433 research outputs found

### Analytical methods in heavy quark physics and the case of $\tau_{1/2}(w)$

Analytical methods in heavy quark physics are shortly reviewed, with emphasis
on the problems of dynamical calculations. Then, attention is attracted to the
various difficulties raised by a tentative experimental determination of
$\tau_{1/2}$Comment: 10 pages, FPCP2003 conference (Paris) [typos corrected,new
references

### 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

### $D_{sJ}(2860)$ and $D_{sJ}(2715)$

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 $B$ to Light Meson Form Factors and the $B \to \psi K(K^{\ast})$ 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

### 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

- âŠ