrme--Faddeev model.Comment: 17pages, 1 figure; English improved; a version appeared in Prog. Theor. Phy

Single and Double Universal Seesaw Mechanisms with Universal Strength for Yukawa Couplings

Single and double universal seesaw mechanisms and the hypothesis of universal strength for Yukawa couplings are applied to formulate a unified theory of fermion mass spectrum in a model based on an extended Pati-Salam symmetry. Five kinds of Higgs fields are postulated to mediate scalar interactions among electroweak doublets of light fermions and electroweak singlets of heavy exotic fermions with relative Yukawa coupling constants of exponential form. At the first-order seesaw approximation, quasi-democratic mass matrices with equal diagonal elements are derived for all charged fermion sectors and a diagonal mass matrix is obtained for the neutrino sector under an additional ansatz. Assuming the vacuum neutrino oscillation, the problems of solar and atmospheric neutrino anomalies are investigated.Comment: 13 pages, LaTeX; a reference adde

Solving the Schwinger-Dyson Equations for Gluodynamics in the Maximal Abelian Gauge

We derive the Schwinger-Dyson equations for the SU(2) Yang-Mills theory in the maximal Abelian gauge and solve them in the infrared asymptotic region. We find that the infrared asymptotic solutions for the gluon and ghost propagators are consistent with the hypothesis of Abelian dominance.Comment: 3 pages, 1 figure; Lattice2003(topology

Approximate Sum Rules of CKM Matrix Elements from Quasi-Democratic Mass Matrices

To extract sum rules of CKM matrix elements, eigenvalue problems for quasi-democratic mass matrices are solved in the first order perturbation approximation with respect to small deviations from the democratic limit. Mass spectra of up and down quark sectors and the CKM matrix are shown to have clear and distinctive hierarchical structures. Numerical analysis shows that the absolute values of calculated CKM matrix elements fit the experimental data quite well. The order of the magnitude of the Jarlskog parameter is estimated by the relation $|J| \approx \sqrt{2}(m_c/m_t + m_s/m_b)|V_{us}|^2|V_{cb}|/4$.Comment: Latex, 15 pages, no figure

Electron Acceleration by Multi-Island Coalescence

Energetic electrons of up to tens of MeV are created during explosive phenomena in the solar corona. While many theoretical models consider magnetic reconnection as a possible way of generating energetic electrons, the precise roles of magnetic reconnection during acceleration and heating of electrons still remain unclear. Here we show from 2D particle-in-cell simulations that coalescence of magnetic islands that naturally form as a consequence of tearing mode instability and associated magnetic reconnection leads to efficient energization of electrons. The key process is the secondary magnetic reconnection at the merging points, or the `anti-reconnection', which is, in a sense, driven by the converging outflows from the initial magnetic reconnection regions. By following the trajectories of the most energetic electrons, we found a variety of different acceleration mechanisms but the energization at the anti-reconnection is found to be the most important process. We discuss possible applications to the energetic electrons observed in the solar flares. We anticipate our results to be a starting point for more sophisticated models of particle acceleration during the explosive energy release phenomena.Comment: 14 pages, 12 figures (degraded figure quality), 1 table. Accepted for publication in ApJ

Renormalizable Abelian-projected effective gauge theory derived from Quantum Chromodynamics

We show that an effective Abelian gauge theory can be obtained as a renormalizable theory from QCD in the maximal Abelian gauge. The derivation improves in a systematic manner the previous version that was obtained by one of the authors and was referred to as the Abelian-projected effective gauge theory. This result supports the view that we can construct an effective Abelian gauge theory from QCD without losing characteristic features of the original non-Abelian gauge theory. In fact, it is shown that the effective coupling constant in the resulting renormalizable theory has a renormalization-scale dependence governed by the $\beta$-function that is exactly the same as that of the original Yang-Mills theory, irrespective of the choice of gauge fixing parameters of the maximal Abelian gauge and the parameters used for identifying the dual variables. Moreover, we evaluate the anomalous dimensions of the fields and parameters in the resultant theory. By choosing the renormalized parameters appropriately, we can switch the theory into an electric or a magnetic theory.Comment: 17 pages, 3 figures(16 eps-files

`Island Surfing' Mechanism of Electron Acceleration During Magnetic Reconnection

One of the key unresolved problems in the study of space plasmas is to explain the production of energetic electrons as magnetic field lines `reconnect' and release energy in a exposive manner. Recent observations suggest possible roles played by small scale magnetic islands in the reconnection region, but their precise roles and the exact mechanism of electron energization have remained unclear. Here we show that secondary islands generated in the reconnection region are indeed efficient electron accelerators. We found that, when electrons are trapped inside the islands, they are energized continuously by the reconnection electric field prevalent in the reconnection diffusion region. The size and the propagation speed of the secondary islands are similar to those of islands observed in the magnetotail containing energertic electrons.Comment: 5 pages, 4 figures, submitted to J. Geophys. Res