Exact solution of the XXX Gaudin model with generic open boundaries
The XXX Gaudin model with generic integrable open boundaries specified by the most general non-diagonal reflecting matrices is studied. Besides the inhomogeneous parameters, the associated Gaudin operators have six free parameters which break the U ( 1 ) -symmetry. With the help of the off-diagonal Bethe ansatz, we successfully obtained the eigenvalues of these Gaudin operators and the corresponding Bethe ansatz equations.

title: Primary fields and screening currents of gl(2|2) non-unitary conformal field theory
abstract: The non-semisimple gl(2)k current superalgebra in the standard basis and the corresponding non-unitary conformal field theory are investigated. Infinite families of primary fields corresponding to all finite-dimensional irreducible typical and atypical representations of gl(212) and three (two even and one odd) screening currents of the first kind are constructed explicitly in terms of ten free fields.

title: THE DRESSING TRANSFORMATION OF THE CONFORMAL AFFINE TODA
abstract: We study the dressing transformations of the conformal affine Todal which can be obtained from a Hamiltonian reduction. As a special case, we obtain the dressing transformations of the sinh-Gordon model. We will show that the dressing group is the semiclassical limit of the quantum group . We will also obtain the algebra of the charges which generate the infinitesimal dressing transformations.

title: Off-diagonal Bethe ansatz solutions of the anisotropic spin-1/2 chains with arbitrary boundary fields
abstract: The anisotropic spin-1/2 chains with arbitrary boundary fields are diagonalized with the off-diagonal Bethe ansatz method. Based on the properties of the R-matrix and the K-matrices, an operator product identity of the transfer matrix is constructed at some special points of the spectral parameter. Combining with the asymptotic behavior (for XXZ case) or the quasi-periodicity properties (for XYZ case) of the transfer matrix, the extended T-Q ansatzes and the corresponding Bethe ansatz equations are derived.

title: Inner structure of Spinc(4) gauge potential on 4-dimensional manifolds
abstract: The decomposition of Spinc(4) gauge potential in terms of the Dirac 4-spinor is investigated, where an important characterizing equation ΔAμ=-λAμ has been discovered. Here, λ is the vacuum expectation value of the spinor field, λ=Φ2, and Aμ the twisting U(1) potential. It is found that when λ takes constant values, the characterizing equation becomes an eigenvalue problem of the Laplacian operator. It provides a revenue to determine the modulus of the spinor field by using the Laplacian spectral theory. The above study could be useful in determining the spinor field and twisting potential in the Seiberg–Witten equations. Moreover, topological characteristic numbers of instantons in the self-dual sub-space are also discussed.

title: Exact solution of the Izergin-Korepin model with general non-diagonal boundary terms
abstract: A bstractThe Izergin-Korepin model with general non-diagonal boundary terms, a typical integrable model beyond A-type and without U(1)-symmetry, is studied via the offdiagonal Bethe ansatz method. Based on some intrinsic properties of the R-matrix and the K-matrices, certain operator product identities of the transfer matrix are obtained at some special points of the spectral parameter. These identities and the asymptotic behaviors of the transfer matrix together allow us to construct the inhomogeneous T − Q relation and the associated Bethe ansatz equations. In the diagonal boundary limit, the reduced results coincide exactly with those obtained via other methods.

title: Fermion Masses and Flavor Mixings from Family Symmetry SU(3)
abstract: We suggest a new particle model based on the symmetry group $SU(3)_{C}\otimes SU(2)_{L}\otimes SU(2)_{L'}\otimes SU(2)_{R}\otimes U(1)_{B-L}\otimes SU(3)_{F}\otimes U(1)_{N}$. The family symmetry and the high-energy left-handed and right-handed isospin subgroups are respectively broken by some flavon and Higgs fields one after another. At the low-energy scale the super-heavy fermions are all integrated out, the model finally leads to an effective theory with the standard model symmetry group. After the electroweak breaking all the fermion mass matrices are elegantly characterized only by six parameters. The model can perfectly fit and explain all the current experimental data about the fermion masses and flavor mixings, in particular, it finely predicts the first generation quark masses and the values of $\theta^{l}_{13}, \langle m_{\beta\beta}\rangle, J_{CP}^{l}$ in neutrino physics. The results are all promising to be tested in future experiments.

title: Fermion masses and flavor mixing in supersymmetric SO(10) model
abstract: We study fermion masses and flavor mixing in a supersymmetric SO ( 10 ) model, where 10, 120 and 126 ¯ Higgs multiplets have Yukawa couplings with matter multiplets and give masses to quarks and leptons through the breaking chain of a Pati–Salam group. This brings about that, at the GUT energy scale, the lepton mass matrices are related to the quark ones via several breaking parameters, and the small neutrino masses arise from a Type II see-saw mechanism. When evolving renormalization group equations for the fermion mass matrices from the GUT scale to the electroweak scale, in a specific parameter scenario, we show that the model can elegantly accommodate all observed values of masses and mixing for the quarks and leptons, especially, it's predictions for the bi-large mixing in the leptonic sector are very well in agreement with the current neutrino experimental data.

title: Decay constants of the pion and B mesons with the Bethe–Salpeter equation
abstract: In this Letter, we investigate the under-structures of the π and B mesons in the framework of the Bethe–Salpeter equation with the confining effective potential (infrared modified flat bottom potential). In bare quark–gluon vertex approximation, we obtain the algebraic expressions for the solutions of the coupled rainbow Schwinger–Dyson equation and ladder Bethe–Salpeter equation. Firstly, we neglect the rainbow Schwinger–Dyson equation, take the bare quark propagator and solve the Bethe–Salpeter equation numerically alone. Although the bare quark propagator cannot embody dynamical chiral symmetry breaking and has a mass pole in the time-like region, it can give reasonable results for the values of decay constants f π and f B compared with the values of experimental data and other theoretical calculations, such as lattice simulations and QCD sum rules. Secondly, we explore those mesons within the framework of the coupled rainbow Schwinger–Dyson equation and ladder Bethe–Salpeter equation. The Schwinger–Dyson functions for the u and d quarks are greatly renormalized at small momentum region and the curves are steep at about q 2 =1 GeV 2 which indicates an explicitly dynamical symmetry breaking. The Euclidean time Fourier-transformed quark propagator has no mass poles in the time-like region which naturally implements confinement. As for the b quark, the current mass is very large, the renormalization is more tender, however, mass pole in the time-like region is also absent. The Bethe–Salpeter wavefunctions for both the π and B mesons have the same type (Gaussian type) momentum dependence as the corresponding wavefunctions with the bare quark propagator, however, the quantitative values are changed and the values for the decay constants f π and f B are changed correspondingly.

title: A Model of Fermion Flavor and Leptogenesis and Cold Dark Matter
abstract: I suggest a new particle model to integrate the fermion flavor, the TeV scale Leptogenesis and cold dark matter. The model has a local gauge symmetry $U(1)_{B-L}$ at the TeV scale and a flavor family symmetry SO(3), in addition, it also contains the fourth generation fermions in which including a cold dark matter neutrino. The model can simultaneously account for the fermion masses and flavor mixings, and the baryon asymmetry and cold dark matter. It not only excellently fits all the current experimental data, but also predicts some new results which are promising to be test in future experiments.

title: Axial form-factor and induced pseudoscalar form-factor of the nucleons
abstract: We calculate the axial and the induced pseudoscalar form-factors GA(t=-Q2) and GP(t=-Q2) of the nucleons in the framework of the light-cone QCD sum-rules approach up to twist-6 three valence quark light-cone distribution amplitudes, and observe that the form-factors GA(t=-Q2) and GP(t=-Q2) at intermediate and large momentum transfers with Q2>2 GeV2 have significant contributions from the end-point (soft) terms. The numerical values for the axial form-factor GA(t=-Q2) are compatible with the experimental data and theoretical calculations; for example, the chiral quark models and lattice QCD. The numerical values for the induced pseudoscalar form-factor GP(t=-Q2) are compatible with the calculation from the Bethe–Salpeter equation.