On P-wave meson decay constants in the heavy quark limit of QCD

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, Late

Heavy-to-Light Form Factors in the Final Hadron Large Energy Limit: Covariant Quark Model Approach

We prove the full covariance of the heavy-to-light weak current matrix elements based on the Bakamjian-Thomas construction of relativistic quark models, in the heavy mass limit for the parent hadron and the large energy limit for the daughter one. Moreover, this quark model representation of the heavy-to-light form factors fulfills the general relations that were recently argued to hold in the corresponding limit of QCD, namely that there are only three independent form factors describing the B -> pi (rho) matrix elements, as well as the factorized scaling law sqrt(M)z(E) of the form factors with respect to the heavy mass M and large energy E. These results constitute another good property of the quark models \`a la Bakamjian-Thomas, which were previously shown to exhibit covariance and Isgur-Wise scaling in the heavy-to-heavy case.Comment: 11 pages, LaTex2e, no figur

Bound on the curvature of the Isgur-Wise function of the baryon semileptonic decay Lambda_b -> Lambda_c + l + nu

In the heavy quark limit of QCD, using the Operator Product Expansion, the formalism of Falk for hadrons or arbitrary spin, and the non-forward amplitude, as proposed by Uraltsev, we formulate sum rules involving the Isgur-Wise function $\xi_{\Lambda} (w)$ of the baryon transition $\Lambda_b \to \Lambda_c \ell \overline{\nu}_{\ell}$, where the light cloud has $j^P=0^+$ for both initial and final baryons. We recover the lower bound for the slope $\rho_\Lambda^2 = - \xi '_\Lambda (1) \geq 0$ obtained by Isgur et al., and we generalize it by demonstrating that the IW function $\xi_{\Lambda} (w)$ is an alternate series in powers of $(w-1)$, i.e. $(-1)^n \xi_{\Lambda}^{(n)} (1) \geq 0$. Moreover, exploiting systematically the sum rules, we get an improved lower bound for the curvature in terms of the slope, $\sigma_\Lambda^2 = \xi "_\Lambda (1) \geq {3 \over 5} [\rho_\Lambda^2 + (\rho_\Lambda^2)^2]$. This bound constrains the shape of the Isgur-Wise function and it will be compelling in the analysis of future precise data on the differential rate of the baryon semileptonic decay $\Lambda_b \to \Lambda_c \ell \overline{\nu}_{\ell}$, that has a large measured branching ratio, of about 5%.Comment: 16 page

Explicit form of the Isgur-Wise function in the BPS limit

Using previously formulated sum rules in the heavy quark limit of QCD, we demonstrate that if the slope rho^2 = -xi'(1) of the Isgur-Wise function xi(w) attains its lower bound 3/4, then all the derivatives (-1)^L xi^(L)(1) attain their lower bounds (2L+1)!!/2^(2L), obtained by Le Yaouanc et al. This implies that the IW function is completely determined, given by the function xi(w) = [2/(w+1)]^(3/2). Since the so-called BPS condition proposed by Uraltsev implies rho^2 = 3/4, it implies also that the IW function is given by the preceding expression.Comment: 19 page

Sum rules for leading and subleading form factors in Heavy Quark Effective Theory using the non-forward amplitude

Within the OPE, we the new sum rules in Heavy Quark Effective Theory in the heavy quark limit and at order 1/m_Q, using the non-forward amplitude. In particular, we obtain new sum rules involving the elastic subleading form factors chi_i(w) (i = 1,2, 3) at order 1/m_Q that originate from the L_kin and L_mag perturbations of the Lagrangian. To the sum rules contribute only the same intermediate states (j^P, J^P) = ((1/2)^-, 1^-), ((3/2)^-, 1^-) that enter in the 1/m_Q^2 corrections of the axial form factor h_(A_1)(w) at zero recoil. This allows to obtain a lower bound on -delta_(1/m^2)^(A_1) in terms of the chi_i(w) and the shape of the elastic IW function xi(w). An important theoretical implication is that chi'_1(1), chi_2(1) and chi'_3(1) (chi_1(1) = chi_3(1) = 0 from Luke theorem) must vanish when the slope and the curvature attain their lowest values rho^2->3/4, sigma^2->15/16. These constraints should be taken into account in the exclusive determination of |V_(cb)|.Comment: Invited talk to the International Workshop on Quantum Chromodynamics : Theory and Experiment, Conversano (Bari, Italy), 16-20 June 200