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This talk is divided in two parts. In the first part, we will summarize the status of the APEmille project that will be completed by the end of the year. We will then devote the rest of the talk to the description of a new project for a multi-TeraFlop machine, apeNEXT. The interested reader will find a much more detailed discussion of all the items touched upon here in the full proposal of the project that will shortly appear on hep-lat. © 2001 Elsevier Science B.V. All rights reserved.

We present results for the Kaon $B$ parameter from a sample of $200$ configurations using the Wilson action and $460$ configurations using the Clover action, on a $18^3 \times 64$ lattice at $\beta=6.0$. A slight improvement of the chiral behaviour of $B_K$ is observed due to the Clover action. We have also compared the results for $B_K$ obtained from two different procedures for the boosting of the coupling constant $g$. We observe a strong dependence of $B_K$ on the prescription adopted for $g$ in the Wilson case, contrary to the results of the Clover case which are almost unaffected by the choice of $g$. Combining some recently obtained non perturbative estimates for the renormalisation constants with our Clover matrix element, we observe a significant improvement in the chiral behaviour of $B_K$., Comment: 3 pages, Latex, Postscript file with figures available at ftp://hpteo.roma1.infn.it/pub/preprints/lat94/donini ; to appear in Lattice '94, Nucl. Phys. (Proc.Suppl.)

We describe APEmille, the latest generation of the APE parallel processors. This machine, an evolution of the APE100 concept, is very efficient for LGT simulations as well as for a broader class of applications requiring massive floating point computations. Several new features characterise this evolution. In particular local addressing capabilities are added to all computing nodes. APEmille also exhibits a higher degree of integration with a network of workstations acting as a global host system. An APEmille system in the Teraflops range will be completed in three-four years. The architecture proposed in this paper is being currently simulated and evaluated. © 1995 Elsevier Science B.V. All rights reserved.

We describe the architecture of the APEmille Parallel Computer, the new generation of the APE family of processors optimized for Lattice Gauge Theory simulations. We emphasize the features of the new machine potentially useful for applications in other areas of computational physics.

We present the results of a numerical calculation of the B\rightarrow K^* \gamma form factors. The results have been obtained by studying the relevant correlation functions at \beta=6.0, on an 18^3 \times 64 lattice, using the {\rm O(a)}-improved fermion action, in the quenched approximation. From the study of the matrix element \langle K^*\vert \bar s \sigma_{\mu\nu} b \vert B\rangle we have obtained the form factor T_1(0) which controls the exclusive decay rate. The results are compared with the recent results from CLEO. We also discuss the compatibility between the scaling laws predicted by the Heavy Quark Effective Theory (HQET) and pole dominance, by studying the mass- and q^2-dependence of the form factors. From our analysis, it appears that the form factors follow a mass behaviour compatible with the predictions of the HQET and that the q^2-dependence of T_2 is weaker than would be predicted by pole dominance. We present the results of a numerical calculation of the $B\rightarrow K~* \gamma$ form factors. The results have been obtained by studying the relevant correlation functions at $\beta=6.0$, on an $18~3 \times 64$ lattice, using the ${\rm O(a)}$-improved fermion action, in the quenched approximation. From the study of the matrix element $ \langle K~*\vert \bar s \sigma_{\mu\nu} b \vert B\rangle$ we have obtained the form factor $T_1(0)$ which controls the exclusive decay rate. The results are compared with the recent results from CLEO. We also discuss the compatibility between the scaling laws predicted by the Heavy Quark Effective Theory (HQET) and pole dominance, by studying the mass- and $q~2$-dependence of the form factors. From our analysis, it appears that the form factors follow a mass behaviour compatible with the predictions of the HQET and that the $q~2$-dependence of $T_2$ is weaker than would be predicted by pole dominance. We present the results of a numerical calculation of the B → K ∗ γ form factors. The results have been obtained by studying the relevant correlation functions at β = 6.0, on an 18 3 × 64 lattice, using the O ( a )-improved fermion action, in the quenched approximation. From the study of the matrix element 〈K ∗ | s σ μν b|B〉 we have obtained the form factor T 1 (0) which controls the exclusive decay rate. The results are compared with the recent results from CLEO. We also discuss the compatibility between the scaling laws predicted by the Heavy Quark Effective Theory (HQET) and pole dominance, by studying the mass- and q 2 -dependence of the form factors. From our analysis, it appears that the form factors follow a mass behaviour compatible with the predictions of the HQET and that the q 2 -dependence of T 2 is weaker than would be predicted by pole dominance.

We present the results of a high statistics lattice calculation of hadronic form factors relevant for $D-$ and $B-$meson semi-leptonic decays into light pseudoscalar and vector mesons. The results have been obtained by averaging over 170 gauge field configurations, generated in the quenched approximation, at $\beta=6.0$, on a $18^3 \times 64$ lattice, using the $O(a)$-improved SW-Clover action.From the study of the matrix element $$, we obtain $f_+ (0)=0.78\pm 0.08$ and from the matrix element $$ we obtain $V(0)=1.08\pm 0.22$, $A_1(0)=0.67\pm 0.11$ and $A_2(0)=0.49\pm 0.34$. We also obtain the ratios $V(0)/A_1(0)=1.6\pm 0.3$ and $A_2(0)/A_1(0)= 0.7\pm 0.4$. Our predictions for the different form factors are in good agreement with the experimental data, although, in the case of $A_2(0)$, the errors are still too large to draw any firm conclusion. With the help of the Heavy Quark Effective Theory (HQET) we have also extrapolated the lattice results to $B$-meson decays. The form factors follow a behaviour compatible with the HQET predictions. Our results are in agreement with a previous lattice calculation, performed at $\beta=6.4$, using the standard Wilson action., Comment: LaTeX, 15 pages, postscript figures attached uuencoded

We present results for the radiative decay B --> K*gamma, obtained by using the Clover action at beta = 6.0 on APE. The compatibility between the scaling laws predicted by the Heavy Quark Effective Theory (HQET) and pole dominance is discussed. The final result depends crucially on the assumed q(2)-dependence of the form factors