Light-Front Holography,Color Confinement,and Supersymmetric Features of QCD

Light-Front Quantization—Dirac’s “Front Form”—provides a physical, frame-independent formalism for hadron dynamics and structure. Observables such as structure functions, transverse momentum distributions, and distribution amplitudes are defined from the hadronic light-front wavefunctions. One obtains new insights into the hadronic spectrum, light-front wavefunctions, and the functional form of the QCD running coupling in the nonperturbative domain using light-front holography—the duality between the front form and AdS₅, the space of isometries of the conformal group. In addition, superconformal algebra leads to remarkable supersymmetric relations between mesons and baryons of the same parity. The mass scale \({\kappa}\) underlying confinement and hadron masses can be connected to the parameter \({\Lambda_{\overline {MS}}}\) in the QCD running coupling by matching the nonperturbative dynamics, as described by the effective conformal theory mapped to the light-front and its embedding in AdS space, to the perturbative QCD regime. The result is an effective coupling defined at all momenta. This matching of the high and low momentum transfer regimes determines a scale Q₀ which sets the interface between perturbative and nonperturbative hadron dynamics. The use of Q₀ to resolve the factorization scale uncertainty for structure functions and distribution amplitudes, in combination with the principle of maximal conformality for setting the renormalization scales, can greatly improve the precision of perturbative QCD predictions for collider phenomenology. The absence of vacuum excitations of the causal, frame-independent front form vacuum has important consequences for the cosmological constant. I also discuss evidence that the antishadowing of nuclear structure functions is non-universal; i.e., flavor dependent, and why shadowing and antishadowing phenomena may be incompatible with the momentum and other sum rules for nuclear parton distribution functions.     

Generalized parton distributions of the photon

We present a first calculation of the generalized parton distributions of the photon (both polarized and unpolarized) using overlaps of light-front wave functions at leading order in α and zeroth order in αs; for non-zero transverse momentum transfer and zero skewness. We present the novel parton content of the photon in transverse position space.     

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     

The transverse momentum of partons

It is shown that when the parton model is formulated in proper, covariant fashion the average transverse momentum of the partons in a hadron varies with their fractional longitudinal momentum x. It is small near x = 0, but could rise to a large as x → 1.     

利用光前量子化方法计算电子的广义横向动量分布函数

强子和轻子是目前实验所能观测到的最小微观结构,但根据量子色动力学（QCD）,强子内还存在着部分子结构。在理论计算中,从Wigner函数出发可以得到多种分布函数,如横向动量分布函数（TMD）、广义部分子分布函数（GPD）以及广义横向动量分布函数（GTMD）。其中GTMD包含粒子内部部分子的三维动量和位置信息,从GTMD出发通过对横向动量积分和取横向转移动量为零分别得到GPD和TMD。本工作通过引入电子的光前波函数计算出物理电子的GTMD,并以此为出发点得到物理电子的TMD和GPD。一方面通过与微扰论的TMD和GPD的结果对比可以证明我们的计算结果是合理的,同时讨论了GPD中P波和S波的贡献。另一方面给出物理电子的内部部分子分布随横向转移动量、部分子横向动量以及纵向动量分数的变化关系。In anlogous to hadron, electron has similar structure because of dressing. So we can define the Transverse Momentum Distribution functions (TMD), the General Parton Distribution functions (GPD) and General Transverse Momentum Distribution functions (GTMD) of electron which come from the Wigner distribution function. The GTMD contain the information of momentum and position of parton in one particle, and the GPD or TMD can be calculated by integration of transverse momentum or setting the transverse transfer momentum which equal to zero. We introduce the light-front wave function of electron to calculate the GTMD of dressed electron, and then get the TMD and GPD. Our results are verified by comparing to calculations in literature and the contribution of GPD of P-wave and S-wave. And we show that the distribution functions at different transverse momentum transfer, transverse momentum of parton and the fraction of longitudinal momentum.     

Polarized coincidence electroproduction scaling laws for the final state

We study the inclusive electroproduction of single hadrons off a polarized target. Bjorken scaling laws and the hadron azimuthal distribution are derived from the quark parton model.The polarization asymmetries scale when the target spin is along the direction of the virtual photon, and (apart from one significant exception) vanish for transverse spin. These results have a simple explanation; emphasis is given both to the general mathematical formalism and to intuitive physical reasoning.Through this framework we consider other cases: quarks with anomalous magnetic moment; renormalization group effects and asymptotic freedom; production of vector mesons (whose spin state is analysed by their decay); relation to large transverse momentum hadron production; and a covariant parton model calculation. We also look into spin-0 partons and Regge singularities.All of these cases (apart from the last two) modify the pattern of conclusions. Vector meson production shows polarization enhancements in the density matrix element ?₀₊; the renormalization group approach does not lead to any significant suppressions. They are also less severe in parton models for large p_T hadrons, and are not supported by the covariantly formulated calculation. The origins of these differences are isolated and used to exemplify the sensitivity that polarized hadron electroproduction has to delicate detail that is otherwise concealed.     

核子(强子)结构和性质的QCD研究

核子 (强子 )是夸克、胶子的束缚态 ,由量子色动力学 QCD描述。由于 QCD的基本特性(高能标度下的渐近自由、低能标度下色禁闭及动力学手征对称性破缺 ) ,对核子 (强子 )结构和性质的 QCD图象是标度相关的 .在高能标度下描述强子的是与探测强子结构的硬过程相联系的QCD部分子模型 .强子的夸克、胶子结构信息通过 QCD部分子求和规则得到 .QCD微扰论是适用的理论 .在低能标度时 ,必须发展 QCD非微扰途径来描述核子 (强子 )物理 .这里简要地讨论各种非微扰途径 (格点 QCD、Dyson- Schwinger方程、有效场论、QCD求和规则 )的某些结果和进展 ,并指出 QCD真空结构在描述低能标度下强子物理中担任重要角色 . The nucleon (hadron) is the bound state of guarks and gluons, which is described by the quantum chromodynamics (QCD). Due to the basic properties of QCD (the asymptotic freedom at the high energy scale, the color confinement and the dynamical chiral symmetry breaking at the low energy scale), the QCD picture for the nucleon’s (hadron’s) structure and property is scale dependent. At high energy scale, the QCD parton model, which is relative to the hard process for testing the...     

Parton densities beyond perturbation theory

I compute non-perturbative corrections to the kernel governing the evolution of non-singlet parton densities. The model used is QED in the limit of many charged particles. I find an infrared renormalon at b₀t = −1, where t is the Borel variable and b₀ is the first coefficient of the β-function. This term has a non-trivial dependence on the variable x = -q²/(2p · q) and its coefficient scales as x³/(1 − x)² (p is the momentum of the hadron and q is the momentum transfer). An extrapolation of my results to QCD implies a breakdown of the parton model near the elastic region.     

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.     

Hadron spectroscopy and structure from AdS/CFT

The AdS/CFT correspondence between conformal field theory and string states in an extended space-time has provided new insights into not only hadron spectra, but also their light-front wave functions. We show that there is an exact correspondence between the fifth-dimensional coordinate of anti-de Sitter space z and a specific impact variable ζ which measures the separation of the constituents within the hadron in ordinary space-time. This connection allows one to predict the form of the light-front wave functions of mesons and baryons, the fundamental entities which encode hadron properties and scattering amplitudes. A new relativistic Schr?dinger light-front equation is found which reproduces the results obtained using the fifth-dimensional theory. Since they are complete and orthonormal, the AdS/CFT model wave functions can be used as an initial ansatz for a variational treatment or as a basis for the diagonalization of the light-front QCD Hamiltonian. A number of applications of light-front wave functions are also discussed.     

Generalized Parton Distributions of the Pion on the Transverse Lattice

The quark-generalized parton distributions of the pion are calculated from light-cone wavefunctions in transverse lattice gauge theory at large N_c. The pion effective size is found to decrease with increasing momentum transfer. An analytic ansatz, consistent with finite bound-state light-cone energy conditions, is given for the light-cone momentum dependence of the wavefunctions. This leads to simple, universal predictions for the behaviour of the distributions near the endpoints, complementing numerical DLCQ data.     

Comparison of the k T-factorization approach and the QCD parton model for charm and beauty hadroproduction

We compare numerical predictions of the conventional QCD parton model and of the k _T-factorization approach (semihard theory) for heavy-quark production in high-energy hadron collisions. The total production cross sections and one-particle rapidity and p _T distributions, as well as two-particle correlations, are considered. The distinction between the predictions of the two approaches is not very large, while the shapes of the distributions are slightly different.     

Scattering Amplitudes Interpolating Between Instant Form and Front Form of Relativistic Dynamics

Among the three forms of relativistic Hamiltonian dynamics proposed by Dirac in 1949, the front form has the largest number of kinematic generators. This distinction provides useful consequences in the analysis of physical observables in hadron physics. Using the method of interpolation between the instant form and the front form, we introduce the interpolating scattering amplitude that links the corresponding time-ordered amplitudes between the two forms of dynamics and provide the physical meaning of the kinematic transformations as they allow the invariance of each individual time-ordered amplitude for an arbitrary interpolation angle. We discuss the rationale for using front form dynamics, nowadays known as light-front dynamics (LFD), and present a few explicit examples of hadron phenomenology that LFD uniquely can offer from first-principles quantum chromodynamics. In particular, model-independent constraints are provided for the analyses of deuteron form factors and the N Δ transition form factors at large momentum transfer squared Q ². The swap of helicity amplitudes between the collinear and non-collinear kinematics is also discussed in deeply virtual Compton scattering.     

Wigner Distributions in Light-Front Quark Models

We discuss the quark Wigner distributions which represent the quantum-mechanical analogues of the classical phase-space distributions. These functions can be obtained through a Fourier transform in the transverse space of the generalized transverse momentum dependent parton distributions, which encode the most general one-body information of partons in momentum space. In particular, we present a study within light-front quark models. The quark orbital angular momentum is also obtained from the phase-space average of the orbital angular momentum operator weighted with the Wigner distribution of unpolarized quark in a longitudinally polarized nucleon. The corresponding results calculated within different light-front quark models are compared with alternative definitions of the quark orbital angular momentum as given in terms of generalized parton distributions and transverse momentum dependent parton distributions.     

Hadron Physics from Superconformal Quantum Mechanics and Its Light-Front Holographic Embedding

The complex nonperturbative color-confining dynamics of QCD is well captured in a semiclassical effective theory based on superconformal quantum mechanics and its extension to the light-front. I describe here how this new approach to hadron physics incorporates confinement, the appearance of nearly massless pseudoscalar particles, and Regge spectroscopy consistent with experiment. It also gives remarkable connections between the meson and baryon spectrum across the light and heavy-light hadron spectrum. I also briefly discuss how higher spin states are consistently described in this framework by the holographic embedding of the superconformal theory in a higher dimensional semiclassical gravity theory.     

An intuitive approach to a generalized parton picture for high-energy lepton-hadron scattering

A generalized parton picture is developed, based on the impulse approximation. A parton is allowed to have non-point-like elastic form factors; inelastic current-parton scattering is taken into account explicitly. The amplitude of any exclusive channel of lepton-induced reactions is written down, with the parts containing the long-distance and the short-distance behavior of interaction dynamics clearly separated. Scaling violation is a natural feature of this picture. The inelastic structure functions, W₁ and νW₂, are studied in this scheme using various different theories; perturbative QCD, the scale-invariant parton model, the hadron bootstrap picture, and a phenomenological stripped-down hadron-parton model. The application of this picture to elastic lepton-hadron scattering and the problem of the selection of an infinite momentum frame are also discussed.     

Helicity-dependent generalized parton distributions for nonzero skewness

We investigate the helicity-dependent generalized parton distributions (GPDs) in momentum as well as transverse position (impact) spaces for the u and d quarks in a proton when the momentum transfer in both the transverse and the longitudinal directions are nonzero. The GPDs are evaluated using the light-front wave functions of a quark–diquark model for nucleon where the wave functions are constructed by the soft-wall AdS/QCD correspondence. We also express the GPDs in the boost-invariant longitudinal position space.     

Multiplicity distributions inside parton cascades developing in a medium

The explanation of the suppression of high-p_T hadron yields at RHIC in terms of jet-quenching implies that the multiplicity distributions of particles inside a jet and jet-like particle correlations differ strongly in nucleus–nucleus collisions at RHIC or at the LHC from those observed at e⁺e^- or hadron colliders. We present a framework for describing the medium-induced modification, which has a direct interpretation in terms of a probabilistic medium-modified parton cascade, and which treats leading and subleading partons on an equal footing. We show that our approach can account for the strong suppression of single inclusive hadron spectra measured in Au–Au collisions at RHIC, and that this implies a characteristic distortion of the single inclusive distribution of soft partons inside the jet. We determine, as a function of the jet energy, to what extent the soft fragments within a jet can be measured above some momentum cut. PACS 12.38.Mh; 25.75.-q