Low-Lying Eigenvalues of the Wilson-Dirac Operator

An exploratory study of the low-lying eigenvalues of the Wilson-Dirac operator and their corresonding eigenvectors is presented. Results for the eigenvalues from quenched and unquenched simulations are discussed. The eigenvectors are studied with respect to their localization properties in the quenched approximation for the cases of SU(2) and SU(3).Comment: Poster presented at LATTICE96(poster). 4 pages, LaTeX, fully coloured versions of Figs. 4 and 5 are included as separate gzipped PostScript files or can be obtained from http://www.desy.de/library/cgi-bin/showprep.pl?desy-rep%2F199615

The Λ\Lambda-parameter in 3-flavour QCD and αs(mZ)\alpha_s(m_Z) by the ALPHA collaboration

We present results by the ALPHA collaboration for the $\Lambda$-parameter in 3-flavour QCD and the strong coupling constant at the electroweak scale, $\alpha_s(m_Z)$, in terms of hadronic quantities computed on the CLS gauge configurations. The first part of this proceedings contribution contains a review of published material \cite{Brida:2016flw,DallaBrida:2016kgh} and yields the $\Lambda$-parameter in units of a low energy scale, $1/L_{\rm had}$. We then discuss how to determine this scale in physical units from experimental data for the pion and kaon decay constants. We obtain $\Lambda_{\overline{\rm MS}}^{(3)} = 332(14)$ MeV which translates to $\alpha_s(M_Z)=0.1179(10)(2)$ using perturbation theory to match between 3-, 4- and 5-flavour QCD.Comment: 21 pages. Collects contributions of A. Ramos, S. Sint and R. Sommer to the 34th annual International Symposium on Lattice Field Theory; LaTeX input encoding problem fixe

CP Violation and Strong Phases from Penguins in B±→VV\bf B^{\pm}\rightarrow VV Decays

We calculate direct CP-violating observables in charged $B\to VV$ decays arising from the interference of amplitudes with different strong and CKM phases. The perturbative strong phases develop at order $\alpha_s$ from absorptive parts of one-loop matrix elements of the next-to-leading logarithm corrected effective Hamiltonian. CPT constraints are maintained. Based on this model, we find that partial rate asymmetries between charge conjugate $B^{\pm}$ decays can be as high as 15-30\% for certain channels with branching ratios in the $10^{-6}$ range. The small values of the coefficients of angular correlations, which we calculated previously to be of order $10^{-2}$, are not significantly degraded by the strong phases. The charge asymmetries of rates and angular distributions would provide unambiguous evidence for direct CP violation.Comment: 24 pages, 3 figures (upon request), LaTeX, preprint DESY 93-19

A new simulation algorithm for lattice QCD with dynamical quarks

A previously introduced multi-boson technique for the simulation of QCD with dynamical quarks is described and some results of first test runs on a $6^3\times12$ lattice with Wilson quarks and gauge group SU(2) are reported.Comment: 7 pages, postscript file (166 KB

Dynamical Simulations of Lattice QCD

Lattice calculations of Quantum Chromodynamics (QCD) are continuously becoming more realistic. Where Ukawa famously concluded only fourteen years ago that simulations including two physically light sea quarks are basically impossible even with today’s computers, algorithmic developments over the last years have changed this situation drastically. Nowadays up and down quark masses light enough to control the chiral extrapolation reliably are standard and also the sea quark effects of strange (and charm) quark are included.Modern lattice simulations are an intricate interplay between a large variety of numerical methods on one side and the computer hardware on the other side. The main areas of progress have been the solvers used for the Dirac equation, fermion determinant factorisations and better integrators for the molecular dynamics which is at the heart of most algorithms used for QCD simulations.In lattice QCD simulations the path integral is computed via a Markov Chain Monte Carlo method. In virtually all projects with dynamical fermions a variant of the Hybrid Monte Carlo algorithm is employed to generate the Markov chain, where the fields are updated using molecular dynamics. But there is considerable freedom in how to include the fermion determinant into the simulation. Factorisations of this determinant have been essential in the progress of recent years, being successful in particular together with improved integrators of the molecular dynamics.The solution of the Dirac equation constitutes the most computer time consuming element of simulations with fermions. The dramatic speedup for small fermion mass due to locally deflated solvers5, 6 has therefore had a significant impact on what is possible in the simulations. These algorithms have practically eliminated the increase in cost of the solution as the quark mass is lowered

Preparing for N(f) = 2 simulations at small lattice spacings

We discuss some large effects of dynamical fermions. One is a cutoff effect, others concern the contribution of multi-pion states to correlation functions and are expected to survive the continuum limit. We then turn to the preparation for simulations at small lattice spacings which we are planning down to around a=0.04fm in order to understand the size of O(a^2)-effects of the standard O(a)-improved theory. The dependence of the lattice spacing on the bare coupling is determined through the Schr'odinger functional renormalized coupling

B-physics with Nf=2N_f=2 Wilson fermions

We report the final results of the ALPHA collaboration for some B-physics observables: $f_B$, $f_{B_s}$ and $m_b$. We employ CLS configurations with 2 flavors of $O(a)$ improved Wilson fermions in the sea and pion masses ranging down to 190 MeV. The b-quark is treated in HQET to order $1/m_b$. The renormalization, the matching and the improvement were performed non-perturbatively, and three lattice spacings reaching $a=0.048$ fm are used in the continuum extrapolation

CP-Violating Asymmetries in Charmless Non-Leptonic Decays B→PP,PV,VVB \to PP, PV, VV in the Factorization Approach

We present estimates of the direct (in decay amplitudes) and indirect (mixing- induced) CP-violating asymmetries in the non-leptonic charmless two-body decay rates for $B \to PP$, $B \to PV$ and $B \to VV$ decays and their charged conjugates, where P(V) is a light pseudoscalar (vector) meson. These estimates are based on a generalized factorization approach making use of next-to-leading order perturbative QCD contributions which generate the required strong phases. No soft final state interactions are included. We study the dependence of the asymmetries on a number of input parameters and show that there are at least two (possibly three) classes of decays in which the asymmetries are parametrically stable in this approach. The decay modes of particular interest are: \optbar{B^0} \to \pi^+ \pi^-, \optbar{B^0} \to K_S^0 \pi^0, \optbar{B^0} \to K_S^0 \eta^\prime, \optbar{B^0} \to K_S^0 \eta and \optbar{B^0} \to \rho^+ \rho^-. Likewise, the CP-violating asymmetry in the decays \optbar{B^0} \to K_S^0 h^0 with $h^0=\pi^0,K_S^0, \eta,\eta^\prime$ is found to be parametrically stable and large. Measurements of these asymmetries will lead to a determination of the phases $\sin 2\alpha$ and $\sin 2 \beta$ and we work out the relationships in these modes in the present theoretical framework. We also show the extent of the so-called "penguin pollution" in the rate asymmetry $A_{CP}(\pi^+ \pi^-)$ and of the "tree shadow" in the asymmetry $A_{CP}(K_S^0\eta^\prime)$ which will effect the determination of $\sin 2 \alpha$ and $\sin 2 \beta$ from the respective measurements. CP-violating asymmetries in $B^\pm \to \pi^\pm \eta^\prime$, $B^\pm \to K^{*\pm} \eta$, $B^\pm \to K^{*\pm} \eta^\prime$ and $B^\pm \to K^{*\pm}\rho^0$ are potentially interesting and are studied here.Comment: 42 pages (LaTex) including 19 figures, requires epsfig.sty; submitted to Phys. Rev.

Progress and status of APEmille

We report on the progress and status of the APEmille project: a SIMD parallel computer with a peak performance in the TeraFlops range which is now in an advanced development phase. We discuss the hardware and software architecture, and present some performance estimates for Lattice Gauge Theory (LGT) applications.Comment: Talk presented at LATTICE97, 3 pages, Late

Direct CP Violation in Hadronic B Decays

There are different approaches for the hadronic B decay calculations, recently. In this paper, we upgrade three of them, namely factorization, QCD factorization and the perturbative QCD approach based on $k_T$ factorization, by using new parameters and full wave functions. Although they get similar results for many of the branching ratios, the direct CP asymmetries predicted by them are different, which can be tested by recent experimental measurements of B factories.Comment: 11 pages, 3 figures, revtex4, Talk given at the Workshop on the Frontiers of Theoretical Physics and Cross-Disciplinary, NSFC, Beijing, March 200