Hadronic Wave Functions Research Articles

Applications of light-front QCD

Light-front Fock state wavefunctions encode the bound state properties of hadrons in terms of their quark and gluon degrees of freedom at the amplitude level. The freedom to choose the light-like quantization four-vector provides an explicitly covariant formulation of light-front quantization and can be used to determine the analytic structure of light-front wave functions. The AdS/CFT correspondence of large N_C supergravity theory in higher-dimensional anti-de Sitter space with supersymmetric QCD in 4-dimensional space-time has interesting implications for hadron phenomenology in the conformal limit, including an all-orders demonstration of counting rules for exclusive processes. String/gauge duality also predicts the QCD power-law behavior of light-front Fock-state hadronic wavefunctions with arbitrary orbital angular momentum at high momentum transfer. The form of these near-conformal wavefunctions can be used as an initial ansatz for a variational treatment of the light-front QCD Hamiltonian. I also briefly review recent work which shows that some leading-twist phenomena such as the diffractive component of deep inelastic scattering, single spin asymmetries, nuclear shadowing and antishadowing cannot be computed from the LFWFs of hadrons in isolation.

Searching evidence for the color glass condensate at RHIC

This contribution discusses the phenomenon of parton saturation, the color glass picture of hadronic wavefunctions, and their relevance in the early stages of nucleus–nucleus collisions. Evidence for the color glass condensate in the presently available RHIC data is critically reviewed.

Predictions fore+e−→J/ψηcwith light-cone wave functions

Predictions for ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}J/\ensuremath{\psi}{\ensuremath{\eta}}_{c}$ from previous studies are made by taking charmonia as a nonrelativistic bound state and by using nonrelativistic QCD (NRQCD) approach. The predicted cross section is smaller by an order of magnitude than the experimentally observed cross section. We study the process by taking charm quark as a light quark and use light-cone wave functions to parameterize nonperturbative effects related to charmonia. The total cross section of ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}J/\ensuremath{\psi}{\ensuremath{\eta}}_{c}$ can be predicted, if these wave functions are known. Motivated by studies of light-cone wave functions of light hadrons, we make a reasonable assumption of the forms of light-cone wave functions. With these light-cone wave functions we can obtain the cross section which is closer to the experimentally observed than that from the NRQCD approach. We also discuss in detail the difference between two approaches.

JLab: probing hadronic physics with electrons and photons

Precision measurements of the structure of nucleons and nuclei in the regime of strong interaction QCD are now possible with the availability of high current polarized electron beams, polarized targets, and recoil polarimeters, in conjunction with modern spectrometers and detector instrumentation. The physics at JLab will be highlighted using two recent measurements of general interest. The ratio of the proton electric to magnetic form factors indicates the importance of the role of angular momentum in the structure of the nucleon. The existence of 5-quark configurations in the ground state wavefunctions of hadrons is confirmed by a narrow peak attributed to an exotic baryon with strangeness S=+1. These and other examples will be used to illustrate the capabilities and focus of the experimental program at JLab.

Correspondence between QCD sum rules and constituent quark models

We compare two widely used approaches to the description of hadron properties: QCD sum rules and constituent quark models. Making use of the dispersion formulation of the quark model, we show that both approaches lead to similar spectral representations for hadron observables with an important difference that quark model is based on Feynman diagrams with massive quarks, whereas QCD sum rules are based on the same Feynman diagrams for current quarks with the additional condensate contributions for light quarks and gluons. We give arguments for a similarity of the smearing function in sum rules and the hadron wave function of the quark model. Analyzing the sum rule for the leptonic decay constant of the heavy pseudoscalar meson containing a light $u$ or $s$ quark, we find that the quark condensates at the chiral symmetry-breaking scale $\mu_\chi\simeq 1$ GeV, $<\bar u u > = - (230 \pm 15 {\rm MeV})^3$ and $<\bar s s > = - (220 \pm 15 {\rm MeV})^3$ correspond to constituent quark masses $m_u\simeq 220$ MeV and $m_s \simeq 350$ MeV, respectively. We also obtain the running of the quark model parameters above the chiral scale $\mu_\chi$. The observed correspondence between constituent quark models and QCD sum rules allows a deeper understanding of both methods and their parameters. It also provides a QCD basis for constituent quark models, extending their applicability above the scale of chiral symmetry breaking.

Light-front hadron dynamics and AdS/CFT correspondence

A remarkable consequence of the AdS/CFT correspondence is the nonperturbative derivation of dimensional counting rules for hard scattering processes. Using string/gauge duality we derive the QCD power behavior of light-front Fock-state hadronic wavefunctions for hard scattering in the large-r region of the AdS space from the conformal isometries which determine the scaling of string states as we approach the boundary from the interior of AdS space. The nonperturbative scaling results are obtained for spin-zero and spin-12 hadrons and are extended to include the orbital angular momentum dependence of the constituents in the light-front Fock-expansion. The correspondence with string states is considered for hadronic states of arbitrary orbital angular momentum for a given hadron of spin ⩽2. We examine the implications of the color configuration of hadronic Fock-states for the QCD structure of scattering amplitudes at large NC. Quark interchange amplitudes emerge as the dominant large NC scattering mechanisms for conformal QCD.

Erratum: Pion and kaon parton distribution functions in a meson-cloud model [Phys. Rev. D67, 034022 (2003)

In a model of hadrons in which the hadron wave function at low $Q^2$ is represented by a hadron-like Fock state expansion, we calculate the $\pi$ and $K$ parton distribution functions by comparing to experimental data. We show that the model gives an accurate description of available data and, in addition, gives a clear prediction of the initial flavors to be considered at the low $Q^2$ scale where perturbative evolution starts

Quark coalescence and elliptic flow of charm hadrons

Elliptic flow of charm hadrons is investigated based on the quark coalescence model. Due to the large difference between the charm quark and light quark masses, hadrons containing both light and charm quarks show a qualitatively different ${v}_{2}({p}_{\ensuremath{\perp}})$ from hadrons containing only light quarks. Simple relations are proposed to infer quark elliptic flow from those of hadrons. The effects of the finite momentum spread of hadron wave functions are also studied, and are found to be small for charm hadrons.

Separation of soft and hard physics in deeply virtual compton scattering

A model for deeply virtual Compton scattering, based on analytical light-cone hadron wave functions is presented and studied at energies currently accessible at Jefferson Laboratory, DESY, and beyond. It is shown that perpendicular vector components play an important role at Q^2 < 10 GeV^2 and that the meson-exchange diagrams are important at all energies. This could significantly impact the physical interpretation of the underlying hadron amplitudes.

Hadron wave functions and the issue of nucleon deformation

Using gauge invariant hadronic two- and three- density correlators we extract information on the spatial distributions of quarks in hadrons, and on hadron shape and multipole moments within quenched lattice QCD. Combined with the calculation of N to Δ transition amplitudes the issue of nucleon deformation can be addressed.

Quenching of highp⊥hadron spectra by hadronic interactions in heavy ion collisions at relativistic energies

Typically the materialization of high energetic transverse partons to hadronic jets is assumed to occur outside the reaction zone in a relativistic heavy ion collision. In contrast, a quantum mechanical estimate yields a time on the order of only a few fm/c for building up the hadronic wavefunction for jets with typical transverse momenta of pT < 10 GeV as accessible at RHIC facilities. The role of possible elastic or inelastic collisions of these high pT particles with the bulk of hadrons inside the fireball is addressed by means of an opacity expansion in the number of collisions. This analysis shows that the hadronic final state interactions can in principle account for the modification of the (moderate) high pT spectrum observed for central collisions at RHIC.

The Colour Glass Condensate

I review the physical and mathematical foundations for the theoretical description of the hadron wavefunction at small χ as a Colour Glass Condensate. In this context, I discuss the phenomenon of gluon saturation and some of its remarkable consequences: a new “geometric scaling” for F 2, which has been recently identified at HERA, and the unitarization of the hadronic cross-sections at high energy. I show that by combining saturation and confinement one obtains cross-sections which saturate the Froissart bound.

Pion and kaon parton distribution functions in a meson-cloud model

In a model of hadrons in which the hadron wave function at low ${Q}^{2}$ is represented by a hadron-like Fock state expansion, we calculate the $\ensuremath{\pi}$ and K parton distribution functions by comparing with the experimental data. We show that the model gives an accurate description of available data and, in addition, gives a clear prediction of the initial flavors to be considered at the low ${Q}^{2}$ scale where perturbative evolution starts.

The dipole picture and saturation in soft processes

We attempt to describe soft hadron interactions in the framework of saturation models, one based upon the Balitsky–Kovchegov non-linear equation and another one due to Golec-Biernat and Wüsthoff. For pp, Kp, and πp scattering the relevant hadronic wave functions are formulated, and total, elastic cross-sections, and the forward elastic slope are calculated and compared to experimental data. The saturation mechanism leads to reasonable reproduction of the data for the quantities analyzed, except for the forward elastic slope, where the predicted increase with energy is too moderate.

Intrinsic charm in B-meson decays

Light cone hadron wave functions support Fock states of arbitrarily high particle number: their heavy quark content arises naturally through QCD interactions. We discuss what role c c pairs, intrinsic to a hadron's structure, can play in B-meson decays. The effects can be prominent in hadronic decays for which the tree-level contributions are Cabibbo-suppressed, as in B → πK decay, and they mimic “charming penguin” contributions.

Probing hadron wave functions in lattice QCD

Gauge-invariant equal-time correlation functions are calculated in lattice QCD within the quenched approximation and with two dynamical quark species. These correlators provide information on the shape and multipole moments of the pion, the rho, the nucleon and the $\Delta$.

Scale dependence of hadronic wave functions and parton densities

We study how the components of hadronic wave functions in light-cone quantization depend on the ultraviolet cut-off by relating them in a systematic way to the matrix elements of a class of quark–gluon operators between the QCD vacuum and the hadrons. From this, we derive an infinite set of scale-evolution equations for the individual contributions to parton distributions from the Fock expansion. When summed over all the contributions, we recover the well-known DGLAP equation.

Froissart bound from gluon saturation

We demonstrate that the dipole–hadron cross-section computed from the non-linear evolution equation for the Colour Glass Condensate saturates the Froissart bound in the case of a fixed coupling and for a small dipole ( Q 2⪢ Λ QCD 2). That is, the cross-section increases as the logarithm squared of the energy, with a proportionality coefficient involving the pion mass and the BFKL intercept ( α s N c / π)4ln2. The pion mass enters via the non-perturbative initial conditions at low energy. The BFKL equation emerges as a limit of the non-linear evolution equation valid in the tail of the hadron wavefunction. We provide a physical picture for the transverse expansion of the hadron with increasing energy, and emphasize the importance of the colour correlations among the saturated gluons in suppressing non-unitary contributions due to long-range Coulomb tails. We present the first calculation of the saturation scale including the impact parameter dependence. We show that the cross-section at high energy exhibits geometric scaling with a different scaling variable as compared to the intermediate energy regime.

The systematic study of B→ π form factors in pQCD approach and its reliability

The study of exclusive B decays in perturbative QCD are complicated by the endpoint problem. In order to perform the perturbative calculation, the Sudakov effects are introduced to regulate the endpoint singularity. We provide a systematic analysis with leading and next-to-leading twist corrections for B→ π form factors in pQCD approach. The intrinsic transverse momentum dependence of hadronic wave function and threshold resummation effects are included in pQCD approach. There are two leading twist B meson distribution amplitudes (or generally wave functions) in general. The QCD equations of motion provide important constraints on B meson wave functions. The reliability of pQCD approach in B→ π form factors is discussed. 70% of the result comes from the region α s ( t)/ π<0.2 and 38% comes from the region where the momentum transfer t⩾1 GeV. The conceptual problems of pQCD approach are discussed in brief. Our conclusion is that pQCD approach in the present form cannot provide a precise prediction for B→ π transition form factors.

Nonlocal operators and distribution amplitudes of definite twist, WW—relations, EC—sum rules and power corrections for hard QCD processes

The decomposition of nonlocal operators (and of their matrix elements) into an (infinite) series w.r.t. geometric twist is used to introduce (new) parton distributions, generalized parton distributions and hadron wave functions of definite twist. Their comparision with the conventional distributions (of definite dynamical twist) leads to Wandzura-Wilczek like relations, Burkhardt-Cottingham like sum rules and allows for power corrections of the various distribution amplitudes. Some general aspects are reviewed.