Indirect determination of the Kugo-Ojima function from lattice data

We study the structure and non-perturbative properties of a special Green's function, u(q), whose infrared behavior has traditionally served as the standard criterion for the realization of the Kugo-Ojima confinement mechanism. It turns out that, in the Landau gauge, u(q) can be determined from a dynamical equation, whose main ingredients are the gluon propagator and the ghost dressing function, integrated over all physical momenta. Using as input for these two (infrared finite) quantities recent lattice data, we obtain an indirect determination of u(q). The results of this mixed procedure are in excellent agreement with those found previously on the lattice, through a direct simulation of this function. Most importantly, in the deep infrared the function deviates considerably from the value associated with the realization of the aforementioned confinement scenario. In addition, the dependence of u(q), and especially of its value at the origin, on the renormalization point is clearly established. Some of the possible implications of these results are briefly discussed.Comment: 25 pages, 10 figures; v2: typos corrected, expanded version that matches the published articl

Vacuum energy as a c-function for theories with dynamically generated masses

We argue that in asymptotically free non-Abelian gauge theories possessing the phenomenon of dynamical mass generation the $\beta$ function is negative up to a value of the coupling constant that corresponds to a non-trivial fixed point, in agreement with recent AdS/QCD analysis. This fixed point happens at the minimum of the vacuum energy ($\Omega$), which, as a characteristic of theories with dynamical mass generation, has the properties of a c-function.Comment: 12 pages, 3 figure

Development of an error compensation case study for 3D printers

The paper developed presents a case study that allows students to learn an easy way to improve the accuracy of low cost 3D printers. The document detailed a methodology to achieve this goal. First, it is necessary to print an initial CAD design. A commercial scanner is calibrated and the pieces are scanned to obtain the different errors. Then, a program is generated to compensate the code numerical control of the printer. This fact allows students to print a new piece having less errors than before, which it involves improve the printer accuracy

Quark gap equation within the analytic approach to QCD

The compatibility between the QCD analytic invariant charge and chiral symmetry breaking is examined in detail. The coupling in question incorporates asymptotic freedom and infrared enhancement into a single expression, and contains only one adjustable parameter with dimension of mass. When inserted into the standard form of the quark gap-equation it gives rise to solutions displaying singular confining behavior at the origin. By relating these solutions to the pion decay constant, a rough estimate of about 880 MeV is obtained for the aforementioned mass-scale.Comment: Talk given by J.P. at 12th International QCD Conference (QCD05), 4 - 9 July 2005, Montpellier, France; 4 pages, 3 figure

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

Non-perturbative momentum dependence of the coupling constant and hadronic models

Models of hadron structure are associated with a hadronic scale which allows by perturbative evolution to calculate observables in the deep inelastic region. The resolution of Dyson-Schwinger equations leads to the freezing of the QCD running coupling (effective charge) in the infrared, which is best understood as a dynamical generation of a gluon mass function, giving rise to a momentum dependence which is free from infrared divergences. We use this new development to understand why perturbative treatments are working reasonably well despite the smallness of the hadronic scale.Comment: Changes in Acknowledgments and PACS number

Education Software for the Modelling and Calibration of Kinematic Mechanisms

AbstractThis paper presents a new software for teaching the most important aspects of modelling, characterization and calibration of parallel mechanisms by means of the kinematic model, the kinematic parameter identification and the control of the system actuators and sensors. This application allows the student to develop competencies such as analysis and synthesis, to solve problems, research skills and to apply their knowledge.The developed tool presents a special interest in areas such as education, industry and research, since the application interface allows the user to carry out the different steps of the calibration procedure in an easy way. Besides, only one application is necessary to perform all the procedure for data acquisition and kinematic parameter identification.Moreover, thanks to the flexibility that the developed software offers in the programming, a senior undergraduate student can modify different algorithm variables and analyze the effects that take place with these changes. This application therefore presents an important utility as a teaching tool for the learning process and analysis of the different steps in the parallel mechanism optimization

Identification and Kinematic Calculation of Laser Tracker Errors

AbstractCalibration of Laser Tracker systems is based most times in the determination of its geometrical errors. Some standards as the ASME B89.4.19 (2006) and the VDI 2617-10 (2011) describe different tests to calculate the geometric misalignments that cause systematic errors in Laser Tracker measurements. These errors are caused not only because of geometrical misalignments and other sources of error must also be taken in count. In this work we want to express the errors in a kinematic form. Errors will be split in two different components, geometric and kinematic errors. The first ones depend on the offsets, tilts and eccentricity of the mechanical and optical components of the system. Kinematic errors are different for every position of the Laser tracker, so they must be formulated as functions of three system variables: range (R), vertical angle (V) and horizontal angle (H). The goal of this work is to set up an evaluation procedure to determine geometric and kinematic errors of Laser Trackers

A study of the Gribov copies in linear covariant gauges in Euclidean Yang-Mills theories

The Gribov copies and their consequences on the infrared behavior of the gluon propagator are investigated in Euclidean Yang-Mills theories quantized in linear covariant gauges. Considering small values of the gauge parameter, it turns out that the transverse component of the gluon propagator is suppressed, while its longitudinal part is left unchanged. A Green function, G_{tr}, which displays infrared enhancement and which reduces to the ghost propagator in the Landau gauge is identified. The inclusion of the dimension two gluon condensate is also considered. In this case, the transverse component of the gluon propagator and the Green function G_{tr} remain suppressed and enhanced, respectively. Moreover, the longitudinal part of the gluon propagator becomes suppressed. A comparison with the results obtained from the studies of the Schwinger-Dyson equations and from lattice simulations is provided.Comment: 20 page

Confinement, the gluon propagator and the interquark potential for heavy mesons

The interquark static potential for heavy mesons described by a massive One Gluon Exchange interaction obtained from the propagator of the truncated Dyson-Schwinger equations does not reproduced the expected Cornell potential. I show that no formulation based on a finite propagator will lead to confinement of quenched QCD. I propose a mechanism based on a singular nonperturbative coupling constant which has the virtue of giving rise to a finite gluon propagator and (almost) linear confinement. The mechanism can be slightly modified to produce the screened potentials of unquenched QCD.Comment: 12 pages and 7 figure