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

Sum rules in the heavy quark limit of QCD

In the leading order of the heavy quark expansion, we propose a method within the OPE and the trace formalism, that allows to obtain, in a systematic way, Bjorken-like sum rules for the derivatives of the elastic Isgur-Wise function $\xi(w)$ in terms of corresponding Isgur-Wise functions of transitions to excited states. A key element is the consideration of the non-forward amplitude, as introduced by Uraltsev. A simplifying feature of our method is to consider currents aligned along the initial and final four-velocities. As an illustration, we give a very simple derivation of Bjorken and Uraltsev sum rules. On the other hand, we obtain a new class of sum rules that involve the products of IW functions at zero recoil and IW functions at any $w$. Special care is given to the needed derivation of the projector on the polarization tensors of particles of arbitrary integer spin. The new sum rules give further information on the slope $\rho^2 = - \xi '(1)$ and also on the curvature $\sigma^2 = \xi '' (1)$, and imply, modulo a very natural assumption, the inequality $\sigma^2 \geq {5\over 4} \rho^2$, and therefore the absolute bound $\sigma^2 \geq {15 \over 16}$.Comment: 64 pages, Late

DsJ(2860)D_{sJ}(2860) and DsJ(2715)D_{sJ}(2715)

Recently Babar Collaboration reported a new $c\bar{s}$ state $D_{sJ}(2860)$ and Belle Collaboration observed $D_{sJ}(2715)$. We investigate the strong decays of the excited $c\bar{s}$ states using the $^{3}P_{0}$ model. After comparing the theoretical decay widths and decay patterns with the available experimental data, we tend to conclude: (1) $D_{sJ}(2715)$ is probably the $1^{-}(1^{3}D_{1})$ $c\bar{s}$ state although the $1^{-}(2^{3}S_{1})$ assignment is not completely excluded; (2) $D_{sJ}(2860)$ seems unlikely to be the $1^{-}(2^{3}S_{1})$ and $1^{-}(1^{3}D_{1})$ candidate; (3) $D_{sJ}(2860)$ as either a $0^{+}(2^{3}P_{0})$ or $3^{-}(1^{3}D_{3})$ $c\bar{s}$ state is consistent with the experimental data; (4) experimental search of $D_{sJ}(2860)$ in the channels $D_s\eta$, $DK^{*}$, $D^{*}K$ and $D_{s}^{*}\eta$ will be crucial to distinguish the above two possibilities.Comment: 18 pages, 7 figures, 2 tables. Some discussions added. The final version to appear at EPJ

Angular analysis of B -> J/psi K1 : towards a model independent determination of the photon polarization with B-> K1 gamma

We propose a model independent extraction of the hadronic information needed to determine the photon polarization of the b-> s gamma process by the method utilizing the B -> K1 gamma -> K pi pi gamma angular distribution. We show that exactly the same hadronic information can be obtained by using the B -> J/psi K1 -> J/psi K pi pi channel, which leads to a much higher precision.Comment: 12 pages, 1 figur

Equation of state of strongly coupled Hamiltonian lattice QCD at finite density

We calculate the equation of state of strongly coupled Hamiltonian lattice QCD at finite density by constructing a solution to the equation of motion corresponding to an effective Hamiltonian using Wilson fermions. We find that up to and beyond the chiral symmetry restoration density the pressure of the quark Fermi sea can be negative indicating its mechanical instability. This result is in qualitative agreement with continuum models and should be verifiable by future numerical simulations.Comment: 14 pages, 2 EPS figures. Revised version - added discussion on the equation of stat

Critical Analysis of Theoretical Estimates for BB to Light Meson Form Factors and the B→ψK(K∗)B \to \psi K(K^{\ast}) Data

We point out that current estimates of form factors fail to explain the non-leptonic decays $B \to \psi K(K^{\ast})$ and that the combination of data on the semi-leptonic decays $D \to K(K^{\ast})\ell \nu$ and on the non-leptonic decays $B \to \psi K(K^{\ast})$ (in particular recent po\-la\-ri\-za\-tion data) severely constrain the form (normalization and $q^2$ dependence) of the heavy-to-light meson form factors, if we assume the factorization hypothesis for the latter. From a simultaneous fit to \bpsi and \dk data we find that strict heavy quark limit scaling laws do not hold when going from $D$ to $B$ and must have large corrections that make softer the dependence on the masses. We find that $A_1(q^2)$ should increase slower with \qq than $A_2, V, f_+$. We propose a simple parametrization of these corrections based on a quark model or on an extension of the \hhs laws to the \hl case, complemented with an approximately constant $A_1(q^2)$. We analyze in the light of these data and theoretical input various theoretical approaches (lattice calculations, QCD sum rules, quark models) and point out the origin of the difficulties encountered by most of these schemes. In particular we check the compatibility of several quark models with the heavy quark scaling relations.Comment: 48 pages, DAPNIA/SPP/94-24, LPTHE-Orsay 94/1