Decay constants of the pion and B mesons with the Bethe–Salpeter equation
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: Magnetic moment of the pentaquark Θ+(1540) as diquark-diquark-antiquark state with QCD sum rules
abstract: In this article, we study the magnetic moment of the pentaquark state Θ+(1540) as a diquark-diquark-antiquark ($[ud][ud]\bar{s}$) state with the QCD sum rules in an external weak electromagnetic field (EFSR) and the light-cone QCD sum rules (LCSR) respectively. The numerical results indicate that the magnetic moment is about $\mu_{\Theta^ + } = -(0.11\pm 0.02)\mu_N$ for the EFSR and $\mu_{\Theta^ + }\approx-(0.1$-$0.5)\mu_N$ for the LCSR. As the values obtained from the EFSR are more stable than the corresponding ones from the LCSR, $\mu_{\Theta^ + } = -(0.11\pm 0.02)\mu_N$ is more reliable.

title: Decay constants of the pseudoscalar mesons in the framework of the coupled Schwinger–Dyson equation and Bethe–Salpeter equation
abstract: In this article, we investigate the structures of the pseudoscalar mesons ( π , K , D , D s , B and B s ) in the framework of the coupled rainbow Schwinger–Dyson equation and ladder Bethe–Salpeter equation with the confining effective potential (infrared modified flat bottom potential). The Schwinger–Dyson functions for the u , d and s 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 propagators have no mass poles in the time-like region which naturally implements confinement. As for the c and b quarks, the current masses are very large, the renormalization are more tender, however, mass poles in the time-like region are also absent. The Bethe–Salpeter wavefunctions for those mesons have the same type (Gaussian type) momentum dependence and center around small momentum which indicate that the bound states exist in the infrared region. The decay constants for those pseudoscalar mesons are compatible with the values of experimental extractions and theoretical calculations, such as lattice simulations and QCD sum rules.

title: CP violation in chargino decays in the MSSM
abstract: In the minimal supersymmetric standard model (MSSM) with complex parameters, supersymmetric loop effects can lead to $\mathrm{CP}$ violation. We calculate the rate asymmetries of decays of charginos into the lightest neutralino and a W boson on the basis of the most important loop contributions in the third generation squark sector. It turns out that the $\mathrm{CP}$ violating asymmetries can be a few percent in typical regions of the parameter space of the MSSM. These processes would provide very promising channels for probing $\mathrm{CP}$ violation in the MSSM at future high-energy colliders.

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.

title: Scalar form-factor of the proton with light-cone QCD sum rules
abstract: We calculate the scalar form factor of the proton in the framework of the light-cone QCD sum rules approach with the three valence quark light-cone distribution amplitudes up to twist-6 and observe the scalar form factor {sigma}(t=-Q{sup 2}) at intermediate and large momentum transfers Q{sup 2}>2 GeV{sup 2} has significant contributions from the end point (or soft) terms. The numerical values for the {sigma}(t=-Q{sup 2}) are compatible with the calculations from the chiral quark model and lattice QCD at the region Q{sup 2}>2 GeV{sup 2}.

title: The dynamical twisting and nondynamical r-matrix structure of the elliptic Ruijsenaars–Schneider model
abstract: From the dynamical twisting of the classical r-matrix, we obtain a new Lax operator for the elliptic Ruijsenaars–Schneider model (cf. Ruijsenaars). The corresponding r-matrix is shown to be the classical Zn-symmetric elliptic r-matrix, which is the same as that obtained in the study of the nonrelativistic version—the An−1 Calogero–Moser model.

title: On the largest Lyapunov exponent for coupled surjective map lattice with weak diffusive coupling
abstract: The largest Lyapunov exponent for one dimensional coupled map lattices with diffusive coupling is considered analytically. It is shown that if the map is surjective there exists a simple relation between the largest Lyapunov exponent λ1 and the coupling strength e, namely λ1 = λ0 - κe0, when e → 0, where λ0 is the Lyapunov exponent for the map and o = 1/p if the mapping function has p-th order maximum.

title: Non-diagonal solutions of the reflection equation for the trigonometric An-1(1) vertex model
abstract: We obtain a class of non-diagonal solutions of the reflection equation for the trigonometric A(n-1)((1)) vertex model. The solutions can be expressed in terms of intertwinner matrix and its inverse, which intertwine two trigonometric R-matrices. In addition to a discrete (positive integer) parameter l, 1 less than or equal to l less than or equal to n, the solution contains n + 2 continuous boundary parameters.

title: gl(4/4) current superalgebra: free field realization and screening currents
abstract: The gl(4 vertical bar 4) current algebra at general level k is investigated. Its free field representation and corresponding energy-momentum tensor are constructed. Seven screening currents of the first kind are also presented.

title: Exact solution of the one-dimensional Hubbard model with arbitrary boundary magnetic fields
abstract: The one-dimensional Hubbard model with arbitrary boundary magnetic fields is solved exactly via the Bethe ansatz methods. With the coordinate Bethe ansatz in the charge sector, the second eigenvalue problem associated with the spin sector is constructed. It is shown that the second eigenvalue problem can be transformed into that of the inhomogeneous XXX spin chain with arbitrary boundary fields which can be solved via the off-diagonal Bethe ansatz method.