Quark Distribution Amplitudes Research Articles

Pseudoscalar mesons: Light front wave functions, GPDs, and PDFs

We develop a unified algebraic model which satisfactorily describes the internal structure of pion and kaon as well as heavy quarkonia (${\ensuremath{\eta}}_{c}$ and ${\ensuremath{\eta}}_{b}$). For each of these mesons, we compute their generalized parton distributions (GPDs), built through the overlap representation of their light front wave function, tightly constrained by the modern and precise knowledge of their quark distribution amplitudes. From this three-dimensional knowledge of mesons, we deduce parton distribution functions (PDFs) as well as electromagnetic form factors and construct the impact parameter space GPDs. The PDFs for mesons formed with light quarks are then evolved from the hadronic scale of around 0.3 to 5.2 GeV, probed in experiments. We make explicit comparisons with experimental results available and with earlier theoretical predictions.

Nonperturbative partonic quasidistributions of the pion from chiral quark models

We evaluate nonperturbatively the quark quasidistribution amplitude and the valence quark quasidistribution function of the pion in the framework of chiral quark models, namely the Nambu–Jona-Lasinio model and the Spectral Quark Model. We arrive at simple analytic expressions, where the nonperturbative dependence on the longitudinal momentum of the pion can be explicitly assessed. The model results for the quark quasidistribution amplitude of the pion compare favorably to the data obtained from the Euclidean lattice simulations. The quark distribution amplitude, arising in the limit of infinite longitudinal momentum of the pion, agrees, after suitable QCD evolution, to the recent data extracted from Euclidean lattices, as well as to the old data from transverse lattice simulations.

Exclusive radiative Z-boson decays to mesons with flavor-singlet components

We present a detailed study of the exclusive radiative decays $Z\to\eta^{(\prime)}\gamma$ employing the QCD factorization approach. We derive a factorization formula for the decay amplitudes valid at leading power in an expansion in $(\Lambda_{QCD}/m_Z)^2$, which includes convolutions of calculable hard-scattering kernels with the leading-twist quark and gluon light-cone distribution amplitudes of the mesons. Large logarithms arising in the evolution from the high scale $m_Z$ down to hadronic scales are resummed using the renormalization group, carefully accounting for the effects of the heavy bottom and charm quarks. Our results for the branching ratios are very sensitive to hadronic input parameters, such as the decay constants and mixing angle characterizing the $\eta-\eta'$ system. Using the most recent estimates of these parameters, we obtain the branching ratios $Br(Z\to\eta\gamma)\sim 1.6\cdot 10^{-10}$ and $Br(Z\to\eta'\gamma)\sim 4.7\cdot 10^{-9}$. A measurement of these processes at a future high-luminosity Z factory could provide interesting information on the gluon distribution amplitude.

LEPTONIC DECAY WIDTHS OF VECTOR MESONS IN A RELATIVISTIC POTENTIAL MODEL

Leptonic decay widths and the corresponding decay constants of neutral vector mesons are calculated in the framework of a square-root potential model of independent quarks. Starting with the assumption that a strong correlation exists between the momenta of the quark and anti-quark inside the meson so as to have their total momenta identically zero in the center-of-mass frame of the meson, we find the quark and anti-quark momentum distribution amplitude which is used to determine the transition probability amplitude for the leptonic decay of mesons. The calculated results for leptonic decay widths and the electromagnetic decay constants for the vector mesons \rho, \omega, \phi and \psi are in good agrement with the corresponding experimental values. The results for the heavy meson \Upsilon are somewhat lower than the experimental values.

TWIST-THREE DISTRIBUTION AMPLITUDES AND OCTET CURRENT DECAY CONSTANTS OF η AND η': A QCD SUM RULE APPROACH

We investigate twist-three distribution amplitudes (DAs) of η and η' using QCD sum rules. Zeroth moments of light quark DAs of η and η' are evaluated and compared with those found in other approaches. The decay constants of the octet axial vector current in the η and η' system are also estimated.

Study of quark distribution amplitudes of 1S and 2S heavy quarkonium states

In this paper, the quark distribution amplitudes of 1S and 2S heavy quarkonium states are studied in terms of Gaussian-type wave functions. The transverse momenta $p_\perp$ integrals of the formulae for the decay constant are performed analytically. Then the quark distribution amplitudes are obtained. In addition, the $\xi$-moments are also calculated. After fixing the relevant parameters appearing in the quark distribution amplitude, the curves of the quark distribution amplitude for 1S and 2S heavy quarkonium states are plotted. Finally, the numerical results of this approach are compared with the other theoretical predictions.

Perturbative QCD analysis of exclusiveJ/ψ+ηcproduction ine+e−annihilation

We analyze the exclusive charmonium $J/\ensuremath{\psi}+{\ensuremath{\eta}}_{c}$ pair production in ${e}^{+}{e}^{\ensuremath{-}}$ annihilation using the nonfactorized perturbative QCD and the light-front quark model (LFQM) that goes beyond the peaking approximation. We effectively include all orders of higher twist terms in the leading order of QCD coupling constant and compare our nonfactorized analysis with the usual factorized analysis in the calculation of the cross section. We also calculate the quark distribution amplitudes, the Gegenbauer moments, and the decay constants for $J/\ensuremath{\psi}$ and ${\ensuremath{\eta}}_{c}$ mesons using our LFQM. Our nonfactorized result enhances the nonrelativistic QCD result by a factor of $3\ensuremath{\sim}4$ at $\sqrt{s}=10.6\text{ }\text{ }\mathrm{GeV}$.

Distribution amplitudes and decay constants for(π,K,ρ,K*)mesons in the light-front quark model

We present a calculation of the quark distribution amplitudes (DAs), the Gegenbauer moments, and decay constants for $\ensuremath{\pi}$, $\ensuremath{\rho}$, $K$, and ${K}^{*}$ mesons using the light-front quark model. While the quark DA for $\ensuremath{\pi}$ is somewhat broader than the asymptotic one, that for $\ensuremath{\rho}$ meson is very close to the asymptotic one. The quark DAs for $K$ and ${K}^{*}$ show asymmetric form due to the flavor SU(3)-symmetry breaking effect. The decay constants for the transversely polarized $\ensuremath{\rho}$ and ${K}^{*}$ mesons (${f}_{\ensuremath{\rho}}^{T}$ and ${f}_{{K}^{*}}^{T}$) as well as the longitudinally polarized ones (${f}_{\ensuremath{\rho}}$ and ${f}_{{K}^{*}}$) are also obtained. Our averaged values for ${f}_{V}^{T}/{f}_{V}$, i.e. $({f}_{\ensuremath{\rho}}^{T}/{f}_{\ensuremath{\rho}}{)}_{\mathrm{av}}=0.78$ and $({f}_{{K}^{*}}^{T}/{f}_{{K}^{*}}{)}_{\mathrm{av}}=0.84$, are found to be consistent with other model predictions. Especially, our results for the decay constants are in good agreement with the SU(6) symmetry relation, ${f}_{\ensuremath{\rho}({K}^{*})}^{T}=({f}_{\ensuremath{\pi}(K)}+{f}_{\ensuremath{\rho}({K}^{*})})/2$.

Analysis of the Σ–n form-factors with light-cone QCD sum rules

In this work, we study the four form-factors f1(Q2), f2(Q2), g1(Q2) and g2(Q2) of the Σ → n in the framework of the light-cone QCD sum rules approach up to twist-6 three valence quark light-cone distribution amplitudes. The f1(0) is the basic input parameter in extracting the CKM matrix element |Vus| from the hyperon decays. The four form-factors f1(Q2), f2(Q2), g1(Q2) and g2(Q2) at intermediate and large momentum transfers with Q2 > 3 GeV2 have significant contributions from the end-point (soft) terms. The numerical values of the four form-factors f1(0), f2(0), g1(0) and g2(0) are compatible with the experimental data and theoretical calculations (in magnitude), although the uncertainties are large.

Conformal symmetry and pion form factor: Soft and hard contributions

We discuss a constraint of conformal symmetry in the analysis of the pion form factor. The usual power-law behavior of the form factor obtained in the perturbative QCD analysis can also be attained by taking negligible quark masses in the nonperturbative quark model analysis, confirming the recent AdS/CFT correspondence. We analyze the transition from soft to hard contributions in the pion form factor considering a momentum-dependent dynamical quark mass from an appreciable constituent quark mass at low momentum region to a negligible current quark mass at high momentum region. We find a correlation between the shape of nonperturbative quark distribution amplitude and the amount of soft and hard contributions to the pion form factor.

Scalar form factor of the proton with light-cone QCD sum rules

In this article, we calculate the scalar form-factor of the proton in the framework of the light-cone QCD sum rules approach with the three valence quark light-cone distribution amplitudes up to twist-6, and observe the scalar form-factor $\sigma(t=-Q^2)$ at intermediate and large momentum transfers $Q^2> 2GeV^2$ has significant contributions from the end-point (or soft) terms. The numerical values for the $\sigma(t=-Q^2)$ are compatible with the calculations from the chiral quark model and lattice QCD at the region $Q^2>2GeV^2$.

Axial form-factor and induced pseudoscalar form-factor of the nucleons

In this article, we calculate the axial and the induced pseudoscalar form-factors $G_A(t=-Q^2)$ and $G_P(t=-Q^2)$ of the nucleons in the framework of the light-cone QCD sum-rules approach up to twist-6 three valence quark light-cone distribution amplitudes, and observe that the form-factors $G_A(t=-Q^2)$ and $G_P(t=-Q^2)$ at intermediate and large momentum transfers with $Q^2> 2 GeV^2$ have significant contributions from the end-point (soft) terms. The numerical values for the axial form-factor $G_A(t=-Q^2)$ are compatible with the experimental data and theoretical calculations, for example, the chiral quark models and lattice QCD. The numerical values for the induced pseudoscalar form-factor $G_P(t=-Q^2)$ are compatible with the calculation from the Bethe-Salpeter equation.

Probing quark-distribution amplitudes through generalized parton distributions at large momentum transfer.

In the large momentum transfer limit, generalized parton distributions can be calculated through a QCD factorization theorem which involves perturbatively calculable hard kernels and light-cone parton distribution amplitudes of hadrons. We illustrate this through the H(q)(x,xi,t) distribution for the pion and the proton, presenting the hard kernels at leading order. As a result, experimental data on the generalized parton distributions in this regime can be used to determine the functional form of the parton distribution amplitudes which has thus far been quite challenging to obtain. Our result can also be used as a constraint in phenomenological generalized parton distribution parametrizations.

Two-gluon components of theηandη′mesons to leading-twist accuracy

We critically reexamine the formalism for treating the leading-twist contributions from the two-gluon Fock components occurring in hard processes that involve eta and eta' mesons and establish a consistent set of conventions for the definition of the gluon distribution amplitudes, the anomalous dimensions as well as the projector of a two-gluon state onto an eta or eta' state. We calculate the eta, eta'--photon transition form factor to order alpha_s and show the cancellation of the collinear and UV singularities explicitly. An estimate of the lowest Gegenbauer coefficients of the gluon and quark distribution amplitudes is obtained from a fit to the eta, eta'--photon transition form factor data. In order to elucidate the role of the two-gluon Fock component further, we analyze electroproduction of eta, eta' mesons and the g*g* eta (eta') vertex.

Pion light-cone wave function and pion distribution amplitude in the Nambu–Jona-Lasinio model

We compute the pion light-cone wave function and the pion quark distribution amplitude in the Nambu-Jona-Lasinio model. We use the Pauli-Villars regularization method and as a result the distribution amplitude satisfies proper normalization and crossing properties. In the chiral limit we obtain the simple results, namely phi_pi(x)=1 for the pion distribution amplitude, and <k_perp^2> = -M <ubar u> / f_pi^2 for the second moment of the pion light-cone wave function, where M is the constituent quark mass and f_pi is the pion decay constant. After the QCD Gegenbauer evolution of the pion distribution amplitude good end-point behavior is recovered, and a satisfactory agreement with the analysis of the experimental data from CLEO is achieved. This allows us to determine the momentum scale corresponding to our model calculation, which is close to the value Q_0 = 313 MeV obtained earlier from the analogous analysis of the pion parton distribution function. The value of <k_perp^2> is, after the QCD evolution, around (400 MeV)^2. In addition, the model predicts a linear integral relation between the pion distribution amplitude and the parton distribution function of the pion, which holds at the leading-order QCD evolution.

Exploring skewed parton distributions with two-body models on the light front: Bimodality

We explore skewed parton distributions for simple, model wave-functions in a truncated two-body Fock space. Consideration of non-Gaussian wave functions is our main emphasis, from which we observe the distributions are bimodal (there can be two distinct peaks) in the Fock-space diagonal overlap region (x > xi). We demonstrate that this behavior arises from convoluting two light-front wave functions to form the skewed parton distribution. Furthermore, the factorization Ansaetze, which have been used often, are shown not to hold. At high t, we can write the skewed parton distribution in terms of quark distribution amplitudes and perturbative wave functions thereby providing new tests.

NLO corrections and contribution of a tensor gluon operator to the process [formula omitted

We have calculated the NLO corrections for the leading twist amplitude of the reaction γ ∗γ→ππ at large virtuality of the photon and at W 2≪ Q 2. With a simple model for the two-pion quark and gluon distribution amplitudes we have estimated that the NLO effects may reduce the leading-order amplitude by as much as 30%. We have found that besides the usual twist-2 quark and gluon operators the NLO amplitude receives contribution from a distribution associated with twist-2 tensor gluon operator. The new gluon distribution can be investigated by studying the azimuthal asymmetry of the cross section for e+ γ→ e′+ ππ.

Compton scattering and the nucleon valence wavefunction

Calculations are presented for real Compton scattering on the nucleon in a PQCD formalism by starting from different quark distribution amplitudes of the nucleon. In a second step we present the formalism to extract this distribution amplitude in a model independent way from hard exclusive Compton scattering data.

Going beyond the peaking approximation in the PQCD analysis of exclusive heavy meson pair production

In the PQCD analyses of the exclusive production of higher generation hadrons, the quark distribution amplitude of the heavy quark system has often been approximated by a {delta} function from the nonrelativistic consideration. Going beyond the peaking approximation, the factorization of the covariant hard scattering amplitude from the nonperturbative quark distribution amplitude is no longer valid. We therefore use the light-cone time-ordered perturbation theory which is the step prior to the usual factorization formula and calculate the form factor of a pseudoscalar meson composed of a heavy quark and antiquark. However, we find that the numerical results for the cross section of exclusive heavy meson pair production in e{sup +}e{sup {minus}} annihilation are not much different from those of the peaking approximation. {copyright} {ital 1997} {ital The American Physical Society}

Heavy Quark Limit of Weak Transition Form Factors in a Light-Cone Constituent Quark Model11The project supported by the Grant LWTZ of The Chinese Academy of Sciences

In the light-cone constituent quark model, the wavefunction for or with three quarks is reduced to a wavefunction for the heavy-quark-diquark picture by assuming that the two light quarks forming a diquark are in comoving. A heavy quark (or diquark) distribution amplitude is obtained. While form factors of weak transition are calculated in the finite mass case, a hadronic-size-dependent form of Isgur-Wise function is obtained in the limit.