Meson Wave Functions Research Articles

Photoproduction ofJ/ψmesons at high energies in the parton model andKT-factorization approach

We consider J/psi meson photoproduction on protons at high energies at the leading order in alpha_s using conventional parton model and k_t-factorization approach of QCD. It is shown that in the both cases the colour singlet mechanism gives correct description for experimental data from HERA for the total cross section and for the J/psi meson z-spectrum at realistic values of a c-quark mass and meson wave function at the origin Psi (0). At the same time our predictions for p_t-spectrum of J/psi meson and for p_t dependence of the spin parameter alpha obtained in k_t-factorization approach are very different from the results obtained in conventional parton model. Such a way the experimental study of a polarized J/psi meson production at the large p_t should be a direct test of BFKL gluons.

Dispersion approach to quark-binding effects in weak decays of heavy mesons

Dispersion approach based on the constituent quark picture and its applications to weak decays of heavy mesons are reviewed. Meson interaction amplitudes are represented within this approach as relativistic spectral integrals over the mass variables in terms of the meson wave functions and spectral densities of the corresponding Feynman diagrams. Various applications of this approach are discussed: Relativistic spectral representations for meson elastic and transition form factors at spacelike momentum transfers are constructed. Form factors at $q^2>0$ are obtained by the analytical continuation. As a result of this procedure, form factors are given in the full $q^2$ range of the weak decay in terms of the wave functions of the participating mesons. The 1/m_Q expansion of the obtained spectral representations for the form factors for the particular limits of the heavy-to-heavy and heavy-to-light transitions are analysed. Their full consistency with the constraints provided by long-distance QCD for these limits is demonstrated. Predictions for form factors for B, B(s), D, and D(s) decays to light mesons are given. The B\to\gamma l\nu decay and the weak annihilation in rare radiative decays are considered. Nonfactorizable corrections to the B^0-\bar B^0 mixing are calculated. Inclusive weak B-decays are analysed and the differential distributions are obtained in terms of the B-meson wave function.

Power corrections of off-forward quark distributions and harmonic operators with definite geometric twist

We introduce a group theoretically motivated procedure of parametrizing non-forward matrix elements of non-local QCD operators by (two-variable) distribution amplitudes of well-defined geometric twist being multiplied by kinematical factors (related to the Lorentz structure of the operators and to the target states) as well as position-dependent coefficient functions resulting from the (infinite) twist decomposition of the operators. These distribution amplitudes are interpreted as (sum over) power corrections of the double distributions. Using the technique of harmonic polynomials for the local operators we determine the (infinite) twist decomposition of totally symmetric operators completely and for operators with non-trivial symmetry type up to twist τ=3. This covers the phenomenological interesting quark–antiquark operators. Using these results we determine the power corrections to the various double distributions and the vector meson wave functions. It is shown that the structure of the kinematical power corrections may be obtained, by harmonic extension, from the corresponding expressions for operators or distribution amplitudes, on the light-cone.

Extended van Royen–Weisskopf formalism for lepton–antilepton meson decay widths within nonrelativistic quark models

The classical van Royen–Weisskopf formula for the decay width of a meson into a lepton–antilepton pair is modified in order to include nonzero quark momentum contributions within the meson as well as relativistic effects. Besides, a phenomenological electromagnetic density for quarks is introduced. The meson wave functions are obtained from two different models: a chiral constituent quark model and a quark potential model including instanton effects. The modified van Royen–Weisskopf formula is found to improve systematically the results for the widths, giving an overall good description of all known decays.

Two-pion decay widths of excited charm mesons

The widths for ππ decay of the L=1 charm mesons are calculated by describing the pion coupling to light constituents quarks by the lowest-order chiral interaction. The wavefunctions of the charm mesons are obtained as solutions to the covariant Blankenbecler–Sugar equation. These solutions correspond to an interaction Hamiltonian modeled as the sum of a linear scalar confining and a screened one-gluon exchange (OGE) interaction. This interaction induces a two-quark contribution to the amplitude for two-pion decay, which is found to interfere destructively with the single-quark amplitude. For the currently known L=1 D mesons, the total ππ-decay widths are found to be ∼1 MeV for the D 1(2420) and ∼3 MeV for the D ∗ 2(2460) if the axial coupling of the constituent quark is taken to be g A q =1 . The as yet undiscovered spin-singlet D 1 ∗ state is predicted to have a larger width of 7–10 MeV for ππ decay.

Radiative decays of basic scalar, vector and tensor mesons and the determination of the P-wave q multiplet

We perform simultaneous calculations of the radiative decays of scalar mesons f 0(980)↦γγ, a 0(980)↦γγ, vector meson φ(1020)↦γf 0(980), γa 0(980), γπ0, γη, γη′ and tensor mesons a 2(1320)↦γγ, f 2(1270)↦γγ, f 2(1525)↦γγ, assuming all these states to be dominantly the q ones. A good description of the considered radiative decays is reached by using almost the same radial wave functions for scalar and tensor mesons that supports the idea for the f 0(980), a 0(980) and a 2(1320), f 2(1270), f 2(1525) to belong to the same P-wave q multiplet.

Instanton and Tensor-Force Effects in the Strong Decays of Mesons

The strong decays of mesons are studied in the framework of the 3 P 0 model with a momentum-dependent vertex. The meson wave functions are obtained from quark-antiquark potentials including a finite quark size, instanton effects, spin-orbit and tensor-force effects. Several prescriptions for treating the decays into three mesons are proposed and analyzed. Comparison to experimental data is presented in detail.

Impact parameter dependent S-matrix for dipole–proton scattering from diffractive meson electroproduction

We extract the S-matrix element for dipole-proton scattering using the data on diffractive electroproduction of vector mesons at HERA. By considering the full t dependence of this process we are able to reliably unfold the profile of the S-matrix for impact parameter values b>0.3 fm. We show that the results depend only weakly on the choice of the form for the vector meson wave function. We relate this result to the discussion about possible saturation effects at HERA.

Hadronic decays of N and Δ resonances in a chiral quark model

π and η decay modes of light baryon resonances are investigated within a chiral quark model whose hyperfine interaction is based on Goldstone-boson exchange. For the decay mechanism a modified version of the 3P0 model is employed. Our primary aim is to provide a further test of the recently proposed Goldstone-boson exchange constituent quark model. We compare the predictions for π and η decay widths with experiment and also with results from a traditional one-gluon exchange constituent quark model. The differences between nonrelativistic and semirelativistic versions of the constituent quark models are outlined. We also discuss the sensitivity of the results on the parameterization of the meson wave function entering the 3P0 model.

Perturbative QCD factorization ofπγ*→γ(π)andB→γ(π)lν¯

We prove factorization theorem for the processes $\pi\gamma^*\to\gamma$ and $\pi\gamma^*\to\pi$ to leading twist in the covariant gauge by means of the Ward identity. Soft divergences cancel and collinear divergences are grouped into a pion wave function defined by a nonlocal matrix element. The gauge invariance and universality of the pion wave function are confirmed. The proof is then extended to the exclusive $B$ meson decays $B\to\gamma l\bar\nu$ and $B\to\pi l\bar\nu$ in the heavy quark limit. It is shown that a light-cone $B$ meson wave function, though absorbing soft dynamics, can be defined in an appropriate frame. Factorization of the $B\to\pi l\bar\nu$ decay in $k_T$ space, $k_T$ being parton transverse momenta, is briefly discussed. We comment on the extraction of the leading-twist pion wave function from experimental data.

Wandzura-Wilczek-type relations of ρ-meson wave functions

We give the geometric Wandzura-Wilczek-type relations between the meson wave functions of dynamical twist by means of the meson wave functions of geometric twist. We discuss the difference between geometric and dynamical Wandzura-Wilczek-type relations. Additionally, the interrelations between the different twist notations of meson wave functions are discussed.

Light vector meson photoproduction at large momentum transfer

We have studied in perturbative QCD all independent helicity amplitudes describing the photoproduction of light vector mesons at large t. We found a new hard production mechanism which is related to the possibility for a real photon to fluctuate into a massless q q pair in a chiral-odd spin configuration. Each helicity amplitude is given as a sum of chiral-even contribution (when the helicities of quark and antiquark are antiparallel) and this additional chiral-odd part (where the helicities of quark and antiquark are parallel). All amplitudes are expressed in terms of short distance asymptotics of the light-cone wave functions of vector meson and photon. The chiral-odd contribution is large, it leads to a dominance of the non spin-flip amplitude in a very broad region of intermediately high | t|.

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

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 do not make any contribution and therefore the possible pollution by them can be avoided, to reexamine $\stackrel{\ensuremath{\rightarrow}}{B}\ensuremath{\pi}$ semileptonic form factors. Also, a comparison between previous results and our results from the light-cone QCD sum rules is made. Our method will be beneficial to the precise extraction of $|{V}_{\mathrm{ub}}|$ from the experimental data on the processes $\stackrel{\ensuremath{\rightarrow}}{B}\ensuremath{\pi}l{\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\nu}}}_{l}.$

Hard exclusive production of tensor mesons

We point out that hard exclusive production of tensor mesons f 2(1270) with helicity λ=±2 is dominated by the gluon component in the meson wave function and can be used to determine gluon admixture in tensor mesons in a theoretically clean manner. We present a detailed analysis of the tensor meson distribution amplitudes and calculate the transition form factor γ+γ ∗→f 2(1270) for one real and one virtual photon.

Penguin enhancement andB→Kπdecays in perturbative QCD

We compute branching ratios of $B\to K\pi$ decays in the framework of perturbative QCD factorization theorem. Decay amplitudes are classified into the topologies of tree, penguin and annihilation, all of which contain both factorizable and nonfactorizable contributions. These contributions are expressed as the convolutions of hard $b$ quark decay amplitudes with universal meson wave functions. It is shown that (1) matrix elements of penguin operators are dynamically enhanced compared to those employed in the factorization assumption; (2) annihilation diagrams are not negligible, contrary to common belief; (3) annihilation diagrams contribute large strong phases; (4) the uncertainty of current data of the ratio $R={\cal B}(B_d^0\to K^\pm\pi^\mp)/{\cal B}(B^\pm\to K^0\pi^\pm)$ and of CP asymmetries is too large to give a constraint of $\phi_3$. Assuming $\phi_3=90^o$ which is extracted from the best fit to the data of $R$, predictions for the branching ratios of the four $B\to K\pi$ modes are consistent with data.

Formula omitted] study of meson decays in a chiral quark model

The strong decays of a meson into two mesons are studied in the framework of the 3P0 model. The meson wave functions are determined by means of a realistic chiral quark model constructed in the baryon sector and comparison is made with a traditional potential of “Coulomb + linear” type. Two different forms for the creation vertex are analyzed. A momentum dependent vertex is proved to be definitively superior. The chiral quark model provides an overall good description of all known transitions and gives results of roughly the same quality as those obtained from phenomenological quark–antiquark potentials.

Meson-meson scattering in the quark model: Spin dependence and exotic channels

We apply a quark interchange model to spin-dependent and exotic meson-meson scattering. The model includes the complete set of standard quark model forces, including OGE spin-orbit and tensor and scalar confinement spin-orbit. Scattering amplitudes derived assuming SHO and Coulomb plus linear plus hyperfine meson wavefunctions are compared. In I=2 pi pi we find approximate agreement with the S-wave phase shift from threshold to 1.5 GeV, where we predict an extremum that is supported by the data. Near threshold we find rapid energy dependence that may reconcile theoretical estimates of small scattering lengths with experimental indications of larger ones based on extrapolation of measurements at moderate kpi^2. In PsV scattering we find that the quark-quark L*S and T forces map into L*S and T meson-meson interactions, and the P-wave L*S force is large. Finally we consider scattering in J^PC-exotic channels, and note that some of the Deck effect mechanisms suggested as possible nonresonant origins of the pi_1(1400) signal are not viable in this model.

Final-state interaction andB→KKdecays in perturbative QCD

We predict branching ratios and CP asymmetries of the $B\to KK$ decays using perturbative QCD factorization theorem, in which tree, penguin, and annihilation contributions, including both factorizable and nonfactorizable ones, are expressed as convolutions of hard six-quark amplitudes with universal meson wave functions. The unitarity angle $\phi_3= 90^o$ and the $B$ and $K$ meson wave functions extracted from experimental data of the $B\to K\pi$ and $\pi\pi$ decays are employed. Since the $B\to KK$ decays are sensitive to final-state-interaction effects, the comparision of our predictions with future data can test the neglect of these effects in the above formalism. The CP asymmetry in the $B^\pm\to K^\pm K^0$ modes and the $B_d^0\to K^\pm K^\mp$ branching ratios depend on annihilation and nonfactorizable amplitudes. The $B\to KK$ data can also verify the evaluation of these contributions.

Hadronic decays of N and Δ resonances in a chiral quark model

\pi and \eta decay modes of light baryon resonances are investigated within a chiral quark model whose hyperfine interaction is based on Goldstone-boson exchange. For the decay mechanism a modified version of the 3P0 model is employed. Our primary aim is to provide a further test of the recently proposed Goldstone-boson-exchange constituent quark model. We compare the predictions for \pi and \eta decay widths with experiment and also with results from a traditional one-gluon-exchange constituent quark model. The differences between nonrelativistic and semirelativistic versions of the constituent quark models are outlined. We also discuss the sensitivity of the results on the parametrization of the meson wave function entering the 3P0 model.

Quark-binding effects in inclusive decays of heavy mesons

We present a new approach to the analysis of quark-binding effects in inclusive decays of heavy mesons within the relativistic dispersion quark model. Various differential distributions, such as electron energy spectrum, $q^2$- and $M_X$-distributions, are calculated in terms of the $B$ meson soft wave function which also determines long-distance effects in exclusive transition form factors. Using the quark-model parameters and the $B$ meson wave function previously determined from the description of the exclusive $b \to u$ transitions within the same dispersion approach, we provide numerical results on various distributions in the inclusive $B \to X_c l\nu$ decays.