Quenched lattice calculation of the B --> D l nu decay rate

We calculate, in the continuum limit of quenched lattice QCD, the form factor that enters in the decay rate of the semileptonic decay B --> D l nu. Making use of the step scaling method (SSM), previously introduced to handle two scale problems in lattice QCD, and of flavour twisted boundary conditions we extract G(w) at finite momentum transfer and at the physical values of the heavy quark masses. Our results can be used in order to extract the CKM matrix element Vcb by the experimental decay rate without model dependent extrapolations.Comment: 5 pages, 4 figures, accepted for publication on Phys. Lett. B, corrected one typ

The three-loop beta function of SU(N) lattice gauge theories with Wilson fermions

We calculate the third coefficient of the lattice beta function associated with the Wilson formulation for both gauge fields and fermions. This allows us to evaluate the three-loop correction (linear in $g_0^2$) to the relation between the lattice Lambda-parameter and the bare coupling $g_0$, which is important in order to verify asymptotic scaling predictions. Our calculation also leads to the two-loop relation between the coupling renormalized in the MSbar scheme and $g_0$. The original version of this paper contained a numerical error in one of the diagrams, which has now been corrected. The calculations, as well as the layout of the paper have remained identical, but there are some important changes in the numerical results.Comment: One 14-page LaTeX file, one PostScript file containing 2 figures. Corrected a numerical error in one of the diagrams. The calculations, as well as the layout of the paper have remained unaffected, but there are some important changes in the numerical result

Higgs mediated flavor violating top quark decays t --> u_i H, u_i gamma, u_i gamma gamma, and the process gamma gamma --> t c in effective theories

The rare top quark couplings $tu_i\gamma$ and $tu_i\gamma \gamma$ ($u_i=u,c$) induced at the one-loop level by a flavor violating $tu_iH$ vertex are studied within the context of an effective Yukawa sector that incorporates $SU_L(2)\times U_Y(1)$-invariant operators of up to dimension six. Data on the recently observed $D^0-\overline{D^0}$ mixing are employed to constrain the $tu_iH$ vertex, which is then used to predict the $t\to u_iH$, $t\to u_i\gamma$, and $t\to u_i\gamma \gamma$ decays, as well as the $\gamma \gamma \to \bar{t}u_i+t\bar{u}_i$ reaction in the context of the ILC. It is found that the $t\to cH$ and $t\to c\gamma \gamma$ decays can reach sizable branching ratios as high as $5\times 10^{-3}$ and $10^{-4}$, respectively. As for the $t\to c\gamma$ decay, it can have a branching ratio of $5\times 10^{-8}$ that is about 6 orders of magnitude larger than the standard model prediction, which, however, is still very small to be detected. As for $tc$ production, it is found that, due to the presence of a resonant effect in the convoluted cross section $\sigma(e^+e^-\to \gamma \gamma \to t\bar{c}+\bar{t}c)$, about $(0.5 - 2.7)\times 10^{3}$ $tc$ events may be produced at the ILC for a value of the Higgs mass near to the top mass.Comment: 5 pages and 3 figure

Brief review on semileptonic B decays

We concisely review semileptonic B decays, focussing on recent progress on both theoretical and experimental sides.Comment: 18 pages, 2 figures; version to be published in Mod. Phys. Lett.

B→D(∗)B \to D^{(*)} Form Factors from QCD Light-Cone Sum Rules

We derive new QCD sum rules for $B\to D$ and $B\to D^*$ form factors. The underlying correlation functions are expanded near the light-cone in terms of $B$-meson distribution amplitudes defined in HQET, whereas the $c$-quark mass is kept finite. The leading-order contributions of two- and three-particle distribution amplitudes are taken into account. From the resulting light-cone sum rules we calculate all B\to \Dst form factors in the region of small momentum transfer (maximal recoil). In the infinite heavy-quark mass limit the sum rules reduce to a single expression for the Isgur-Wise function. We compare our predictions with the form factors extracted from experimental B\to \Dst l \nu_l decay rates fitted to dispersive parameterizations.Comment: 20 pages, 6 figures; one reference, one figure and several comments added; version to appear in European Physical Journal

Non-perturbative determination of improvement b

We present our preliminary results of the non-perturbative determination of the valence mass dependent coefficients bA - bP and bm as well as the ratio ZPZm=ZA entering the flavour non-singlet PCAC relation in lattice QCD with Nf = 3 dynamical flavours. We apply the method proposed in the past for quenched approximation and Nf = 2 cases, employing a set of finite-volume ALPHA configurations with Schrödinger functional boundary conditions, generated with O(a) improved Wilson fermions and the tree-level Symanzik-improved gauge action for a range of couplings relevant for simulations at lattice spacings of about 0.09 fm and below

The (LATTICE) QCD Potential and Running Coupling: How to Accurately Interpolate between Multi-Loop QCD and the String Picture

We present a simple parameterization of a running coupling constant, defined via the static potential, that interpolates between 2-loop QCD in the UV and the string prediction in the IR. Besides the usual \Lam-parameter and the string tension, the coupling depends on one dimensionless parameter, determining how fast the crossover from UV to IR behavior occurs (in principle we know how to take into account any number of loops by adding more parameters). Using a new Ansatz for the LATTICE potential in terms of the continuum coupling, we can fit quenched and unquenched Monte Carlo results for the potential down to ONE lattice spacing, and at the same time extract the running coupling to high precision. We compare our Ansatz with 1-loop results for the lattice potential, and use the coupling from our fits to quantitatively check the accuracy of 2-loop evolution, compare with the Lepage-Mackenzie estimate of the coupling extracted from the plaquette, and determine Sommer's scale $r_0$ much more accurately than previously possible. For pure SU(3) we find that the coupling scales on the percent level for $\beta\geq 6$.Comment: 47 pages, incl. 4 figures in LaTeX [Added remarks on correlated vs. uncorrelated fits in sect. 4; corrected misprints; updated references.

Infrared behavior of the gluon propagator in lattice Landau gauge: the three-dimensional case

We evaluate numerically the three-momentum-space gluon propagator in the lattice Landau gauge, for three-dimensional pure-SU(2) lattice gauge theory with periodic boundary conditions. Simulations are done for nine different values of the coupling $\beta$, from $\beta = 0$ (strong coupling) to $\beta = 6.0$ (in the scaling region), and for lattice sizes up to $V = 64^3$. In the limit of large lattice volume we observe, in all cases, a gluon propagator decreasing for momenta smaller than a constant value $p_{dec}$. From our data we estimate $p_{dec} \approx 350$ MeV. The result of a gluon propagator decreasing in the infrared limit has a straightforward interpretation as resulting from the proximity of the so-called first Gribov horizon in the infrared directions.Comment: 14 pages, BI-TP 99/03 preprint, correction in the Acknowledgments section. To appear in Phys.Rev.

Non-perturbative renormalization of QCD

In these lectures, we discuss different types of renormalization problems in QCD and their non-perturbative solution in the framework of the lattice formulation. In particular the recursive finite size methods to compute the scale-dependence of renormalized quantities is explained. An important ingredient in the practical applications is the Schr\"odinger functional. It is introduced and its renormalization properties are discussed. Concerning applications, the computation of the running coupling and the running quark mass are covered in detail and it is shown how the $\Lambda$-parameter and renormalization group invariant quark mass can be obtained. Further topics are the renormalization of isovector currents and non-perturbative Symanzik improvement.Comment: 49 pages, lectures at Schladming-9