Twist-3 Distribution Amplitudes Research Articles

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 $Br(B_c \to\eta_c l\nu) = \left( 9.31^{+2.27}_{-2.01} \right) \times 10^{-3}$.

Light-Front Quark Model Phenomenology Consistent with Chiral Symmetry

We discuss the link between the chiral symmetry of QCD and the numerical results of the light-front quark model, analyzing both the twist-2 and twist-3 distribution amplitudes of a pion. In particular, we exhibit that the pion twist-3 distribution amplitude can flip the sign of curvature as the cutoff scale for the transverse momentum gets lower than a typical scale of around 1 GeV.

Consistency of the light-front quark model with chiral symmetry in the pseudoscalar meson analysis

We discuss the link between the chiral symmetry of QCD and the numerical results of the light-front quark model (LFQM), analyzing both the two-point and three-point functions of a pseudoscalar meson from the perspective of the vacuum fluctuation consistent with the chiral symmetry of QCD. The two-point and three-point functions are exemplified in this work by the twist-2 and twist-3 distribution amplitudes of a pseudoscalar meson and the pion elastic form factor, respectively. The present analysis of the pseudoscalar meson commensurates with the previous analysis of the vector meson two-point function and fortifies our observation that the light-front quark model with effective degrees of freedom represented by the constituent quark and antiquark may provide the view of effective zero-mode cloud around the quark and antiquark inside the meson. Consequently, the constituents dressed by the zero-mode cloud may be expected to satisfy the chiral symmetry of QCD. Our results appear consistent with this expectation and effectively indicate that the constituent quark and antiquark in the LFQM may be considered as the dressed constituents including the zero-mode quantum fluctuations from the vacuum.

Self-Consistent Covariant Description of Twist-3 Distribution Amplitude of a Pseudoscalar Meson in the Light-Front Quark Model

We discuss the light-front zero-mode issue in the light-front quark model prediction of the twist-3 distribution amplitude of a pseudoscalar meson from the perspective of the vacuum fluctuation consistent with the chiral symmetry of QCD.

Form factors for B meson weak decays in QCD light cone sum rules with a chiral current correlator

We report some applications of QCD light cone sum rules (LCSR) to \(B\) meson weak decays. Special emphasis is on estimates of the form factors for \(B\) decays into a pseudoscalar (\(P\))/vector (\(V\)) meson, with a certain chiral current correlator. The main new ingredient, as compared with the case of the standard correlators, is that in the operator product expansion calculations, the contributions due to the twist-3 distribution amplitudes of the related light mesons, which are less known and would bring a larger uncertainty to the calculations with the standard correlators, cancel out fully in the \(B\rightarrow P\) case and do out partially in the \(B\rightarrow V\) one. An important observation, which is similar to that in soft collinear effective theory, is made in twist-3 approximation: whereas only one independent form factor is needed for parameterizing the hadronic matrix elements for a \(B\rightarrow P\) transition induced by all the relevant heavy-light quark currents, there exist two independent form factors under the condition of neglecting the terms suppressed by a factor of \(m_V^2\), for the \(B\rightarrow V\) transition. Therefore, the improved LCSR approach could be of stronger predictive power for the weak form factors. Also, this approach is employed to understand the \(B\rightarrow D\) transitions by introducing a leading twist-2 DA for an energetic \(D\) meson, combined with some of other QCD-based approaches. A detailed QCD next-to-leading order calculation of the \(B\rightarrow \pi \) form factors is presented for an illustrative purpose, and the sum rule results are used to extract the Cabibbo–Kobayashi–Maskawa matrix element \(|V_{ub}|\) from the latest BaBar data.

Self-consistent covariant description of vector meson decay constants and chirality-even quark-antiquark distribution amplitudes up to twist 3 in the light-front quark model

Although the meson decay amplitude described by a two-point function may be regarded as one of the simplest possible physical observable, it is interesting that this apparently simple amplitude bears abundant fundamental informations on QCD vacuum dynamics and chiral symmetry. The light-front zero-mode issue of the vector meson decay constant $f_V$ is in this respect highly non-trivial and deserves careful analyses. We discuss the zero-mode issue in the light-front quark model (LFQM) prediction of $f_V$ from the perspective of the vacuum fluctuation consistent with the chiral symmetry of QCD. We extend the exactly solvable manifestly covariant Bethe-Salpeter model calculation to the more phenomenologically accessible realistic LFQM and present a self-consistent covariant description of $f_V$ analyzing the twist-2 and twist-3 quark-antiquark distribution amplitudes with even chirality.

Light-Front Zero-Mode Issue on the Vector Meson Decay Constant

We discuss the light-front zero-mode issue in the light-front quark model (LFQM) prediction of a vector meson decay constant from the perspective of the vacuum fluctuation consistent with the chiral symmetry of QCD. We extend the exactly solvable manifestly covariant Bethe-Salpeter model calculation to the more phenomenologically accessible realistic LFQM and present a self-consistent covariant description of the vector meson decay constant analyzing the twist-2 and twist-3 quark-antiquark distribution amplitudes with even chirality.

Revisiting the Twist-3 Distribution Amplitudes of K Meson Within the QCD Background Field Approach

In the present paper, we investigate the kaon twist-3 distribution amplitudes (DAs) φKp,σ within the QCD background field approach. The SUf (3)-breaking effects are studied in detail under a systematical way, especially the sum rules for the moments of φKp,σ are obtained by keeping all the mass terms in the s-quark propagator consistently. After adding all the uncertainties in quadrature, the first two Gegenbauler moments of φKp,σ are a1K,p(1 GeV) = − 0.376+0.103−0.148, a2K,p(1 GeV) = 0.701+0.481−0.491, a1K,σ(1 GeV) = −0.160+0.051−0.074, and a2K,σ(1 GeV) = 0.369+0.163−0.149, respectively. Their normalization parameters μpK|1 GeV = 1.188+0.039−0.043 GeV and μσK|1 GeV = 1.021+0.036−0.055 GeV. A detailed discussion on the properties of φKp,σ moments shows that the higher-order s-quark mass terms can indeed provide sizable contributions. Furthermore, based on the newly obtained moments, a model for the kaon twist-3 wavefunction ΨKp,σ (x, k⊥) with a better end-point behavior is constructed, which shall be useful for perturbative QCD calculations. As a byproduct, we make a discussion on the properties of the pion twist-3 DAs.

Properties of the quark-antiquark-gluon Fock state in theηcmeson

In this paper, the twist-3 distribution amplitude of the quark-antiquark-gluon Fock state in the ${\ensuremath{\eta}}_{c}$ meson is studied. To calculate the moments of this distribution amplitude, QCD sum rules are applied. Using the results of the calculation, the model of this distribution amplitude is built. In addition, nonrelativistic QCD matrix elements that determine the properties of the quark-antiquark-gluon Fock state are determined. In particular, the following properties have been calculated: probability amplitude to find the quark-antiquark pair in the color-octet state, fraction of momentum carried by gluon, relative velocity of the color-octet quark-antiquark pair.

GVSγcoupling constant in light cone QCD

We recalculated the coupling constants ${g}_{\ensuremath{\phi}\ensuremath{\sigma}\ensuremath{\gamma}}$, ${g}_{\ensuremath{\phi}{a}_{0}\ensuremath{\gamma}}$, ${g}_{\ensuremath{\omega}\ensuremath{\sigma}\ensuremath{\gamma}}$, ${g}_{{a}_{0}\ensuremath{\omega}\ensuremath{\gamma}}$, ${g}_{\ensuremath{\rho}\ensuremath{\sigma}\ensuremath{\gamma}}$, and ${g}_{{a}_{0}\ensuremath{\rho}\ensuremath{\gamma}}$ by taking into account the contributions of the three-particle up to twist-4 distribution amplitudes of the photon involving quark-gluon and quark-anti-quark-photon fields in the light-cone sum-rule framework.

Extracting the Distribution Amplitudes of the ρ meson from the Color Glass Condensate

We extract the twist-2 and twist-3 Distribution Amplitudes (DAs) of the ρ meson using the HERA data on diffractive ρ photoproduction. We do so using several Colour Glass Condensate (CGC) inspired and a Regge inspired dipole models. We find that our extracted twist-2 DA is not much model dependent and is consistent with QCD Sum Rules and lattice predictions. The extracted twist-3 DA is more model dependent but is still consistent with the Sum Rules prediction.

Phenomenological study of helicity amplitudes of high energy exclusive leptoproduction of theρmeson

We apply a previously developed scheme to consistently include the twist-3 distribution amplitudes for transversely polarized rho meson in order to evaluate, in the framework of kT factorization, the helicity amplitudes for exclusive leptoproduction of a light vector meson, at leading order in alphaS. We compare our results with high energy experimental data for the ratios of helicity amplitudes T11/T00 and T01/T00 and get a good description of the data.

New results on pionic twist-3 distribution amplitudes within the QCD sum rules

We present an improved calculation on the pionic twist-3 distribution amplitudes ${\ensuremath{\phi}}_{p}^{\ensuremath{\pi}}$ and ${\ensuremath{\phi}}_{\ensuremath{\sigma}}^{\ensuremath{\pi}}$, which are studied within the QCD sum rules. By adding all the uncertainties in quadrature, it is found that $⟨{\ensuremath{\xi}}_{p}^{2}⟩={0.248}_{\ensuremath{-}0.052}^{+0.076}$, $⟨{\ensuremath{\xi}}_{p}^{4}⟩={0.262}_{\ensuremath{-}0.055}^{+0.080}$, $⟨{\ensuremath{\xi}}_{\ensuremath{\sigma}}^{2}⟩={0.102}_{\ensuremath{-}0.025}^{+0.035}$ and $⟨{\ensuremath{\xi}}_{\ensuremath{\sigma}}^{4}⟩={0.094}_{\ensuremath{-}0.020}^{+0.028}$. Furthermore, with the help of these moments, we construct a model for the twist-3 wave functions ${\ensuremath{\psi}}_{p,\ensuremath{\sigma}}^{\ensuremath{\pi}}(x,{\mathbf{k}}_{\ensuremath{\perp}})$, which have better end point behavior and are helpful for perturbative QCD approach. The obtained twist-3 distribution amplitudes are adopted to calculate the $B\ensuremath{\rightarrow}\ensuremath{\pi}$ transition form factor ${f}_{B\ensuremath{\pi}}^{+}$ within the QCD light cone sum rules up to next-to-leading order. By suitable choice of the parameters, we obtain a consistent ${f}_{B\ensuremath{\pi}}^{+}$ with those obtained in the literature.

B(s)→Stransitions in the light cone sum rules with the chiral current

$B_{(s)}$ semi-leptonic decays to the light scalar meson, $B_{(s)}\to S l\bar{\nu}_l, S l \bar{l}\,\,(l=e,\mu,\tau)$, are investigated in the QCD light-cone sum rules (LCSR) with chiral current correlator. Having little knowledge of ingredients of the scalar mesons, we confine ourself to the two quark picture for them and work with the two possible Scenarios. The resulting sum rules for the form factors receive no contributions from the twist-3 distribution amplitudes (DA's), in comparison with the calculation of the conventional LCSR approach where the twist-3 parts play usually an important role. We specify the range of the squared momentum transfer $q^2$, in which the operator product expansion (OPE) for the correlators remains valid approximately. It is found that the form factors satisfy a relation consistent with the prediction of soft collinear effective theory (SCET). In the effective range we investigate behaviors of the form factors and differential decay widthes and compare our calculations with the observations from other approaches. The present findings can be beneficial to experimentally identify physical properties of the scalar mesons.

Radiative vertex VPγ and [formula omitted] mixing in light-cone sum rules

In this work, we calculate radiative vertex VPγ (V=ϕ,ω,ρ and P=η,η′) by utilizing ω–ϕ mixing scheme and taking into account the contributions of the three-particle twist-4 distribution amplitudes of the photon in QCD sum rules on light cone. According to experimental data of V→Pγ and P→Vγ from PDG, a value of the η–η′ mixing angle, φ=(40.9±0.5)°, is extracted in the framework of the quark-flavor basis to describe the η–η′ system.

COUPLING gϕa0γ AND gϕσγ IN LIGHT-CONE SUM-RULES

In this paper, we calculate the coupling constants gϕa0γ and gϕσγ by utilizing ω–ϕ mixing scheme and taking into account the contributions of the three-particle twist-4 distribution amplitudes of the photon in the light-cone sum-rule approach. Our results: (1) 0.130 ≤ gϕa0γ ≤ 0.194 is in agreement with the previous estimations of these coupling constants which obtained from phenomenological considerations but less than the experimental value gϕa0γ = 1.64±0.05; (2) 0.055 ≤ gϕσγ ≤ 0.076 is consistent with the phenomenological value and the experimental value gϕσγ = 0.060±0.008.

The cross section of the process e ++e −→J/ψ+η c within the QCD light-cone sum rules

We calculate the cross section of the exclusive process $e^{+} +e^{-}\to J/\psi+\eta_c$ at the leading order approximation within the QCD light-cone sum rules (LCSR) approach. It is found that the form factor $F_{VP}(V=J/\psi,P=\eta_c)$ depends mainly on the behavior of the twist-2 distribution amplitude of the $\eta_c$-meson at the scale of this process. Thus in order to obtain a reliable estimation of the cross section, it is important to have a realistic distribution amplitude of the $\eta_c$ meson, and to deal with the evolution of the distribution amplitude to the effective energy scale of the process. Our results show that one can obtain a compatible prediction with the Belle and BarBar experimental data.

Two-pseudoscalar-meson decay ofχcJwith twist-3 corrections

The decays of ${\ensuremath{\chi}}_{cJ}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$, ${K}^{+}{K}^{\ensuremath{-}}$ ($J=0,2$) are discussed within the standard and modified hard-scattering approach when including the contributions from twist-3 distribution amplitudes and wave functions of the light pseudoscalar meson. A model for twist-2 and twist-3 distribution amplitudes and wave functions of the pion and kaon with BHL prescription are proposed as the solution to the end-point singularities. The results show that the contributions from twist-3 parts are actually not power suppressed comparing with the leading-twist contribution. After including the effects from the transverse momentum of light meson valence-quark state and Sudakov factors, the decay widths of the ${\ensuremath{\chi}}_{cJ}$ into pions or kaons are comparable with the their experimental data.

Double charmonium production atBfactories within light cone formalism

This paper is devoted to the study of the processes e^+e^- \to J/\Psi \eta_c, J/\Psi \eta_c', \psi' \eta_c, \psi' \eta_c' within light cone formalism. It is shown that if one disregards the contribution of higher fock states, the twist-3 distribution amplitudes needed in the calculation can be unambiguously determined from the twist-2 distribution amplitudes and equations of motion. Using models of the twist-2 distribution amplitudes the cross sections of the processes under study have been calculated. The results of the calculation are in agreement with Belle and BaBar experiments. It is also shown that relativistic and radiative corrections to the cross sections play crucial role in the achievement of the agreement between the theory and experiments. The comparison of the results of this paper with the results obtained in other papers has been carried out. In particular, it is shown that the results of papers where relativistic and radiative corrections were calculated within NRQCD are overestimated by a factor of ~1.5.

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.