3,063 research outputs found

### $V_{cb}$ from the semileptonic decay $B\to D \ell \bar{\nu}_{\ell}$ and the properties of the $D$ meson distribution amplitude

The improved QCD light-cone sum rule (LCSR) provides an effective way to deal
with the heavy-to-light transition form factors (TFFs). Firstly, we adopt the
improved LCSR approach to deal with the $B\to D$ TFF $f^{+}(q^2)$ up to twist-4
accuracy. Due to the elimination of the most uncertain twist-3 contribution and
the large suppression of the twist-4 contribution, the obtained LCSR shall
provide us a good platform for testing the $D$-meson leading-twist DA. For the
purpose, we suggest a new model for the $D$-meson leading-twist DA
($\phi_{3D}$), whose longitudinal behavior is dominantly determined by a
parameter $B$. Moreover, we find its second Gegenbauer moment $a^D_2\sim B$.
Varying $B$ within certain region, one can conveniently mimic the $D$-meson DA
behavior suggested in the literature. Inversely, by comparing the estimations
with the experimental data on the $D$-meson involved processes, one can get a
possible range for the parameter $B$ and a determined behavior for the
$D$-meson DA. Secondly, we discuss the $B\to D$ TFF at the maximum recoil
region and present a detailed comparison of it with the pQCD estimation and the
experimental measurements. Thirdly, by applying the LCSR on $f^{+}(q^2)$, we
study the CKM matrix element \Vcb together with its uncertainties by adopting
two types of processes, i.e. the $B^0/\bar{B}^0$-type and the $B^{\pm}$-type.
It is noted that a smaller $B \precsim 0.20$ shows a better agreement with the
experimental value on \Vcb. For example, for the case of $B=0.00$, we obtain
$|V_{cb}|(B^0/\bar{B}^0-{\rm type})=(41.28 {^{+5.68}_{-4.82}}
{^{+1.13}_{-1.16}}) \times 10^{-3}$ and $|V_{cb}|(B^{\pm}-{\rm type})=(40.44
{^{+5.56}_{-4.72}} {^{+0.98}_{-1.00}}) \times 10^{-3}$, whose first (second)
uncertainty comes from the squared average of the mentioned theoretical
(experimental) uncertainties.Comment: 13 pages, 10 figures. Reference updated and discussion improved. To
be published in Nucl.Phys.

### Twist-3 light-cone distribution amplitudes of the scalar mesons within the QCD sum rules and their application to the $B \to S$ transition form factors

We investigate the twist-3 light-cone distribution amplitudes (LCDAs) of the
scalar mesons $a_0$, $K^{\ast}_0$ and $f_0$ within the QCD sum rules. The QCD
sum rules are improved by a consistent treatment of the sizable $s$-quark mass
effects within the framework of the background field approach. Adopting the
valence quark component $(\bar{q}_1 q_2)$ as the dominant structure of the
scalar mesons, our estimation for their masses are close to the measured
$a_0(1450)$, $K^{\ast}_0(1430)$ and $f_0(1710)$. From the sum rules, we obtain
the first two non-zero moments of the twist-3 LCDAs $\phi^{s,\sigma}_{a_0}$:
$\langle \xi_{s,a_0}^{2(4)} \rangle=0.369 \;(0.245)$ and $\langle
\xi_{\sigma,a_0}^{2(4)} \rangle=0.203 \;(0.093)$; those of the twist-3 LCDAs
$\phi_{K^*_0}^{s,\sigma}$: $\langle \xi_{s,K^{\ast}_0}^{1(2)} \rangle
=0.004\;(0.355)$ and $\langle \xi_{\sigma,K^{\ast}_0}^{1(2)} \rangle
=0.018\;(0.207)$; and those of the twist-3 LCDAs $\phi_{f_0}^{s,\sigma}$:
$\langle \xi_{s,f_0}^{2(4)} \rangle=0.335 \;(0.212)$ and $\langle
\xi_{\sigma,f_0}^{2(4)} \rangle=0.196 \; (0.088)$, respectively. As an
application of those twist-3 LCDAs, we study the $B \to S$ transition form
factors by introducing proper chiral currents into the correlator, which is
constructed such that the twist-3 LCDAs give dominant contribution and the
twist-2 LCDAs make negligible contribution. Our results of the $B \to S$
transition form factors at the large recoil region $q^2 \simeq 0$ are
consistent with those obtained in the literature, which inversely shows the
present twist-3 LCDAs are acceptable.Comment: 14 pages, 12 figures, 7 table

### The $\rho$-meson longitudinal leading-twist distribution amplitude

In the present paper, we suggest a convenient model for the vector
$\rho$-meson longitudinal leading-twist distribution amplitude
$\phi_{2;\rho}^\|$, whose distribution is controlled by a single parameter
$B^\|_{2;\rho}$. By choosing proper chiral current in the correlator, we obtain
new light-cone sum rules (LCSR) for the $B\to\rho$ TFFs $A_1$, $A_2$ and $V$,
in which the $\delta^1$-order $\phi_{2;\rho}^\|$ provides dominant
contributions. Then we make a detailed discussion on the $\phi_{2;\rho}^\|$
properties via those $B\to\rho$ TFFs. A proper choice of $B^\|_{2;\rho}$ can
make all the TFFs agree with the lattice QCD predictions. A prediction of
$|V_{\rm ub}|$ has also been presented by using the extrapolated TFFs, which
indicates that a larger $B^{\|}_{2;\rho}$ leads to a larger $|V_{\rm ub}|$. To
compare with the BABAR data on $|V_{\rm ub}|$, the longitudinal leading-twist
DA $\phi_{2;\rho}^\|$ prefers a doubly-humped behavior.Comment: 7 pages, 3 figures. Discussions improved and references updated. To
be published in Phys.Lett.

### Revisiting the Pion Leading-Twist Distribution Amplitude within the QCD Background Field Theory

We study the pion leading-twist distribution amplitude (DA) within the
framework of SVZ sum rules under the background field theory. To improve the
accuracy of the sum rules, we expand both the quark propagator and the vertex
(z\cdot \tensor{D})^n of the correlator up to dimension-six operators in the
background field theory. The sum rules for the pion DA moments are obtained, in
which all condensates up to dimension-six have been taken into consideration.
Using the sum rules, we obtain \left|_{\rm 1\;GeV} = 0.338 \pm
0.032, \left|_{\rm 1\;GeV} = 0.211 \pm 0.030 and
\left|_{\rm 1\;GeV} = 0.163 \pm 0.030. It is shown that the
dimension-six condensates shall provide sizable contributions to the pion DA
moments. We show that the first Gegenbauer moment of the pion leading-twist DA
is $a^\pi_2|_{\rm 1\;GeV} = 0.403 \pm 0.093$, which is consistent with those
obtained in the literature within errors but prefers a larger central value as
indicated by lattice QCD predictions.Comment: 13 pages, 7 figure

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