A dynamical gluon mass solution in a coupled system of the Schwinger-Dyson equations

We study numerically the Schwinger-Dyson equations for the coupled system of gluon and ghost propagators in the Landau gauge and in the case of pure gauge QCD. We show that a dynamical mass for the gluon propagator arises as a solution while the ghost propagator develops an enhanced behavior in the infrared regime of QCD. Simple analytical expressions are proposed for the propagators, and the mass dependency on the $\Lambda_{QCD}$ scale and its perturbative scaling are studied. We discuss the implications of our results for the infrared behavior of the coupling constant, which, according to fits for the propagators infrared behavior, seems to indicate that $\alpha_s (q^2) \to 0$ as $q^2 \to 0$.Comment: 17 pages, 7 figures - Revised version to be consistent with erratum to appear in JHE

Gluon mass generation in the PT-BFM scheme

In this article we study the general structure and special properties of the Schwinger-Dyson equation for the gluon propagator constructed with the pinch technique, together with the question of how to obtain infrared finite solutions, associated with the generation of an effective gluon mass. Exploiting the known all-order correspondence between the pinch technique and the background field method, we demonstrate that, contrary to the standard formulation, the non-perturbative gluon self-energy is transverse order-by-order in the dressed loop expansion, and separately for gluonic and ghost contributions. We next present a comprehensive review of several subtle issues relevant to the search of infrared finite solutions, paying particular attention to the role of the seagull graph in enforcing transversality, the necessity of introducing massless poles in the three-gluon vertex, and the incorporation of the correct renormalization group properties. In addition, we present a method for regulating the seagull-type contributions based on dimensional regularization; its applicability depends crucially on the asymptotic behavior of the solutions in the deep ultraviolet, and in particular on the anomalous dimension of the dynamically generated gluon mass. A linearized version of the truncated Schwinger-Dyson equation is derived, using a vertex that satisfies the required Ward identity and contains massless poles belonging to different Lorentz structures. The resulting integral equation is then solved numerically, the infrared and ultraviolet properties of the obtained solutions are examined in detail, and the allowed range for the effective gluon mass is determined. Various open questions and possible connections with different approaches in the literature are discussed.Comment: 54 pages, 24 figure

Induction: Fibonacci Identities

= 1155 1156-1 10 34 \Theta 89 = 3026 3025 +1 Now we conjecture that Fn\Gamma1 Fn+1 \Gamma F 2 n = (\Gamma1) n : We will prove this by induction. First, we need a base case. If we look at n = 1, we need to know what F 0 is. But we haven't defined that Fibonacci number yet, so we will start at n = 2. In that case, we have F 1 F 3 \Gamma F 2 2 = 1 \Theta 2 \Gamma 1 = 2 \Gamma 1 = 1 = (\Gamma1) 2 : Next, we assume that F k\Gamma1 F k+1 \Gamma F 2 k = (\Gamma1) k and prove that F k<F43

Tiling and adaptive image compression

10.1109/18.857791IEEE Transactions on Information Theory4651789-1799IETT