The self-dual gauge fields and the domain wall fermion zero modes

A new type of gauge fixing of the Coulomb gauge domain wall fermion system that reduces the fluctuation of the effective running coupling and the effective mass of arbitrary momentum direction including the region outside the cylinder cut region is proposed and tested in the $16^3\times 32\times 16$ gauge configurations of RBC/UKQCD collaboration. The running coupling at the lowest momentum point does not show infrared suppression and compatible with the experimental data extracted from the JLab collaboration. The source of the fluctuation of the effective mass near momentum $p=$0.6GeV region is expected to be due to the domain wall fermion zero modes.Comment: 12 pages 2 figures, extended arguments and references adde

Four-quark energies in SU(2) lattice Monte Carlo using a tetrahedral geometry

This contribution -- a continuation of earlier work -- reports on recent developments in the calculation and understanding of 4-quark energies generated using lattice Monte Carlo techniques.Comment: 3 pages, latex, no figures, contribution to Lattice 9

Numerical Study of the Ghost-Gluon Vertex in Landau gauge

We present a numerical study of the ghost-gluon vertex and of the corresponding renormalization function \widetilde{Z}_1(p^2) in minimal Landau gauge for SU(2) lattice gauge theory. Data were obtained for three different lattice volumes (V = 4^4, 8^4, 16^4) and for three lattice couplings \beta = 2.2, 2.3, 2.4. Gribov-copy effects have been analyzed using the so-called smeared gauge fixing. We also consider two different sets of momenta (orbits) in order to check for possible effects due to the breaking of rotational symmetry. The vertex has been evaluated at the asymmetric point (0;p,-p) in momentum-subtraction scheme. We find that \widetilde{Z}_1(p^2) is approximately constant and equal to 1, at least for momenta p > ~ 1 GeV. This constitutes a nonperturbative verification of the so-called nonrenormalization of the Landau ghost-gluon vertex. Finally, we use our data to evaluate the running coupling constant \alpha_s(p^2).Comment: 19 pages, 6 figures, 9 tables, using axodraw.sty; minor modifications in the abstract, introduction and conclusion

The gluon and ghost propagator and the influence of Gribov copies

The dependence of the Landau gauge gluon and ghost propagators on the choice of Gribov copies is studied in pure SU(3) lattice gauge theory. Whereas the influence on the gluon propagator is small, the ghost propagator becomes clearly affected by the copies in the infrared region. We compare our data with the infrared exponents predicted by the Dyson-Schwinger equation approachComment: Talk presented at Lattice2004(topology), Fermilab, June 21-26, 2004, 3 pages, 3 figure

Pion wave functions from holographic QCD and the role of infrared renormalons in photon-photon collisions

In this article, we calculate the contribution of the higher-twist Feynman diagrams to the large-$p_T$ inclusive single pion production cross section in photon-photon collisions in case of the running coupling and frozen coupling approaches within holographic QCD. We compare the resummed higher-twist cross sections with the ones obtained in the framework of the frozen coupling approach and leading-twist cross section. Also, we show that in the context of frozen coupling approach a higher-twist contribution to the photon-photon collisions cross section is normalized in terms of the pion electromagnetic form factor.Comment: 21 pages, 15 figures. arXiv admin note: text overlap with arXiv:0709.2072 by other author

QCD Approach to B->D \pi Decays and CP Violation

The branching ratios and CP violations of the $B\to D\pi$ decays, including both the color-allowed and the color-suppressed modes, are investigated in detail within QCD framework by considering all diagrams which lead to three effective currents of two quarks. An intrinsic mass scale as a dynamical gluon mass is introduced to treat the infrared divergence caused by the soft collinear approximation in the endpoint regions, and the Cutkosky rule is adopted to deal with a physical-region singularity of the on mass-shell quark propagators. When the dynamical gluon mass $\mu_g$ is regarded as a universal scale, it is extracted to be around $\mu_g = 440$ MeV from one of the well-measured $B\to D\pi$ decay modes. The resulting predictions for all branching ratios are in agreement with the current experimental measurements. As these decays have no penguin contributions, there are no direct $CP$ asymmetries. Due to interference between the Cabibbo-suppressed and the Cabibbo-favored amplitudes, mixing-induced CP violations are predicted in the $B\to D^{\pm}\pi^{\mp}$ decays to be consistent with the experimental data at 1-$\sigma$ level. More precise measurements will be helpful to extract weak angle $2\beta+\gamma$.Comment: 21pages,5 figures,3 tables, typos corrected and numerical result for one of decay channels is improve

The flavor symmetry in the standard model and the triality symmetry

A Dirac fermion is expressed by a 4 component spinor which is a combination of two quaternions and which can be treated as an octonion. The octonion possesses the triality symmetry, which defines symmetry of fermion spinors and bosonic vector fields. The triality symmetry relates three sets of spinors and two sets of vectors, which are transformed among themselves via transformations $G_{23}, G_{12}, G_{13}$, $G_{123}$ and $G_{132}$. If the electromagnetic (EM) interaction is sensitive to the triality symmetry, i.e. EM probe selects one triality sector, EM signals from the 5 transformed world would not be detected, and be treated as the dark matter. According to an astrophysical measurement, the ratio of the dark to ordinary matter in the universe as a whole is almost exactly 5. We expect quarks are insensitive to the triality, and triality will appear as three times larger flavor degrees of freedom in the lattice simulation.Comment: 16 pages 8 figures, To be published in International Journal of Modern Physics

Large volume behavior of Yang-Mills propagators

We summarize results on finite-volume effects in the propagators of Landau gauge Yang-Mills theory using Dyson-Schwinger equations on a 4-dimensional torus. We demonstrate explicitly how the solutions for the gluon and the ghost propagator tend towards their respective infinite volume forms in the corresponding limit. We discuss the relation of our solutions with results from lattice Monte-Carlo simulations.Comment: 7 pages, 2 figures, Presented by CF at the XXV International Symposium on Lattice Field Theory, July 30 - August 4 2007, Regensburg, German

Landau gauge ghost and gluon propagators and the Faddeev-Popov operator spectrum

In this talk we report on a recent lattice investigation of the Landau gauge gluon and ghost propagators in pure SU(3) lattice gauge theory with a special emphasis on the Gribov copy problem. In the (infrared) region of momenta $q^2 \le 0.3 \mathrm{GeV}^2$ we find the corresponding MOM scheme running coupling $\alpha_s(q^2)$ to rise in $q$. We also report on a first SU(3) computation of the ghost-gluon vertex function showing that it deviates only weakly from being constant. In addition we study the spectrum of low-lying eigenvalues and eigenfunctions of the Faddeev-Popov operator as well as the spectral representation of the ghost propagator.Comment: talk given by M. M.-P. at the Workshop on Computational Hadron Physics, Cyprus, September 200

Renormalization Group Analysis of \rho-Meson Properties at Finite Density

We calculate the density dependence of the $\rho$-meson mass and coupling constant($g_{\rho NN}$) for $\rho$-nucleon-nucleon vertex at one loop using the lagrangian where the $\rho$-meson is included as a dynamical gauge boson of a hidden local symmetry. From the condition that thermodynamic potential should not depend on the arbitrary energy scale, renormalization scale, one can construct a renormalization group equation for the thermodynamic potential and argue that the various renormalization group coefficients are functions of the density or temperature. We calculate the $\beta$-function for $\rho$-nucleon-nucleon coupling constant ($g_{\rho NN}$) and $\gamma$-function for $\rho$-meson mass ($\gamma_{m_\rho}$). We found that the $\rho$-meson mass and the coupling constant for $g_{\rho NN}$ drop as density increases in the low energy limit.Comment: 24 pages, 10 figures, revised versio