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We systematically examine various proposals which aim at increasing the accuracy in the determination of the renormalization of two-fermion lattice operators. We concentrate on three finite quantities which are particularly suitable for our study: the renormalization constants of the vector and axial currents and the ratio of the renormalization constants of the scalar and pseudoscalar densities. We calculate these quantities in boosted perturbation theory, with several running boosted couplings, at the "optimal" scale q*. We find that the results of boosted perturbation theory are usually (but not always) in better agreement with non-perturbative determinations of the renormalization constants than those obtained with standard perturbation theory. The finite renormalization constants of two-fermion lattice operators are also obtained non-perturbatively, using Ward Identities, both with the Wilson and the tree-level Clover improved actions, at fixed cutoff ($\beta$=6.4 and 6.0 respectively). In order to amplify finite cutoff effects, the quark masses (in lattice units) are varied in a large interval 0, Comment: 54 pages, Latex, 5 figures. Minor changes in text between eqs.(86) and (88)

We present results for the kaon $B$-parameter $B_K$ from a sample of $200$ configurations using the Wilson action and $460$ configurations using the SW-Clover action, on a $18^3 \times 64$ lattice at $��=6.0$. We compare results obtained by renormalizing the relevant operator with different ``boosted" values of the strong coupling constant $��_s$. In the case of the SW-Clover action, we also use the operator renormalized non-perturbatively. In the Wilson case, we observe a strong dependence of $B_K$ on the prescription adopted for $��_s$, contrary to the results of the Clover case which are almost unaffected by the choice of the coupling. We also find that the matrix element of the operator renormalized non-perturbatively has a better chiral behaviour. This gives us our best estimate of the renormalization group invariant $B$-parameter, $\hat B_K=0.86 \pm 0.15$., LaTeX, 17 pages, 3 postscript figures uuencoded

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 $��=6.0$. 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 $B_K$., 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 present a calculation of $f_B$ in the static limit, obtained by numerical simulation of quenched QCD, at $��=6.2$ on a $18^3 \times 64$ lattice, using the SW-Clover quark action. The decay constant has been extracted by studying heavy(static)-light correlation functions of different smeared operators, on a sample of 220 gauge field configurations. We have obtained $f_B^{static}=(290 \pm 15 \pm 45)$ MeV, where the first error comes from the uncertainty in the determination of the matrix element and the second comes from the uncertainty in the lattice spacing. We also obtain $M_{B_s}-M_{B_d}= (70 \pm 10)$ MeV and $f^{stat}_{B_s}/f^{stat}_{B_d}=1.11(3)$. A comparison of our results with other calculations of the same quantity is made., 12 pages, LaTex, 3 figs. (figures not included; available upon request from lubicz@roma1.infn.it) ROME prep. 94/981, 18 February 1994

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

The decay constant for the B-meson in the static limit is calculated using the Wilson and clover actions at various lattice spacings. We show that both the contamination of our results by excited states and the effects finite lattice spacing are at most the order of the statistical uncertainties. A comparison is made of our results and those obtained in other studies. Values for $f^{stat}_{B_S}/f^{stat}_B$ and $M_{B_S} - M_B$ are also given., Contribution to Lattice'94, 3 pages PostScript, uuencoded compressed

Using the results of several quenched lattice simulations, we predict the value of the strange and charm quark masses in the continuum at the next-to-leading order, $m^{\overline{MS}}_s(\mu=2\,\, \rm{GeV})= (127 \pm 18)\,\, \rm{MeV}$ and $m^{\overline{MS}}_{ch}(\mu=2 \,\,\rm{GeV})=(1.47 \pm 0.28)\,\, \rm{GeV}$. The errors quoted above have been estimated by taking into account the original statistical error of the lattice results and the uncertainties coming from the matching of the lattice to the continuum theory. A detailed presentation of the relevant formulae at the next-to-leading order and a discussion of the main sources of errors is also presented., Comment: 26 pages (2 postscript file included), LaTeX, CERN-TH.7256/94, ROME prep. 94/1018

Recent results for semi-leptonic decays of $D$ and $B$ mesons at $\beta=6.4$, using the Wilson action, and at $\beta=6.0$, using the Clover action, are reported., Comment: at the Dallas Lattice Conference, October 1993. 3 pages in a single postscript file, uuencoded form. Rome Preprint 93/986

We present the results of a numerical calculation of semi-leptonic form factors relevant for heavy flavour meson decays into light mesons, at $\beta=6.4$ on a $24^3 \times 60$ lattice, using the Wilson action in the quenched approximation. We obtain $f^+_K(0)=0.65\pm 0.18$, $V(0)=0.95\pm 0.34$, $A_1(0)=0.63\pm 0.14 $ and $A_2(0)=0.45\pm 0.33 $. We also obtain $A_1(q^2_{max})=0.62\pm 0.09$, $V(0)/A_1(0)=1.5\pm 0.28 $ and $A_2(0)/A_1(0)=0.7\pm 0.4$. The results for $f^+_K(0)$, $V(0)$ and $A_1(0)$ are consistent with the experimental data and with previous lattice determinations with larger lattice spacings. In the case of $A_2(0)$ the errors are too large to draw any firm conclusion. We have also extrapolated the form factors to the B meson, showing a behaviour compatible with the predictions by the heavy quark effective theory (HQET). Within large uncertainties, our results suggest that $A_2/A_1$ increases with the heavy quark mass. We also get very rough estimates for the partial decay widths $B \rightarrow \pi l \nu_l)=\vert V_{ub} \vert^2 (12 \pm 8) 10^{12} s^{-1}$ and $\Gamma(B \rightarrow \rho l \nu_l)=\vert V_{ub} \vert^2 (13 \pm12) 10^{12} s^{-1}$, which can be used to give upper bounds on the rates, Comment: 21 pages, LaTeX

The decay constants of the heavy-light pseudoscalar mesons are studied in a high statistics run using the Wilson action at $\beta=6.0$ and $\beta=6.2$, and the clover action at $\beta=6.0$. The systematics of $O(a)$ discretisation errors are discussed. Our best estimates of the decay constants are: $f_D$ = 218(9) MeV, $f_D/f_{Ds}$ = 1.11(1) and we obtain preliminary values for $f_B$., Comment: at the Dallas Lattice Conference, October 1993. 3 pages in a single postscript file, uuencoded form. Rome Preprint 93/985

We present a high statistics study of the D- and B-meson decay constants. The results were obtained by using the Clover and Wilson lattice actions at two different values of the lattice spacing $a$, corresponding to $\beta=6.0$ and 6.2. After a careful analysis of the systematic errors present in the extraction of the physical results, by assuming quite conservative discretization errors, we find $f_{D_s}=237 \pm 16$ MeV, $f_{D} = 221 \pm 17$ MeV ($f_{D_s}/f_D=1.07(4)$), $f_{B_s} = 205 \pm 35$ MeV, $f_{B} = 180 \pm 32$ MeV ($f_{B_s}/f_B=1.14(8)$), in good agreement with previous estimates., Comment: 15 pages, Latex with one postscript figure