Information on the Pion Distribution Amplitude from the Pion-Photon Transition Form Factor with the Belle and BaBar Data

The pion-photon transition form factor (TFF) provides strong constraints on the pion distribution amplitude (DA). We perform an analysis of all existing data (CELLO, CLEO, BaBar, Belle) on the pion-photon TFF by means of light-cone pQCD approach in which we include the next-to-leading order correction to the valence-quark contribution and estimate the non-valence-quark contribution by a phenomenological model based on the TFF's limiting behavior at both $Q^2\to 0$ and $Q^2\to\infty$. At present, the pion DA is not definitely determined, it is helpful to have a pion DA model that can mimic all the suggested behaviors, especially to agree with the constraints from the pion-photon TFF in whole measured region within a consistent way. For the purpose, we adopt the conventional model for pion wavefunction/DA that has been constructed in our previous paper \cite{hw1}, whose broadness is controlled by a parameter $B$. We fix the DA parameters by using the CELLO, CLEO, BABAR and Belle data within the smaller $Q^2$ region ($Q^2 \leq 15$ GeV$^2$), where all the data are consistent with each other. And then the pion-photon TFF is extrapolated into larger $Q^2$ region. We observe that the BABAR favors $B=0.60$ which has the behavior close to the Chernyak-Zhitnitsky DA, whereas the recent Belle favors $B=0.00$ which is close to the asymptotic DA. We need more accurate data at large $Q^2$ region to determine the precise value of $B$, and the definite behavior of pion DA can be concluded finally by the consistent data in the coming future.Comment: 6 pages, 5 figures. Slightly changed and references update

Transverse momentum dependence in the perturbative calculation of pion form factor

By reanalysing transverse momentum dependence in the perturbative calculation of pion form factor an improved expression of pion form factor which takes into account the transverse momentum dependenc in hard scattering amplitude and intrinsic transverse momentum dependence associated with pion wave functions is given to leading order, which is available for momentum transfers of the order of a few GeV as well as for $Q \to \infty$. Our scheme can be extended to evaluate the contributions to the pion form factor beyond leading order.Comment: 13 pages in LaTeX, plus 3 Postscript figure

Semileptonic B(Bs,Bc)B(B_s, B_c) decays in the light-cone QCD sum rules

Semileptonic $B$($B_s, B_c$) decays are investigated systematically in the light-cone QCD sum rules. Special emphasis is put on the LCSR calculation on weak form factors with an adequate chiral current correlator, which turns out to be particularly effective to control the pollution by higher twist components of spectator mesons. The result for each channel depends on the distribution amplitude of the the producing meson. The leading twist distribution amplitudes of the related heavy mesons and charmonium are worked out by a model approach in the reasonable way. A practical scenario is suggested to understand the behavior of weak form factors in the whole kinematically accessible ranges. The decay widths and branching ratios are estimated for several $B$($B_c$) decay modes of current interest.Comment: 8 pages, talk given by the first arthur at 4th International Conference on Flavor Physics (ICFP 2007), Beijing, China, Sept 24-28, 200

An Implication on the Pion Distribution Amplitude from the Pion-Photon Transition Form Factor with the New BABAR Data

The new BABAR data on the pion-photon transition form factor arouses people's new interests on the determination of pion distribution amplitude. To explain the data, we take both the leading valence quark state's and the non-valence quark states' contributions into consideration, where the valence quark part up to next-to-leading order is presented and the non-valence quark part is estimated by a phenomenological model based on its limiting behavior at both $Q^2\to 0$ and $Q^2\to\infty$. Our results show that to be consistent with the new BABAR data at large $Q^2$ region, a broader other than the asymptotic-like pion distribution amplitude should be adopted. The broadness of the pion distribution amplitude is controlled by a parameter $B$. It has been found that the new BABAR data at low and high energy regions can be explained simultaneously by setting $B$ to be around 0.60, in which the pion distribution amplitude is closed to the Chernyak-Zhitnitsky form.Comment: 19 pages, 6 figures, 2 tables. Slightly changed, references updated. To be published in Phys.Rev.

Pion Form Factor in the kTk_T Factorization Formalism

Based on the light-cone (LC) framework and the $k_T$ factorization formalism, the transverse momentum effects and the different helicity components' contributions to the pion form factor $F_{\pi}(Q^2)$ are recalculated. In particular, the contribution to the pion form factor from the higher helicity components ($\lambda_1+\lambda_2=\pm 1$), which come from the spin-space Wigner rotation, are analyzed in the soft and hard energy regions respectively. Our results show that the right power behavior of the hard contribution from the higher helicity components can only be obtained by fully keeping the $k_T$ dependence in the hard amplitude, and that the $k_T$ dependence in LC wave function affects the hard and soft contributions substantially. As an example, we employ a model LC wave function to calculate the pion form factor and then compare the numerical predictions with the experimental data. It is shown that the soft contribution is less important at the intermediate energy region.Comment: 21 pages, 4 figure

Improved approach to the heavy-to-light form factors in the light-cone QCD sum

A systematic analysis shows that the main uncertainties in the form factors are due to the twist-3 wave functions of the light mesons in the light-cone QCD sum rules. We propose an improved approach, in which the twist-3 wave functions doesn't make any contribution and therefore the possible pollution by them can be avoided, to re-examine $B \to \pi$ semileptonic form factors. Also, a comparison between the previous and our results from the light-cone QCD sum rules is made. Our method will be beneficial to the precise extracting of $\mid{V_{ub}}\mid$ from the experimental data on the processes $B \to \pi \ell \widetilde{\nu_\ell}$.Comment: New version to appear in PR

The Necessary and Sufficient Conditions of Separability for Multipartite Pure States

In this paper we present the necessary and sufficient conditions of separability for multipartite pure states. These conditions are very simple, and they don't require Schmidt decomposition or tracing out operations. We also give a necessary condition for a local unitary equivalence class for a bipartite system in terms of the determinant of the matrix of amplitudes and explore a variance as a measure of entanglement for multipartite pure states.Comment: Submitted to PRL in Sep. 2004, the paper No is LV9637. Submitted to SIAM on computing, in Jan., 2005, the paper No. is SICOMP 44687. Under reviewing no

Radiative Corrections on the B→PB\to P Form Factors with Chiral Current in the Light-Cone Sum Rules

Based on the approach of the vector form factor $F^{+}_{B\to\pi, K}(q^2)$ in our previous papers, we extend the calculation of the radiative corrections to the $B\to P$ ($P$ stands $\pi$, $K$ and all light pseudoscalar mesons) scalar and tensor form factors $F^{0,T}_{B\to P}(q^2)$ with chiral current in the light-cone sum rules (LCSRs). The most uncertain twist-3 contributions to the $B\to P$ form factors can be naturally eliminated through a properly designed correlator. We present the next-leading-order formulae of $F^{+,0,T}_{B\to P}(q^2)$ with the $b$-quark pole mass that is universal. It has been shown that our results are simpler and less uncertain under the same parameter regions since we only need to calculate the next leading order on the twist-2 part from the obtained LCSR. Second, we obtain $f^{+,0}_{B\to\pi}(0)=0.260^{+0.059}_{-0.040}$, $f^{T}_{B\to\pi}(0)=0.276^{+0.052}_{-0.039}$, $f^{+,0}_{B\to K}(0)=0.334^{+0.094}_{-0.069}$ and $f^{T}_{B\to K}(0) =0.379^{+0.092}_{-0.077}$ at $q^2=0$ and the $SU_f(3)$-breaking effects are discussed too.Comment: 26 pages, 9 figures. References added and typo error corrected. To be published in Phys.Rev.

Heavy-to-light transition form factors and their relations in light-cone QCD sum rules

The improved light-cone QCD sum rules by using chiral current correlator is systematically reviewed and applied to the calculation of all the heavy-to-light form factors, including all the semileptonic and penguin ones. By choosing suitable chiral currents, the light-cone sum rules for all the form factors are greatly simplified and depend mainly on one leading twist distribution amplitude of the light meson. As a result, relations between these form factors arise naturally. At the considered accuracy these relations reproduce the results obtained in the literature. Moreover, since the explicit dependence on the leading twist distribution amplitudes is preserved, these relations may be more useful to simulate the experimental data and extract the information on the distribution amplitude.Comment: 1+16 pages, no figure