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Motivated by the calculation of observables in the decays $\Lambda_b \to \Lambda_c\left({1 \over 2}^\pm \right) \ell \overline{\nu}$, as tests of Lepton Flavor Universality, we present a calculation of form factors in the quark model. Our scheme combines a spectroscopic model, providing the internal wave functions, and the Bakamjian-Thomas relativistic formalism to deduce the wave functions in motion and current matrix elements, that amount in the heavy quark limit to the Isgur-Wise (IW) function. For baryons we meet difficulties using standard spectroscopic models, leading us to propose a simple phenomenological model : a Q-pointlike-diquark model, non-relativistic with harmonic oscillator forces, with a reasonable low-lying spectrum and good slope of the IW function. We extract this slope from Lattice data and find $\rho_\Lambda^2 \sim 2$. We are not able to reproduce the right $\rho_\Lambda^2$ when using standard linear + Coulomb potential models, both with three quarks $Qqq$ or in a Q-pointlike-diquark picture. These difficulties seem to derive from the high sensitivity of $\rho_\Lambda^2$ to the structure of the light quark subsystem. After fixing the parameters of our interim model to yield correct spectrum and $\rho_\Lambda^2$, we compute observables. Bjorken sum rule shows that the inelastic IW function is large, and therefore $\Lambda_b \to \Lambda_c \left({1 \over 2}^-, {3 \over 2}^- \right) \ell \overline{\nu}$ could be studied at LHCb. Some observables in the $\tau$ case present zeroes for specific values of $q^2$ that could be tests of the Standard Model., Comment: 62 pages, 30 figures

We compute the decays ${B\to D^\ast_0}$ and ${B\to D^\ast_2}$ with finite masses for the $b$ and $c$ quarks. We first discuss the spectral properties of both the $B$ meson as a function of its momentum and of the $D^\ast_0$ and $D^\ast_2$ at rest. We compute the theoretical formulae leading to the decay amplitudes from the three-point and two-point correlators. We then compute the amplitudes at zero recoil of ${B\to D^\ast_0}$ which turns out not to be vanishing contrary to what happens in the heavy quark limit. This opens a possibility to get a better agreement with experiment. To improve the continuum limit we have added a set of data with smaller lattice spacing. The ${B\to D^\ast_2}$ vanishes at zero recoil and we show a convincing signal but only slightly more than 1 sigma from 0. In order to reach quantitatively significant results, we plan to fully exploit smaller lattice spacings as well as another lattice regularization., Comment: 31 pages with 15 figures ; sections 5 and 6 revised and updated

This letter reports on a new procedure for the lattice spacing setting that takes advantage of the very precise determination of the strong coupling in Taylor scheme. Although it can be applied for the physical scale setting with the experimental value of $\Lambda_{\overline{\rm MS}}$ as an input, the procedure is particularly appropriate for relative "calibrations". The method is here applied for simulations with four degenerate light quarks in the sea and leads to prove that their physical scale is compatible with the same one for simulations with two light and two heavy flavours., Comment: 5 pages, 2 tables

We present a lattice calculation of the renormalized running coupling constant in symmetric (MOM) and asymmetric ($\widetilde{\rm MOM}$) momentum substraction schemes including $u$, $d$, $s$ and $c$ quarks in the sea. An Operator Product Expansion dominated by the dimension-two $\langle A^2\rangle$ condensate is used to fit the running of the coupling. We argue that the agreement in the predicted $\langle A^2\rangle$ condensate for both schemes is a strong support for the validity of the OPE approach and the effect of this non-gauge invariant condensate over the running of the strong coupling., Comment: Revised version (8 pages, 5 figures)

This paper reports on the determination of $\alpha_S$ from lattice simulations with 2+1+1 twisted-mass dynamical flavours {\it via} the computation of the ghost-gluon coupling renormalized in the MOM Taylor scheme. A high-statistics sample of gauge configurations, used to evaluate the coupling from ghost and gluon propagators, allows for the appropriate update of previous results, now performing an improved analysis of data with reduced statistical errors and the systematical uncertainties under a better control., Comment: 15 pages, 7 figs (final version published in Phys.Rev.D)

Gluon and ghost propagators data, obtained in Landau gauge from lattice simulations with two light and two heavy dynamical quark flavours ($N_f$=2+1+1), are described here with a running formula including a four-loop perturbative expression and a nonperturbative OPE correction dominated by the local operator $A^2$. The Wilson coefficients and their variation as a function of the coupling constant are extracted from the numerical data and compared with the theoretical expressions that, after being properly renormalized, are known at ${\cal O}(\alpha^4)$. As also $\Lambda_{\msbar}$ is rather well known for $N_f$=2+1+1, this allows for a precise consistency test of the OPE approach in the joint description of different observables., Comment: 12 pages, 11 figures, 3 tables

We report on an estimate of \alpha_s, renormalised in the MSbar scheme at the tau and Z^0 mass scales, by means of lattice QCD. Our major improvement compared to previous lattice calculations is that, for the first time, no perturbative treatment at the charm threshold has been required since we have used statistical samples of gluon fields built by incorporating the vacuum polarisation effects of u/d, s and c sea quarks. Extracting \alpha_s in the Taylor scheme from the lattice measurement of the ghost-ghost-gluon vertex, we obtain \alpha_s^{MSbar}(m^2_Z)=0.1200(14) and \alpha_s^{MSbar}(m^2_tau)=0.339(13)., Comment: Proceedings of the "QCD 12" conference in Montpellier

This letter reports on the first computation, from data obtained in lattice QCD with $u,d,s$ and $c$ quarks in the sea, of the running strong coupling via the ghost-gluon coupling renormalized in the MOM Taylor scheme. We provide with estimates of $\ams(m_\tau^2)$ and $\ams(m_Z^2)$ in very good agreement with experimental results. Including a dynamical c quark makes safer the needed running of $\ams$., Comment: 5 pages, 4 figures, 1 table (references updated)

We study RI/MOM renormalization constants of bilinear quark operators for $N_f=4$ and the strong coupling constant for $N_f=2+1+1$ using Wilson twisted-mass fermions. We use the "egalitarian" method to remove H(4) hypercubic artifacts non-perturbatively, which enables us to study physical quantities in a wide range of momenta. We then apply OPE in studying the running behavior of $Z_q$ and $\alpha_s$, from which we are able to extract the Landau gauge dimension-two gluon condensate $$ which is of phenomenological interest., Comment: 7 pages, talk presented at The XXIX International Symposium on Lattice Field Theory - Lattice 2011, July 10-16, 2011, Squaw Valley, Lake Tahoe, California

This paper is a first report on the determination of $\Lambda_{\msbar}$ from lattice simulations with 2+1+1 twisted-mass dynamical flavours {\it via} the computation of the ghost-gluon coupling renormalized in the MOM Taylor scheme. We show this approach allows a very good control of the lattice artefacts and confirm the picture from previous works with quenched and ${\rm N}_f$=2 twisted-mass field configurations which prove the necessity to include non-perturbative power corrections in the description of the running. We provide with an estimate of $\Lambda_{\msbar}$ in very good agreement with experimental results. To our knowledge it is the first calculation with a dynamical charm quark which makes the running up to $\alpha_s(M_Z)$ much safer., Comment: 11 pages, 3 figures, 3 tables (new version accepted to be published in Phys. Rev. D)

We argue from LQCD that there is a non vanishing v.e.v of $A_a^\mu A^a_\mu$ in QCD in the Landau gauge. We use operator product expansion to provide a clear definition of $A_a^\mu A^a_\mu$ and extract a number both in the quenched and unquenched case., Comment: 10 pages, 5 figures, talk at the workshop "The many faces of QCD", November 2-5, 2010, Gent, Belgium

Some very recent computations of $\alpha_{\bar{\rm MS}}(M_Z)$ from $N_f=1+1$ lattice simulations and of the running of the Strong coupling, obtained from the lattice ghost-gluon vertex, over a large momentum window are very briefly reviewed., Comment: Oral contribution to the 35th ICHEP; Paris, July 22-28, 2010

We present results concerning the non-perturbative evaluation of the renormalisation constant for the quark field, $Z_q$, from lattice simulations with twisted mass quarks and three values of the lattice spacing. We use the RI'-MOM scheme. $Z_q$ has very large lattice spacing artefacts; it is considered here as a test bed to elaborate accurate methods which will be used for other renormalisation constants. We recall and develop the non-perturbative correction methods and propose tools to test the quality of the correction. These tests are also applied to the perturbative correction method. We check that the lattice spacing artefacts scale indeed as $a^2p^2$. We then study the running of $Z_q$ with particular attention to the non-perturbative effects, presumably dominated by the dimension-two gluon condensate $\VEV{A^2}$ in Landau gauge. We show indeed that this effect is present, and not small. We check its scaling in physical units confirming that it is a continuum effect. It gives a $\sim 4%$ contribution at 2 GeV. Different variants are used in order to test the reliability of our result and estimate the systematic uncertainties. Finally combining all our results and using the known Wilson coefficient of $\VEV{A^2}$ we find $g^2(\mu^2) \VEV{A^2}_{\mu^2\; CM} = 2.01(11)(^{+0.61}_{- 0.73}) \;\mathrm {GeV}^2$ at $\mu=10\, \mathrm{GeV}$, in fair agreement within uncertainties with the value indepently extracted from the strong coupling constant., Comment: 38 pages, 8 tables, 8 figures

A non-perturbative calculation of the ghost-gluon running QCD coupling constant is performed using $N_f=2$ twisted-mass dynamical fermions. The extraction of $\Lambda_{\bar{MS}}$ in the chiral limit reveals the presence of a non-perturbative OPE contribution that is assumed to be dominated by a dimension-two $\VEV{A^2}$ condensate. In this contest a novel method for calibrating the lattice spacing in lattice simulations is presented., Comment: 7 pages, 4 figures, XXVIII International Symposium on Lattice Field Theory 2010

We present results concerning the non-perturbative evaluation of the ghost-gluon running QCD coupling constant from $N_f=2$ twisted-mass lattice calculations. A novel method for calibrating the lattice spacing, independent of the string tension and hadron spectrum is presented with results in agreement with previous estimates. The value of $\Lambda_{\overline{MS}}$ is computed from the running of the QCD coupling only after extrapolating to zero dynamical quark mass and after removing a non-perturbative OPE contribution that is assumed to be dominated by the dimension-two $\VEV{A^2}$ gluon condensate. The effect due to the dynamical quark mass in the determination of $\Lams$ is discussed., Comment: 33 pages, 6 figs

We give the analytical expressions and numerical values of radiative corrections to the covariant derivative operator on the static quark line, used for the lattice calculation of the Isgur-Wise form factors $\tau_{1/2}(1)$ and $\tau_{3/2}(1)$. Those corrections induce an enhancement of renormalized quantities if an hypercubic blocking is applied to the Wilson line, whereas there is a reduction without such a blocking.

We propose a method to compute the Isgur-Wise form factors tau_1/2(1) and tau_3/2(1) for the decay of B mesons into orbitally excited (P wave) D** charmed mesons on the lattice in the static limit. We also present the result of an exploratory numerical simulation which shows that the signal/noise ratio allows for a more dedicated computation. We find tau_1/2(1)=0.38(5) and tau_3/2(1)= 0.53(8), with yet unknown systematic errors. These preliminary numbers agree fairly well with theoretical expectation., Comment: LaTeX, 13 pages, 3 eps figures

We present the APE (Array Processor Experiment) project for the development of dedicated parallel computers for numerical simulations in lattice gauge theories. While APEmille is a production machine in today's physics simulations at various sites in Europe, a new machine, apeNEXT, is currently being developed to provide multi-Tflops computing performance. Like previous APE machines, the new supercomputer is largely custom designed and specifically optimized for simulations of Lattice QCD., Comment: Poster at the XXIII Physics in Collisions Conference (PIC03), Zeuthen, Germany, June 2003, 3 pages, Latex. PSN FRAP15. Replaced for adding forgotten author

We present the current status of the apeNEXT project. Aim of this project is the development of the next generation of APE machines which will provide multi-teraflop computing power. Like previous machines, apeNEXT is based on a custom designed processor, which is specifically optimized for simulating QCD. We discuss the machine design, report on benchmarks, and give an overview on the status of the software development., Comment: Talk from the 2003 Computing in High Energy and Nuclear Physics (CHEP03), La Jolla, Ca, USA, March 2003, 8 pages, LaTeX, 12 eps figures. PSN THIT005

Trying a global fit of the experimental branching ratios and CP-asymmetries of the charmless $B\to PV$ decays according to QCD factorization, we find it impossible to reach a satisfactory agreement, the confidence level (CL) of the best fit is smaller than .1 %. This failure reflects the difficulty to accommodate several large experimental branching ratios of the strange channels. Furthermore, experiment was not able to exclude a large direct CP asymmetry in $\bar {B}^0\to\rho^+ \pi^-$, which is predicted very small by QCD factorization. Proposing a fit with QCD factorization complemented by a charming-penguin inspired model we reach a best fit which is not excluded by experiment (CL of about 8 %) but is not fully convincing. These negative results must be tempered by the remark that some of the experimental data used are recent and might still evolve significantly., Comment: 8 pages, 2 figures (requires epsfig, psfrag),talk presented at the XXXVIIIth Rencontres de Moriond: Electroweak Interactions and Unified Theories,Les Arcs, France, March 15-22, 2003. To be published in the Proceedings

We try a global fit of the experimental branching ratios and CP-asymmetries of the charmless $B\to PV$ decays according to QCD factorisation. We find it impossible to reach a satisfactory agreement, the confidence level (CL) of the best fit is smaller than .1 %. The main reason for this failure is the difficulty to accomodate several large experimental branching ratios of the strange channels. Furthermore, experiment was not able to exclude a large direct CP asymmetry in $\bar {B^0}\to\rho^+ \pi^-$, which is predicted very small by QCD factorisation. Trying a fit with QCD factorisation complemented by a charming-penguin inspired model we reach a best fit which is not excluded by experiment (CL of about 8 %) but is not fully convincing. These negative results must be tempered by the remark that some of the experimental data used are recent and might still evolve significantly., Comment: 21 pages, 4 figures; several typos corrected, added one footnote and two references, comments added about PQCD. To appear in Phys.Rev. D

We present the current status of the apeNEXT project. Aim of this project is the development of the next generation of APE machines which will provide multi-teraflop computing power. Like previous machines, apeNEXT is based on a custom designed processor, which is specifically optimized for simulating QCD. We discuss the machine design, report on benchmarks, and give an overview on the status of the software development., Comment: 3 pages, Lattice2002(machines). Replaced for adding forgotten author

We underline a problem existing in the heavy quark limit of QCD concerning the rates of semileptonic B decays into P-wave $D_J(j)$ mesons, where $j = {1 \over 2}$ (wide states) or $j = {3 \over 2}$ (narrow states). The leading order sum rules of Bjorken and Uraltsev suggest $\Gamma [ \bar{B} \to D_{0,1} ({1 \over 2}) \ell \nu ] \ll \Gamma [ \bar{B} \to D_{1,2} ({3 \over 2}) \ell \nu ]$, in contradiction with experiment. The same trend follows also from a sum rule for the subleading $1/m_Q$ curent matrix element correction $\xi_3(1)$. The problem is made explicit in relativistic quarks models \`a la Bakamjian and Thomas, that give a transparent physical interpretation of the latter as due, not to a $L \cdot S$ force, but to the Wigner rotation of the light quark spin. We point out moreover that the selection rule for decay constants of $j = {3 \over 2}$ states, $f_{3/2} = 0$, predicts, assuming the model of factorization, the opposite hierarchy $\Gamma [ \bar{B} \to \bar{D}_{s_{1,2}} ({3 \over 2}) D^{(*)} ] \ll \Gamma [ \bar{B} \to \bar{D}_{s_{0,1}} ({1 \over 2}) D^{(*)} ]$., Comment: Contribution to the International Europhysics Conference on HEP, Budapest, July 2001 (presented by L. Oliver); 5 pages

APENEXT is a new generation APE processor, optimized for LGT simulations. The project follows the basic ideas of previous APE machines and develops simple and cheap parallel systems with multi T-Flops processing power. This paper describes the main features of this new development., Comment: Lattice2001(plenary/machinestatus), 4 pages, 1 eps figure

This paper presents the status of the APEmille project, which is essentially completed, as far as machine development and construction is concerned. Several large installations of APEmille are in use for physics production runs leading to many new results presented at this conference. This paper briefly summarizes the APEmille architecture, reviews the status of the installations and presents some performance figures for physics codes., Comment: Lattice2001(algorithms), 3 pages, 1 eps figure

In previous work it has been shown that, either from a sum rule for the subleading Isgur-Wise function $\xi_3(1)$ or from a combination of Uraltsev and Bjorken SR, one infers for $P$-wave states $|\tau_{1/2}(1)| \ll |\tau_{3/2}(1)|$. This implies, in the heavy quark limit of QCD, a hierarchy for the {\it production} rates of $P$-states $\Gamma(\bar{B}_d \to D ({1 \over 2}) \ell \nu) \ll \Gamma(\bar{B}_d \to D ({3 \over 2}) \ell \nu)$ that seems at present to be contradicted by experiment. It was also shown that the decay constants of $j = {3 \over 2}$ $P$-states vanish in the heavy quark limit of QCD, $f_{3/2}^{(n)} = 0$. Assuming the {\it model} of factorization in the decays $\bar{B}_d \to \bar{D}_s^{**}D$, one expects the opposite hierarchy for the {\it emission} rates $\Gamma(\bar{B}_d \to \bar{D}_s ({3 \over 2}) D) \ll \Gamma(\bar{B}_d \to \bar{D}_s ({1 \over 2}) D)$, since $j = {1 \over 2}$ $P$-states are coupled to vacuum. Moreover, using Bjorken SR and previously discovered SR involving heavy-light meson decay constants and IW functions, one can prove that the sums $\sum\limits_n ({f^{(n)} \over f^{(0)}})^2$, $\sum\limits_n ({f_{1/2}^{(n)} \over f^{(0)}})^2$ (where $f^{(n)}$ and $f_{1/2}^{(n)}$ are the decay constants of $S$-states and $j = {1\over 2}$ $P$-states) are divergent. This situation seems to be realized in the relativistic quark models \`a la Bakamjian and Thomas, that satisfy HQET and predict decays constants $f^{(n)}$ and $f_{1/2}^{(n)}$ that do not decrease with the radial quantum number $n$., Comment: 7 pages, Latex

Making use of the nonrelativistic potential model for the description of mesons, and working in the Shifman-Voloshin limit, we compare the integrated rate $\Gamma(B\to X_cl\nu)$ calculated as a sum of the individual decay rates to the quantum-mechanical analog of the OPE. In the case of a potential regular at the origin, we find a well-defined duality violation, which is however exponentially small. It corresponds to the charm resonances kinematically forbidden in the decay process, but apparently picked up by the OPE. For singular potentials, we do not obtain a full OPE series, but only a limited Taylor expansion, since the cofficients become infinite beyond some order. In this case, we do not find an indication of duality violation: the difference is smaller than the last term of the limited expansion. This emphasizes that the case of singular potentials, which may be relevant for QCD, deserves further study., Comment: revtex, 6 pages

The detailed way in which duality between sum of exclusive states and the free quark model description operates in semileptonic total decay widths, is analysed. It is made very explicit by the use of the non relativistic harmonic oscillator quark model in the SV limit, and a simple interaction current with the lepton pair. In particular, the Voloshin sum rule is found to eliminate the mismatches of order $\delta m/m_b^2$., Comment: 11 pages, Latex2e, AMS-LaTeX

Quark-hadron duality in the inclusive semileptonic decay $B\to X_c l\nu$ in the Shifman-Voloshin limit $\Lambda \ll \delta m=m_b - m_c \ll m_b, m_c$ is studied within a nonrelativistic potential model. The integrated semileptonic decay rate is calculated in two ways: first, by constructing the Operator Product Expansion, and second by a direct summation of the exclusive channels. Sum rules (Bjorken, Voloshin, etc.) for the potential model are derived, providing a possibility to compare the two representations for $\Gamma(B\to X_c l\nu)$. An explicit difference between them referred to as duality-violation effect is found. The origin of this effect is related to higher charm resonances which are kinematically forbidden in the decay process but are nevertheless picked up by the OPE. Within the considered $1/m_c^2$ order the OPE and the sum over exclusive channels match each other, up to the contributions of higher resonances, by virtue of the sum rules. In particular this is true for the terms of order $\delta m^2/m_c^2$ and $\Lambda \delta m/m_c^2$ which are present in each of the decay channels and cancel in the sum of these channels due to the Bjorken and Voloshin sum rules, respectively. The size of the duality violation effects is estimated to be of the order $O(\Lambda^{2+b}/m_c^2\delta m^b)$ with $b>0$ depending on the details of the potential. Constraints for a better accuracy are discussed., Comment: revtex, 19 pages, a comment on the OPE in the potential model has been added and several typoes corrected

We explicitly check quark-hadron duality to order $(m_b-m_c)\Lambda/m_b^2$ for $b \to c l\nu$ decays in the limit $m_b-m_c \ll m_b$ including ground state and orbitally excited hadrons. Duality occurs thanks to a new sum rule which expresses the subleading HQET form factor $\xi_3$ or, in other notations, $a_+^{(1)}$ in terms of the infinite mass limit form factors and some level splittings. We also demonstrate the sum rule, which is not restricted to the condition $m_b-m_c \ll m_b$, applying OPE to the longitudinal axial component of the hadronic tensor without neglecting the $1/m_b$ subleading contributions to the form factors. We argue that this method should produce a new class of sum rules, depending on the current, beyond Bjorken, Voloshin and the known tower of higher moments. Applying OPE to the vector currents we find another derivation of the Voloshin sum rule. From independent results on $\xi_3$ we derive a sum rule which involves only the $\tau_{1/2}^{(n)}$ and $\tau_{3/2}^{(n)}$ form factors and the corresponding level splittings. The latter strongly supports a theoretical evidence that the $B$ semileptonic decay into narrow orbitally-excited resonances dominates over the decay into the broad ones, in apparent contradiction with some recent experiments. We discuss this issue., Comment: 9 pages

In quark models \`a la Bakamjian and Thomas, that yield covariance and Isgur-Wise scaling of form factors in the heavy quark limit, we compute the decay constants $f^{(n)}$ and $f^{(n)}_{1/2}$ of S-wave and P-wave mesons composed of heavy and light quarks. Heavy quark limit scaling $\sqrt{M} f = Cst$ is obtained, and it is shown that this class of models satisfies the sum rules involving decay constants and Isgur-Wise functions recently formulated by us in the heavy quark limit of QCD. Moreover, the model also satisfies the selection rules of the type $f^{(n)}_{3/2} = 0$ that must hold in this limit. We discuss different Ans\"atze for the dynamics of the mass operator at rest. For non-relativistic kinetic energies ${p^2 \over 2m}$ the decay constants are finite even if the potential $V(r)$ has a Coulomb part. For the relativistic form $\sqrt{p^2 + m^2}$, the S-wave decay constants diverge if there is a Coulomb singularity. Using phenomenological models of the spectrum with relativistic kinetic energy and regularized short distance part (Godfrey-Isgur model or Richardson potential of Colangelo et al.), that yield $\rho^2 \simeq 1$ for the elastic Isgur-Wise function, we compute the decay constants in the heavy quark limit, and obtain $f_B \simeq$ 300 MeV, of the same order although slightly smaller than in the static limit of lattice QCD. We find the decay constants of $D^{**}$ with $j =1/2$ of the same order of magnitude. The convergence of the heavy quark limit sum rules is also studied., Comment: 21 pages, 2 figures, LaTeX2e, amsbsy (from the AMS-LaTeX package), epsf

Once chosen the dynamics in one frame, the rest frame in this paper, the Bakamjian and Thomas method allows to define relativistic quark models in any frame. These models have been shown to provide, in the infinite quark mass limit, fully covariant current form factors as matrix elements of the quark current operator. In this paper we use the rest frame dynamics fitted from the meson spectrum by various authors, already shown to provide a reasonable value for $\rho^2$. From the general formulae for the scaling invariant form factors $\xi^{(n)}(w)$, $\tau_{1/2}^{(n)}(w)$ and $\tau_{3/2}^{(n)}(w)$, we predict quantitavely the $B$ semileptonic branching ratios to the ground state and orbitally excited charmed mesons $D, D^\ast$ and $D^{\ast\ast}$. We check Bjorken's sum rule and discuss the respective contributions to it. We find $\xi(w)\simeq (2/(1+w)) ^2$, resulting from the fact that the ground state wave function is Coulomb-like. We also find $\tau_{3/2}\simeq 0.5 (2/(1+w))^3$ and $\tau_{1/2}(w)\ll \tau_{3/2}(w)$. Very small branching ratios into $j=1/2$ orbitally excited $D$'s results. The overall agreement with experiment is rather good within the present accuracy which is poor for the orbitally excited charmed mesons. We predict a ratio $Br(B\to D^\ast_2 l \nu)/Br(B\to D_1 l \nu)=1.55\pm 0.15$ as a mere consequence of the heavy quark symmetry. If some faint experimental indications that $Br(B\to D_1 l \nu)\simeq Br(B\to D^\ast_2 l \nu)$ were confirmed, it would indicate a sizeable $O(1/m_c)$ correction., Comment: 18 pages, 6 figures, Latex2e, AMS-LaTeX, corrections in the figures

The slope of the Isgur-Wise function for ground state mesons is evaluated for the heavy mass limit of quark models \`a la Bakamjian-Thomas, which has been previously discussed by us in general terms. A full calculation in various spectroscopic models with relativistic kinetic energy gives a rather stable result $\rho^2 \approx 1$, much lower than previous estimates. Attention is paid to a careful comparison of this result with the ones of QCD fundamental methods (lattice QCD, QCD sum rules) and with experimental data., Comment: 15 pages, Latex, AMS-LaTeX

Once chosen the dynamics in one frame, for example the rest frame, the Bakamjian and Thomas method allows to define relativistic quark models in any frame. These models have been shown to provide, in the heavy quark limit, fully covariant current form factors as matrix elements of the quark current operator. They also verify the Isgur-Wise scaling and give a slope parameter $\rho^2>3/4$ for all the possible choices of the dynamics. In this paper we study the $L=1$ excited states and derive the general formula, valid for any dynamics, for the scaling invariant form factors $\tau_{1/2}^{(n)}(w)$ and $\tau_{3/2}^{(n)}(w)$. We also check the Bjorken-Isgur-Wise sum rule already demonstrated elsewhere in this class of models., Comment: 14 pages, Latex2e, AMS-LaTeX