Meson Wave Functions Research Articles

AdS/QCD and light front holography: A new approximation to QCD

The combination of Anti-de Sitter space (AdS) methods with light-front holography leads to a semi-classical first approximation to the spectrum and wavefunctions of meson and baryon light-quark bound states. Starting from the bound-state Hamiltonian equation of motion in QCD, we derive relativistic light-front wave equations in terms of an invariant impact variable ζ which measures the separation of the quark and gluonic constituents within the hadron at equal light-front time. These equations of motion in physical space-time are equivalent to the equations of motion which describe the propagation of spin-J modes in anti–de Sitter (AdS) space. Its eigenvalues give the hadronic spectrum, and its eigenmodes represent the probability distributions of the hadronic constituents at a given scale. Applications to the light meson and baryon spectra are presented. The predicted meson spectrum has a string-theory Regge form M2 = 4κ2(n + L + S/2); i.e., the square of the eigenmass is linear in both L and n, where n counts the number of nodes of the wavefunction in the radial variable ζ. The space-like pion and nucleon form factors are also well reproduced. One thus obtains a remarkable connection between the description of hadronic modes in AdS space and the Hamiltonian formulation of QCD in physical space-time quantized on the light-front at fixed light-front time τ. The model can be systematically improved by using its complete orthonormal solutions to diagonalize the full QCD light-front Hamiltonian or by applying the Lippmann–Schwinger method in order to systematically include the QCD interaction terms.

Rare semileptonic decays ofBandBcmesons in the relativistic quark model

Rare semileptonic decays of B and B_c mesons are investigated in the framework of the QCD-motivated relativistic quark model based on the quasipotential approach. Form factors parametrizing the matrix elements of the weak transitions between corresponding meson states are calculated with the complete account of the relativistic effects including contributions of intermediate negative energy states and relativistic transformations of the meson wave functions. The momentum transfer dependence of the form factors is reliably determined in the whole accessible kinematical range. On this basis the total and differential branching fractions of the B\to K^{(*)}l^+l^-(\nu\bar\nu) and B_c\to D_s^{(*)}l^+l^-(\nu\bar\nu), B_c\to D^{(*)}l^+l^-(\nu\bar\nu) decays as well as the longitudinal polarization fractions F_L of the final vector meson and the muon forward-backward asymmetries A_{FB} are calculated. Good agreement of the obtained results with the recent detailed experimental data on the B\to K^{(*)}\mu^+\mu^- decays from Belle and CDF is found. Predictions for the rare semileptonic decays of the B_c mesons are given.

Semileptonic and nonleptonic decays ofBcmesons to orbitally excited heavy mesons in the relativistic quark model

The form factors of weak decays of the B_c meson to orbitally excited charmonium, D, B_s and B mesons are calculated in the framework of the QCD-motivated relativistic quark model based on the quasipotential approach. Relativistic effects are systematically taken into account. The form factor dependence on the momentum transfer is reliably determined in the whole kinematical range. The form factors are expressed trough the overlap integrals of the meson wave functions which are known from the previous mass spectra calculations within the same model. On this basis semileptonic and nonleptonic B_c decay rates to orbitally excited heavy mesons are calculated. Predictions for the B_c decays to the orbitally and radially excited 2P and 3S charmonium states are given which could be used for clarifying the nature of the recently observed charmonium-like states above the open charm production threshold.

Single meson production in photon-photon collisions and infrared renormalons

In this article, we investigate the contribution of the higher-twist Feynman diagrams to the large-$p_T$ inclusive single meson production cross section in photon-photon collisions and present the general formulas for the higher-twist differential cross sections in case of the running coupling and frozen coupling approaches. The structure of infrared renormalon singularities of the higher-twist subprocess cross section and the resummed expression (the Borel sum) for it are found. We compared the resummed higher-twist cross sections with the ones obtained in the framework of the frozen coupling approach and leading-twist cross section. We obtain, that ratio $R=(\Sigma_{M^{+}}^{HT})^{res}$ / $(\Sigma_{M^{+}}^{HT})^{0}$, for all values of the transverse momentum $p_{T}$ of the meson identically equivalent to ratio $r$=($\Delta_{M}^{HT})^{res}$ / $(\Delta_{M}^{HT})^{0}$. It is shown that the resummed result depends on the choice of the meson wave functions used in calculation. Phenomenological effects of the obtained results are discussed.

Scattering vector mesons in D4/D8 model

We review in this proceedings some recent results for vector meson form factors obtained using the holographic D4-D8 brane model. The D4-D8 brane model, proposed by Sakai and Sugimoto, is a holographic dual of a semi-realistic strongly coupled large N_c QCD since it breaks supersymmetry and incorporates chiral symmetry breaking. We analyze the vector meson wave functions and Regge trajectories as well.

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.

Meson wave function from holographic models

We consider the light-front wave function for the valence quark state of mesons using the AdS/CFT correspondence, as has been suggested by Brodsky and Teramond. Two kinds of wave functions, obtained in different holographic Soft-Wall models, are discussed.

Infrared renormalons and single meson production in proton-proton collisions

In this article, we investigate the contribution of the higher-twist Feynman diagrams to the large-${p}_{T}$ inclusive pion production cross section in proton-proton collisions and present the general formulas for the higher-twist differential cross sections in the case of the running coupling and frozen coupling approaches. The structure of infrared renormalon singularities of the higher-twist subprocess cross section and the resummed expression (the Borel sum) for it are found. We compared the resummed higher-twist cross sections with the ones obtained in the framework of the frozen coupling approach and leading-twist cross section. We obtain, that ratio $R=({\ensuremath{\Sigma}}_{{\ensuremath{\pi}}^{+}}^{\mathrm{HT}}{)}^{\mathrm{res}}/({\ensuremath{\Sigma}}_{{\ensuremath{\pi}}^{+}}^{\mathrm{HT}}{)}^{0}$, for all values of the transverse momentum ${p}_{T}$ of the pion identically equivalent to ratio $r=({\ensuremath{\Delta}}_{\ensuremath{\pi}}^{\mathrm{HT}}{)}^{\mathrm{res}}/({\ensuremath{\Delta}}_{\ensuremath{\pi}}^{\mathrm{HT}}{)}^{0}$. It is shown that the resummed result depends on the choice of the meson wave functions used in calculation. Phenomenological effects of the obtained results are discussed.

Uncertainty Study of Bd(Bs) → γνν̄ Decays

B0(Bs) → γνν̄ decays are useful to determining the decay constants fB(fBs) and B(Bs) meson wave function. Using the B meson wave function determined in hadronic B(Bs) decays, we study the uncertainties due to the types of B meson wave functions. We find that the branching ratios are sensitive to the type of wave functions and input parameters, but the energy spectrum is independent. The predicted branching ratios are (0.45–1.04) × 10-9 and (2.14–3.27) × 10-8 for B0 and Bs decay, respectively.

Construction of Lorentz-Invariant Amplitudes from Rest-Frame Wave Functions in HQET: Application to the Isgur-Wise Function

Succeeding in predicting 0^+ and 1^+ states of D and D_s heavy mesons by our semi-relativistic quark potential model, we examine a method how to construct Lorentz-invariant scattering amplitudes and/or decay widths and develop a formulation to calculate Lorentz-boosted ones given the rest frame wave functions in our model. To show how effective this is, we apply the formulation to calculate the semileptonic weak form factors out of the rest frame wave functions of heavy mesons and numerically calculate the dynamical 1/m_Q corrections to those for the process B-bar -> D^{(*)}\ell\nu based on our model for heavy mesons. It is shown that nonvanishing expressions for \rho_1(\omega)=\rho_2(\omega) and \rho_3(\omega)=\rho_4(\omega)=0 are obtained in a special Lorentz frame, where \rho_i(\omega) are the parameters used in the Neubert-Rieckert decomposition of form factors. Various values of form factors are estimated, which are compatible with recent experimental data as well as other theoretical calculations.

On theπandKasqq¯bound states and approximate Nambu-Goldstone bosons

We reconsider the two different facets of $\ensuremath{\pi}$ and $K$ mesons as $q\overline{q}$ bound states and approximate Nambu-Goldstone bosons. We address several topics, including masses, mass splittings between $\ensuremath{\pi}$ and $\ensuremath{\rho}$ and between $K$ and ${K}^{*}$, meson wave functions, charge radii, and the $K\ensuremath{-}\ensuremath{\pi}$ wave function overlap.

An approach towards a constituent quark model on the light cone

We use the vacuum expectation value of a Wegner–Wilson loop representing a fast moving quark–antiquark pair to derive the light cone Hamiltonian for a q q ¯ meson. We solve the corresponding Schrödinger equation for various trial wave functions. The result shows how confinement determines the meson mass and wave function for valence quarks on the light cone. We also parametrize the effect of the spin-dependent splitting for a light meson and charmonium. The correct chiral-symmetry breaking pattern for the pion mass is obtained due to the self-energy of the quark.

Relativistic description of the double charmonium production in [formula omitted] annihilation

New evaluation of the relativistic effects in the double production of S-wave charmonium states is performed on the basis of perturbative QCD and the relativistic quark model. The main improvement consists in the exact account of properties of the relativistic meson wave functions. For the gluon and quark propagators entering the production vertex function we use a truncated expansion in the ratio of the relative quark momenta to the center-of-mass energy s up to the second order. The exact relativistic treatment of the wave functions makes all such second order terms convergent, thus allowing the reliable calculation of their contributions to the production cross section. Compared to the nonrelativistic calculation we obtain a significant increase of the cross sections for the S-wave double charmonium production. This brings new theoretical results in good agreement with the available experimental data.

Cross sections for charmonia dissociation in collisions with pions, rhos and kaons**Supported by National Natural Science Foundation of China (10675079)

We calculate the unpolarized cross sections for dissociation reactions of charmonia in collisions with π, ρ and K in a potential that is derived from QCD. The reactions are governed by the quark-interchange processes. The mesonic quark-antiquark relative-motion wave functions are determined by the central spinindependent terms of the potential. The numerical wave functions and cross sections are parametrized. The difference of transition amplitudes in the prior form and in the post form is explored by deriving and examining the transition amplitudes of the one-gluon-exchange spin-spin term of the potential in the two forms. We find that the post-prior discrepancy in meson-meson elastic scattering that is governed by quark-interchange processes depends on the difference of quark or antiquark masses and of quark-antiquark spatial distributions of the two mesons.

Diffractive vector meson electroproduction at small Bjorken x within GPD approach

We study light vector meson electroproduction at small x within the generalized parton distributions (GPDs) model. The modified perturbative approach is used, where the quark transverse degrees of freedom in the vector meson wave function and hard subprocess are considered. Our results on the cross section and spin observables are in good agreement with experiment.

B(Bs)→D(s)P,D(s)V,D(s)*P, andD(s)*Vdecays in the perturbative QCD approach

Two-body charmed decays B{sub (s)}{yields}D{sub (s)}P, D{sub (s)}*P, D{sub (s)}V, and D{sub (s)}*V, where P and V denote the light pseudoscalar meson and vector meson, respectively, are analyzed in the perturbative QCD (pQCD) approach. Using the experimental data of six B{yields}DP channels, we test the D meson wave function by {chi}{sup 2} fit. We give the branching ratios of all the charmed B decay channels, most of which agree with experiments amazingly well. The predicted B{sub s} decays can be confronted with the future experimental data. By straightforward calculations, our pQCD approach gives the right relative strong phase of a{sub 2}/a{sub 1} that agrees with experiments. We also predict the percentage of transverse polarizations in B{sub (s)}{yields}D*V decay channels.

HIGHER TWIST EFFECTS IN PHOTON–PHOTON COLLISIONS

In this article, we investigate the contribution of the high twist Feynman diagrams to the large-pT single pseudoscalar and vector mesons inclusive production cross section in two-photon collisions and we present the general formulae for the high and leading twist differential cross sections. The pion wave function where two non-trivial Gegenbauer coefficients a2 and a4 have been extracted from the CLEO data, Braun–Filyanov pion wave function, the asymptotic and the Chernyak–Zhitnitsky wave functions are all used in the calculations. For ρ-meson we used the Ball–Braun wave function. The results of the calculations reveal that the high twist cross sections, the ratio R, the dependence transverse momentum pT and the rapidity y of meson in the Φ CLEO (x, Q2) wave function case is very close to the Φ asy (x) asymptotic wave function case. It is shown that the high twist contribution to the cross section depends on the choice of the meson wave functions.

Light-front dynamics and AdS/QCD correspondence: The pion form factor in the space- and time-like regions

The AdS/CFT correspondence between string theory in AdS space and conformal field theories in physical space-time leads to an analytic, semiclassical model for strongly-coupled QCD which has scale invariance and dimensional counting at short distances and color confinement at large distances. The AdS/CFT correspondence also provides insights into the inherently nonperturbative aspects of QCD such as the orbital and radial spectra of hadrons and the form of hadronic wavefunctions. In particular, we show that there is an exact correspondence between the fifth-dimensional coordinate of anti--de Sitter (AdS) space $z$ and a specific light-front impact variable $\ensuremath{\zeta}$ which measures the separation of the quark and gluonic constituents within the hadron in ordinary space-time. This connection allows one to compute the analytic form of the frame-independent light-front wavefunctions of mesons and baryons, the fundamental entities which encode hadron properties and which allow the computation of decay constants, form factors and other exclusive scattering amplitudes. Relativistic light-front equations in ordinary space-time are found which reproduce the results obtained using the fifth-dimensional theory. As specific examples we compute the pion coupling constant ${f}_{\ensuremath{\pi}}$, the pion charge radius $⟨{r}_{\ensuremath{\pi}}^{2}⟩$ and examine the propagation of the electromagnetic current in AdS space, which determines the space and timelike behavior of the pion form factor and the pole of the $\ensuremath{\rho}$ meson.

Spin dependence of heavy quark fragmentation

We propose that the non-perturbative part of the fragmentation function describing the transition from a heavy quark to a heavy meson is proportional to the square of the produced meson wave function at the origin, taking into account hyperfine interactions. We analyze the effects of this proposal on the number of pseudoscalar mesons compared to the number of vector mesons produced and find a good agreement with experimental data. Finally, we discuss further experimental checks for our hypothesis.

Study of leading twist light cone wave functions of2Sstate charmonium mesons

In this paper leading twist light cone wave functions of 2S state charmonium mesons are studied and models of these functions are built.