RI/MOM Renormalization Window and Goldstone Pole Contamination

We perform a comparative study of the ratio of lattice (Wilson fermion) renormalization constants Z_P/Z_S, obtained non-perturbatively from the RI/MOM renormalization conditions and from Ward Identities of on- and off-shell Green's functions. The off-shell Ward Identity used in this work relies on correlation functions with non-degenerate quark masses. We find that, due to discretization effects, there is a 10-15% discrepancy between the two Ward Identity determinations at current bare couplings (beta values). The RI/MOM result is in the same range and has a similar systematic error of 10-15%. Thus, contrary to a previous claim, the contamination of the RI/MOM result from the presence of a Goldstone pole at scales of about 2 GeV is subdominant, compared to finite cutoff effects.Comment: LATEX, 12 pages final version to appear on Phys. Lett.

A Theoretical Prediction of the Bs-Meson Lifetime Difference

We present the results of a quenched lattice calculation of the operator matrix elements relevant for predicting the Bs width difference. Our main result is (\Delta\Gamma_Bs/\Gamma_Bs)= (4.7 +/- 1.5 +/- 1.6) 10^(-2), obtained from the ratio of matrix elements, R(m_b)=/<\bar B_s^0|Q_L|B_s^0>=-0.93(3)^(+0.00)_(-0.01). R(m_b) was evaluated from the two relevant B-parameters, B_S^{MSbar}(m_b)=0.86(2)^(+0.02)_(-0.03) and B_Bs^{MSbar}(m_b) = 0.91(3)^(+0.00)_(-0.06), which we computed in our simulation.Comment: 21 pages, 7 PostScript figure

Composition Operators on the Dirichlet Space and Related Problems

In this paper we investigate the following problem: when a bounded analytic function $\phi$ on the unit disk $\mathbb{D}$, fixing 0, is such that $\{\phi^n : n = 0, 1, 2, . . . \}$ is orthogonal in $\mathbb{D}$?, and consider the problem of characterizing the univalent, full self-maps of $\mathbb{D}$ in terms of the norm of the composition operator induced. The first problem is analogous to a celebrated question asked by W. Rudin on the Hardy space setting that was answered recently ([3] and [15]). The second problem is analogous to a problem investigated by J. Shapiro in [14] about characterization of inner functions in the setting of $H^2$.Comment: 8 pages, 1 figure. See also http://webdelprofesor.ula.ve/nucleotachira/gchacon or http://webdelprofesor.ula.ve/humanidades/grchaco

Topological Hunds rules and the electronic properties of a triple lateral quantum dot molecule

We analyze theoretically and experimentally the electronic structure and charging diagram of three coupled lateral quantum dots filled with electrons. Using the Hubbard model and real-space exact diagonalization techniques we show that the electronic properties of this artificial molecule can be understood using a set of topological Hunds rules. These rules relate the multi-electron energy levels to spin and the inter-dot tunneling $t$, and control charging energies. We map out the charging diagram for up to N=6 electrons and predict a spin-polarized phase for two holes. The theoretical charging diagram is compared with the measured charging diagram of the gated triple-dot device.Comment: 31 pages, 7 figures, accepted to March 15, 2007 issue of Phys. Rev. B, vol. 7

Non-perturbative Renormalization of the Complete Basis of Four-fermion Operators and B-parameters

We present results on the B-parameters $B_K$, $B^{3/2}_7$ and $B^{3/2}_8$, at $\beta=6.0$, with the tree-level Clover action. The renormalization of the complete basis of dimension-six four-fermion operators has been performed non-perturbatively. Our results for $B_K$ and $B^{3/2}_7$ are in reasonable agreement with those obtained with the (unimproved) Wilson action. This is not the case for $B^{3/2}_8$. We also discuss some subtleties arising from a recently proposed modified definition of the B-parameters.Comment: Talk presented at Lattice '97, Edinburgh (UK), July 1997. LaTeX 3 pages, uses espcrc

Visualizing the Doppler Effect

The development of Information and Communication Technologies suggests some spectacular changes in the methods used for teaching scientific subjects. Nowadays, the development of software and hardware makes it possible to simulate processes as close to reality as we want. However, when we are trying to explain some complex physical processes, it is better to simplify the problem under study using simplified pictures of the total process by eliminating some elements that make it difficult to understand this process. In this work we focus our attention on the Doppler effect which requires the space-time visualization that is very difficult to obtain using the traditional teaching resources. We have designed digital simulations as a complement of the theoretical explanation in order to help students understand this phenomenon.Comment: 16 pages, 8 figure

Quark masses and the chiral condensate with a non-perturbative renormalization procedure

We determine the quark masses and the chiral condensate in the MSbar scheme at NNLO from Lattice QCD in the quenched approximation at beta=6.0, beta=6.2 and beta=6.4 using both the Wilson and the tree-level improved SW-Clover fermion action. We extract these quantities using the Vector and the Axial Ward Identities and non-perturbative values of the renormalization constants. We compare the results obtained with the two methods and we study the O(a) dependence of the quark masses for both actions.Comment: LATTICE98(spectrum), 3 pages, 1 figure, Edinburgh 98/1