Distribution Amplitude Moments Research Articles

Uncertainties of the Brightarrow D transition form factor from the D-meson leading-twist distribution amplitude

The Brightarrow D transition form factor (TFF) f^{Brightarrow D}_+(q^2) is determined mainly by the D-meson leading-twist distribution amplitude (DA) , phi _{2;D}, if the proper chiral current correlation function is adopted within the light-cone QCD sum rules. It is therefore significant to make a comprehensive study of DA phi _{2;D} and its impact on f^{Brightarrow D}_+(q^2). In this paper, we calculate the moments of phi _{2;D} with the QCD sum rules under the framework of the background field theory. New sum rules for the leading-twist DA moments leftlangle xi ^nrightrangle _D up to fourth order and up to dimension-six condensates are presented. At the scale mu = 2 ,mathrm{GeV}, the values of the first four moments are: leftlangle xi ^1rightrangle _D = -0.418^{+0.021}_{-0.022}, leftlangle xi ^2rightrangle _D = 0.289^{+0.023}_{-0.022}, leftlangle xi ^3rightrangle _D = -0.178 pm 0.010 and leftlangle xi ^4rightrangle _D = 0.142^{+0.013}_{-0.012}. Basing on the values of leftlangle xi ^nrightrangle _D(n=1,2,3,4), a better model of phi _{2;D} is constructed. Applying this model for the TFF f^{Brightarrow D}_+(q^2) under the light cone sum rules, we obtain f^{Brightarrow D}_+(0) = 0.673^{+0.038}_{-0.041} and f^{Brightarrow D}_+(q^2_{mathrm{max}}) = 1.117^{+0.051}_{-0.054}. The uncertainty of f^{Brightarrow D}_+(q^2) from phi _{2;D} is estimated and we find its impact should be taken into account, especially in low and central energy region. The branching ratio mathcal {B}(Brightarrow Dlbar{nu }_l) is calculated, which is consistent with experimental data.

Heavy pseudoscalar twist-3 distribution amplitudes within QCD theory in background fields

In this paper, we study the properties of the twist-3 distribution amplitude (DA) of the heavy pseudo-scalars such as $\eta_c$, $B_c$ and $\eta_b$. New sum rules for the twist-3 DA moments $\left<\xi^n_P\right>_{\rm HP}$ and $\left<\xi^n_\sigma\right>_{\rm HP}$ up to sixth orders and up to dimension-six condensates are deduced under the framework of the background field theory. Based on the sum rules for the twist-3 DA moments, we construct a new model for the two twist-3 DAs of the heavy pseudo-scalar with the help of the Brodsky-Huang-Lepage prescription. Furthermore, we apply them to the $B_c\to\eta_c$ transition form factor ($f^{B_c\to\eta_c}_+(q^2)$) within the light-cone sum rules approach, and the results are comparable with other approaches. It has been found that the twist-3 DAs $\phi^P_{3;\eta_c}$ and $\phi^\sigma_{3;\eta_c}$ are important for a reliable prediction of $f^{B_c\to\eta_c}_+(q^2)$. For example, at the maximum recoil region, we have $f^{B_c\to\eta_c}_+(0) = 0.674 \pm 0.066$, in which those two twist-3 terms provide $\sim33\%$ and $\sim22\%$ contributions. Also we calculate the branching ratio of the semi-leptonic decay $B_c \to\eta_c l\nu$ as $Br(B_c \to\eta_c l\nu) = \left( 9.31^{+2.27}_{-2.01} \right) \times 10^{-3}$.

Heavy pseudoscalar leading-twist distribution amplitudes within QCD theory in background fields

In this paper, we study the leading-twist distribution amplitude (DA) of the heavy pseudoscalars (HPs), such as $\eta_c$, $\eta_b$ and $B_c$, within the QCD theory in the background fields. New sum rules up to dimension-six condensates for both the HP decay constants and their leading-twist DA moments are presented. From the sum rules for the HP decay constants, we obtain $f_{\eta_c} = 453 \pm 4 \textrm{MeV}$, $f_{B_c} = 498 \pm 14 \textrm{MeV}$, and $f_{\eta_b} = 811 \pm 34 \textrm{MeV}$. Basing on the sum rules for the HPs' leading-twist DA moments, we construct a new model for the $\eta_c$, $\eta_b$ and $B_c$ leading-twist DAs. Our present HP DA model can also be adaptable for the light pseudo-scalar DAs, such as the pion and kaon DAs. Thus, it shall be applicable for a wide range of QCD exclusive processes. As an application, we apply the $\eta_c$ leading-twist DA to calculate the $B_c \to \eta_c$ transition form factor $f_+^{B_c \to \eta_c}(q^2)$. At the maximum recoil region, we obtain $f_+^{B_c \to \eta_c}(0) = 0.612^{+0.053}_{-0.052}$. After further extrapolating the TFF $f_+^{B_c \to \eta_c}(q^2)$ to its allowable $q^2$ region, we predict the branching ratio for the semi-leptonic decay $B_c \to \eta_c l \nu$. We obtain ${\cal B}(B_c \to \eta_c l \nu)=\left(7.70^{+1.65}_{-1.48}\right) \times 10^{-3}$ for massless leptons, which is consistent with the LCSRs estimation obtained in the literature.

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 $\left<\xi^2\right>|_{\rm 1\;GeV} = 0.338 \pm 0.032$, $\left<\xi^4\right>|_{\rm 1\;GeV} = 0.211 \pm 0.030$ and $\left<\xi^6\right>|_{\rm 1\;GeV} = 0.163 \pm 0.030$. 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.

B→K transition form factor up to $\mathcal{O}(1/m^2_b)$ within the kT factorization approach

We apply the k(T) factorization approach to deal with the B-->K transition form factor F-+,0(B-->K) (q(2)) in the large recoil regions. The B-meson wave functions Psi(B) and Psi(B) that include the 3-particle Fock states' contributions are adopted to give a consistent PQCD analysis of the form factor up to O(1/m(b)(2)). It has been found that the two wave functions Psi(B) and Psi(B) can give sizable contributions to the form factor and should be kept for a better understanding of the B-meson decays. Next the contributions from different twist structures of the kaon wave function are discussed, including SUf(3)-breaking effects. A sizable contribution from the twist-3 wave function Psi(p) is found, whose model dependence is discussed by taking two groups of parameters that are determined by different distribution amplitude moments obtained in the literature. It is also shown that F-+,0(B-->K) (0) = 0.30 +/- 0.04 and [F-+,0(B-->K) (0)/F-+,0(B-->pi) (0)] = 1.13 +/- 0.02, which are more reasonable and consistent with the light-cone sum rule results in the large recoil regions.

A COMPREHENSIVE ANALYSIS OF THE PION–PHOTON TRANSITION FORM FACTOR IN THE LEADING ORDER APPROXIMATION

We perform a comprehensive analysis of the pion–photon transition form factor Fπγ(Q2) involving the transverse momentum corrections in the leading order approximation with the present CLEO experimental data, in which the contributions beyond the leading Fock state have been taken into consideration. As is well known, the leading Fock-state contribution dominates of Fπγ(Q2) at large momentum transfer (Q2) region. One should include the contributions beyond the leading Fock state in small Q2 region. In this paper, we construct a phenomenological expression to estimate the contributions beyond the leading Fock state based on its asymptotic behavior at Q2→0. Our present theoretical results agree well with the experimental data in the whole Q2 region. Then, we extract some useful information of the pionic leading twist-2 distribution amplitude (DA) by comparing our results of Fπγ(Q2) with the CLEO data. By taking best fit, we have the distribution amplitude moments, [Formula: see text] and all of higher moments, which are closed to the asymptotic-like behavior of the pion wave function.

A bound for the three-quark component of the nucleon wave function

We constrain the probability for the three-quark component of the nucleon wave function by comparing its contribution to the deep-inelastic structure function data for F 2( x). The three-quark wave function is constrained by QCD sum rules, i.e., its longitudinal projection has to agree with the Chernyak-Zhitnitski distribution amplitude moments. To relate the distribution amplitudes to F 2( x) a specific model for the transverse momentum distribution is needed. We compare two such models and find that both give rather similar results. We conclude that the probability of finding only three quarks in a nucleon could be as large as (3–5)% for experimentally accessible values of Q 2.

Simple relativistic model for the b1 structure function of the rho meson.

Motivated by the recent discussion of the ${b}_{1}$ structure function in spin-1 systems in QCD, we discuss a simple, constituent-quark, light-cone wave-function model for the $\ensuremath{\rho}$ meson. When the constraints following from the calculation of $\ensuremath{\rho}$ distribution amplitude moments, as found by QCD sum rules, are incorporated into the model, helicity-zero and -one wave functions have quite different shapes. As a consequence, we obtain ${b}_{1}\ensuremath{\sim}{F}_{1}$.

Determining probabilities and momentum fractions from distribution amplitudes.

We study what various distribution amplitudes suggest for probability and momentum-fraction sharing among valence quarks of given flavor and helicity. If only because squaring and integrating are done in different orders, a strong asymmetry seen in distribution amplitude moments need not imply a strong asymmetry when probabilities or expectation values of momentum fractions are calculated, or even an asymmetry in the same direction. For example, regardless of the moments an asymmetric wave function always gives a lower probability for finding positive-helicity up quarks in a positive-helicity proton than a symmetric wave function gives. We calculate, using a factored approximation for the wave function, the distribution of probability and momentum fraction for several popular distribution amplitudes.

Synthesis of Perturbative and Nonperturbative Quantum Chromodynamics

Hadronic structure in QCD has been analyzed by using the Fock state wavefunctions of hadrons defined by quantizing quantum chromodynamics at equal time of the light-cone. They provide a unified approach to QCD phenomenology. We have presented a convenient method for operator product expansion in the external background fields and have obtained the distribution amplitude moments values from QCD sum rule by introducing the condensate effect of quarks and gluons. These results are in agreement with the present data.