QCD on the Light-Front

Light-front Hamiltonian theory, derived from the quantization of the QCD Lagrangian at fixed light-front time x ⁺ = x ⁰ + x ³, provides a rigorous frame-independent framework for solving nonperturbative QCD. The eigenvalues of the light-front QCD Hamiltonian H _LF predict the hadronic mass spectrum, and the corresponding eigensolutions provide the light-front wavefunctions which describe hadron structure, providing a direct connection to the QCD Lagrangian. In the semiclassical approximation the valence Fock-state wavefunctions of the light-front QCD Hamiltonian satisfy a single-variable relativistic equation of motion, analogous to the nonrelativistic radial Schrödinger equation, with an effective confining potential U which systematically incorporates the effects of higher quark and gluon Fock states. Remarkably, the potential U has a unique form of a harmonic oscillator potential if one requires that the chiral QCD action remains conformally invariant. A mass gap and the color confinement scale also arises when one extends the formalism of de Alfaro, Fubini and Furlan to light-front Hamiltonian theory. In the case of mesons, the valence Fock-state wavefunctions of H _LF for zero quark mass satisfy a single-variable relativistic equation of motion in the invariant variable \({\zeta^2=b^2_\perp x(1-x)}\) , which is conjugate to the invariant mass squared \({{M^2_{q\bar q}}}\) . The result is a nonperturbative relativistic light-front quantum mechanical wave equation which incorporates color confinement and other essential spectroscopic and dynamical features of hadron physics, including a massless pion for zero quark mass and linear Regge trajectories \({M^2(n, L, S) = 4\kappa^2( n+L +S/2)}\) with the same slope in the radial quantum number n and orbital angular momentum L. Only one mass parameter \({\kappa}\) appears. The corresponding light-front Dirac equation provides a dynamical and spectroscopic model of nucleons. The same light-front equations arise from the holographic mapping of the soft-wall model modification of AdS₅ space with a unique dilaton profile to QCD (3 + 1) at fixed light-front time. Light-front holography thus provides a precise relation between the bound-state amplitudes in the fifth dimension of AdS space and the boost-invariant light-front wavefunctions describing the internal structure of hadrons in physical space-time. We also discuss the implications of the underlying conformal template of QCD for renormalization scale-setting and the implications of light-front quantization for the value of the cosmological constant.     

New Results in Light-Front Phenomenology

The light-front quantization of gauge theories in light-cone gauge provides a frame-independent wavefunction representation of relativistic bound states, simple forms for current matrix elements, explicit unitarity, and a trivial vacuum. In this talk I review the theoretical methods and constraints which can be used to determine these central elements of QCD phenomenology. 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 and define a kinematical definition of angular momentum. The AdS/CFT correspondence of large N_C supergravity theory in higher-dimensional anti-de Sitter space with supersymmetric QCD in four-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. The 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 nonperturbative Fock-state wavefunctions contain intrinsic gluons, and sea quarks at any scale Q with asymmetries such as . Intrinsic charm and bottom quarks appear at large x in the light-front wavefunctions since this minimizes the invariant mass and off-shellness of the higher Fock state. In the case of nuclei, the Fock state expansion contains “hidden color” states which cannot be classified in terms of nucleonic degrees of freedom. I also briefly review recent analyses which show 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.Work supported by Department of Energy contract DE-AC02-76SF00515     

AdS/QCD and Applications of Light-Front Holography

Light-front holography leads to a rigorous connection between hadronic amplitudes in a higher dimensional anti-de Sitter(AdS) space and frame-independent light-front wavefunctions of hadrons in(3 + 1)-dimensional physical space-time,thus providing a compelling physical interpretation of the AdS/CFT correspondence principle and AdS/QCD,a useful framework which describes the correspondence between theories in a modified AdS 5 background and confining field theories in physical space-time.To a first semiclassical approximation,where quantum loops and quark masses are not included,this approach leads to a single-variable light-front Schro¨dinger equation which determines the eigenspectrum and the light-front wavefunctions of hadrons for general spin and orbital angular momentum.The coordinate z in AdS space is uniquely identified with a Lorentz-invariant coordinate ζ which measures the separation of the constituents within a hadron at equal light-front time.The internal structure of hadrons is explicitly introduced and the angular momentum of the constituents plays a key role.We give an overview of the light-front holographic approach to strongly coupled QCD.In particular,we study the photon-to-meson transition form factors(TFFs) FMγ(Q 2) for γ→ M using light-front holographic methods.The results for the TFFs for the η and η ' mesons are also presented.Some novel features of QCD are discussed,including the consequences of confinement for quark and gluon condensates.A method for computing the hadronization of quark and gluon jets at the amplitude level is outlined.     

Measurement of QCD parameters by using the single dressed gluon approximation

This article is based on renormalization analysis by using the single dressed gluon (SDG) approximation. This model is used to measure the coupling constant in perturbative as well as in the nonperturbative part of the QCD theory. We employ the event shape observables 〈B _T〉, 〈B _W〉, 〈1 ? T〉, 〈C〉, and 〈ρ〉. By fitting both Monte Carlo and the real data with SDG, we find the mean values \({\alpha _S}\left( {{M_{{Z^0}}}} \right)\) = (0.1215 ± 0.0030) GeV and ν = (1.2685 ± 0.0173) GeV in the perturbative and nonperturbative regions, respectively. Our results are consistent with those obtained from other experiments at different energies. We explain all these features in this paper.     

Non-perturbative momentum dependence of the coupling constant and hadronic models

Models of hadron structure are associated with a hadronic scale which allows by perturbative evolution to calculate observables in the deep inelastic region. The resolution of Dyson-Schwinger equations leads to the freezing of the QCD running coupling (effective charge) in the infrared, which is best understood as a dynamical generation of a gluon mass function, giving rise to a momentum dependence which is free from infrared divergences. We use this new development to understand why perturbative treatments are working reasonably well despite the smallness of the hadronic scale.     

The spectrum of theP-wave baryons and hadronic loops

In current QCD inspired analyses of the hadron spectrum nonperturbative quark loops are generally neglected. We study the validity of this assumption by estimating mass splittings and mixings induced by hadronic mass renormalization to the (70,1^?) baryon multiplet. All intermediate states in the loop composed of a ground state meson (0^?+, 1^??) and a ground state baryon (1/2⁺, 3/2⁺) are included. We use a³ P ₀ type model for the partial decay widths and spectral functions. Using unitarity and analyticity one finds a definite prediction for the masses and mixings, in good agreement with experiment, even when the perturbative one-gluon exchange is completely ignored. Our result thus allows for a smaller one-gluon exchange overall contribution, which would resolve the difficulty of the apparent smallness of the observed spin-orbit coupling. In particular if one adds the (nonperturbative) unitarity corrections to the one-gluon exchange contribution the gluon coupling constant can be reduced by a factor of 3 giving a reasonable value α_s≈0.3.     

Nonperturbative phenomena in QCD at finite temperature in a magnetic field

The norperturbative QCD vacuum at finite temperature in a external magnetic field is studied. Equations that relate nonperturbative QCD condensates at finite temperature to the thermodynamic pressure at T ≠ 0 and H ≠ 0 are obtained, and low-energy theorems are derived. The free energy of the QCD vacuum in the hadronic phase at H ≠ 0 is calculated, and expressions for the quark and gluon condensates are obtained. Various limiting cases for the behavior of the condensates at low and high temperatures and in weak and strong magnetic fields are investigated. A new interesting phenomenon that consists in the freezing of the quark condensate by a magnetic field is found. The character of spontaneous chiral-symmetry breaking in finite-temperature QCD in a magnetic field is studied. For this purpose, the Gell-Mann-Oakes-Renner formula relating the pion mass M _π and the axial-vector coupling constant F _π to the quark condensate is derived at T ≠ 0 and H ≠ 0. It is shown that this formula preserves its form at finite temperature after taking into account a magnetic field—that is, no additional terms independent of T and H appear. Thus, the scheme of soft chiral-symmetry breaking remains unchanged. The quark-hadron phase transition in QCD in a magnetic field is studied. It is shown that the phase-transition temperature becomes lower than that in the case of zero magnetic field.     

Hadronic production of doubly charmed baryons and intrinsic charm in the proton

The production of baryons involving two charmed quarks (Ξ _cc ^* or Ξ_cc) in hadron interactions at high energies and high transverse momenta is considered. It is assumed that a Ξ_cc baryon is formed in the nonperturbative fragmentation of a (cc) diquark produced in the hard partonic process of the scattering of charmed quarks from colliding hadrons: c+c → (cc)+g. It is shown that, upon the inclusion of this mechanism, the cross section for the production of doubly charmed baryons becomes approximately twice as large as that which is expected at the Tevatron and LHC colliders according to the predictions based on the model of gluon-gluon production of a (cc) diquark and obtained in the leading order of perturbative QCD.     

Testing the Concept of Quark–Hadron Duality with the ALEPH τ Decay Data

We propose a modified procedure for extracting the numerical value for the strong coupling constant α _s from the τ lepton hadronic decay rate into non-strange particles in the vector channel. We employ the concept of the quark–hadron duality specifically, introducing a boundary energy squared s _p > 0, the onset of the perturbative QCD continuum in Minkowski space (Bertlmann et al. in Nucl Phys B 250:61, 1985; de Rafael in An introduction to sum rules in QCD. In: Lectures at the Les Houches Summer School. arXiv: 9802448 [hep-ph], 1997; Peris et al. in JHEP 9805:011, 1998). To approximate the hadronic spectral function in the region s > s _p, we use analytic perturbation theory (APT) up to the fifth order. A new feature of our procedure is that it enables us to extract from the data simultaneously the QCD scale parameter ${\Lambda_{\overline{\rm MS}}}$ and the boundary energy squared s _p. We carefully determine the experimental errors on these parameters which come from the errors on the invariant mass squared distribution. For the ${\overline{\rm MS}}$ scheme coupling constant, we obtain ${\alpha_s(m^{2}_{\tau})=0.3204\pm 0.0159_{exp.}}$ . We show that our numerical analysis is much more stable against higher-order corrections than the standard one. Additionally, we recalculate the “experimental” Adler function in the infrared region using final ALEPH results. The uncertainty on this function is also determined.     

QCD average hadronic multiplicity in the ψ(1S) decay

The average hadronic multiplicity in the ψ(1S) decay, via the mode ψ→ggg, is studied in the framework of Quantum Chromodynamics. We test the predictions of perturbative QCD working to \(O(\sqrt {\alpha _s } )\) in the coupling constant.     

Quark-hadron duality and production of charmonia and doubly charmed baryons in <Emphasis Type="Italic">e</Emphasis><Superscript>+</Superscript><Emphasis Type="Italic">e</Emphasis><Superscript>−</Superscript> anninhilation

The cross sections for the production of charmonia and doubly charmed baryons in e ⁺ e ^? annihilation at an interaction energy of \(\sqrt s \) = 10.6 GeV are predicted under the assumption of quark—hadron duality. The method used is shown to remove some contradictions between experimental data and perturbative QCD.     

Interaction of dirac particle AMM with Coulomb field of a superheavy nucleus: Perturbative and nonperturbative aspects

The interaction ΔU_AMM of the Dirac particle anomalous magnetic moment (AMM) with the Coulomb field of a nucleus and its effect on the low-lying atomic levels are studied for Zα > 1 using both perturbative and essentially nonperturbative approaches. The Zα dependence of particle wavefunctions (WFs) is fully taken into account from the beginning. In deriving the ΔU_AMM contribution, the nucleus is viewed either as a uniformly charged extended Coulomb source or as a distributed system formed by pointlike u and d quarks. When estimated nonperturbatively, the ΔU_AMM-induced effects in the Dirac equation framework prove to be identical for these two cases. At the same time, the ΔU_AMM-induced effect is specific in that its perturbative and nonperturbative estimates are very different for Δg ? const and practically identical as soon as the dynamical screening of AMM at short distances is taken into account in the Dirac equation.     

Parton physics from large-momentum effective field theory

Parton physics,when formulated as light-front correlations,are difficult to study non-perturbatively,despite the promise of lightfront quantization.Recently an alternative approach to partons have been proposed by re-visiting original Feynman picture of a hadron moving at asymptotically large momentum.Here I formulate the approach in the language of an effective field theory for a large hadron momentum P in lattice QCD,LaMET for short.I show that using this new effective theory,parton properties,including light-front parton wave functions,can be extracted from lattice observables in a systematic expansion of 1/P,much like that the parton distributions can be extracted from the hard scattering data at momentum scales of a few GeV.     

(Medium-modified) fragmentation functions

We discuss some of the recent advances in the field of parton fragmentation processes into hadrons as well as their possible modifications in QCD media. Hadron-production data in e ⁺ e ⁻, deep inelastic scattering and hadronic collisions are presented, together with global analyses of fragmentation functions into light and heavy hadrons and developments on parton fragmentation in perturbative QCD at small momentum fraction. Motivated by the recent RHIC data indicating a significant suppression of large-p _⊥ hadron production in heavy-ion collisions, several recent attempts to model medium-modified fragmentation, e.g. by solving “medium” evolution equations or through Monte Carlo studies, have been proposed and are discussed in detail. Finally, we mention the possibility to extract medium-modified fragmentation functions using photon–hadron correlations.     

Analyticity and power corrections in hard-scattering hadronic functions

Demanding the analyticity of hadronic observables (calculated in terms of power series of the running coupling) as a whole, we show that they are free of the Landau singularity. Employing resummation and dispersion-relation techniques, we compute in a unifying way power corrections to two different hard-scattering functions in perturbative QCD: the electromagnetic pion form factor to leading order and the inclusive cross section of the Drell–Yan process. In the second case, the leading nonperturbative power correction in bΛ_QCD gives rise to a Sudakov-like exponential factor in the impact parameter space which provides enhancement rather than suppression.