Stanley J. Brodsky

Quantum chromodynamics and other field theories on the light cone

Abstract In recent years light-cone quantization of quantum field theory has emerged as a promising method for solving problems in the strong coupling regime. The approach has a number of unique features that make it particularly appealing, most notably, the ground state of the free theory is also a ground state of the full theory. We discuss the light-cone quantization of gauge theories from two perspectives: as a calculational tool for representing hadrons as QCD bound states of relativistic quarks and gluons, and also as a novel method for simulating quantum field theory on a computer. The light-cone Fock state expansion of wavefunctions provides a precise definition of the parton model and a general calculus for hadronic matrix elements. We present several new applications of light-cone Fock methods, including calculations of exclusive weak decays of heavy hadrons, and intrinsic heavy-quark contributions to structure functions. A general non-perturbative method for numerically solving quantum field theories, “discretized light-cone quantization”, is outlined and applied to several gauge theories. This method is invariant under the large class of light-cone Lorentz transformations, and it can be formulated such that ultraviolet regularization is independent of the momentum space discretization. Both the bound-state spectrum and the corresponding relativistic light-cone wavefunctions can be obtained by matrix diagonalization and related techniques. We also discuss the construction of the light-cone Fock basis, the structure of the light-cone vacuum, and outline the renormalization techniques required for solving gauge theories within the Hamiltonian formalism on the light cone.

Exclusive processes in quantum chromodynamics: Evolution equations for hadronic wavefunctions and the form factors of mesons☆

Abstract The predictions of quantum chromodynamics for meson form factors at large momentum transfer are given. Evolution equations are derived which determine the structure of hadronic wavefunctions at short distances from their form at large distances. The eigenvalues of the evolution equations appear as exponents in anomalous logarithm corrections to the nominal power law of form factors determined by dimensional counting. The results lead to detailed tests of the spin and scaling structure of QCD at short distances. The predictions for the charged pion, kaon and rho form factors and the γ → π 0 transition form factor of the photon are absolutely normalized at asymptotic momentum transfer.

Final-state interactions and single-spin asymmetries in semi-inclusive deep inelastic scattering

Abstract Recent measurements from the HERMES and SMC Collaborations show a remarkably large azimuthal single-spin asymmetries AUL and AUT of the proton in semi-inclusive pion leptoproduction γ ∗ (q)p→πX . We show that final-state interactions from gluon exchange between the outgoing quark and the target spectator system lead to single-spin asymmetries in deep inelastic lepton–proton scattering at leading twist in perturbative QCD; i.e., the rescattering corrections are not power-law suppressed at large photon virtuality Q2 at fixed xbj. The existence of such single-spin asymmetries requires a phase difference between two amplitudes coupling the proton target with Jzp=±1/2 to the same final-state, the same amplitudes which are necessary to produce a nonzero proton anomalous magnetic moment. We show that the exchange of gauge particles between the outgoing quark and the proton spectators produces a Coulomb-like complex phase which depends on the angular momentum Lz of the protons constituents and is thus distinct for different proton spin amplitudes. The single-spin asymmetry which arises from such final-state interactions does not factorize into a product of distribution function and fragmentation function, and it is not related to the transversity distribution δq(x,Q) which correlates transversely polarized quarks with the spin of the transversely polarized target nucleon.

The Intrinsic Charm of the Proton

Recent data give unexpectedly large cross-sections for charmed particle production at high xF in hadron collisions. This may imply that the proton has a non-negligible uudcc Fock component. The interesting consequences of such a hypothesis are explored.

Chiral symmetry and the spin of the proton

Abstract Recent EMC data on the spin-dependent proton structure function suggest that very little of the proton spin is due to the helicity of its constituent quarks. We argue that, at leading order in the 1 N c expansion, none of the proton spin would be carried by quarks in the chiral limit where mq=0. This result is derived in the Skyrme model, which is also used to estimate quark contribution to the proton spin when chiral symmetry and SU(3) are broken: this contribution turns out to be small. Therefore, even in the real world most of the proton spin is due to gluons and/or orbital angular momentum, as suggested by the EMC. We mention other experiments to test this suggestion.

Diffractive leptoproduction of vector mesons in QCD

We demonstrate that the distinctive features of the forward differential cross section of diffractive leptoproduction of a vector meson can be legitimately calculated in perturbative QCD in terms of the light-cone [ital q[bar q]] wave function of the vector meson and the gluon distribution of the target. In particular, we calculate the [ital Q][sup 2] and nuclear dependence of the diffractive leptoproduction of vector mesons and estimate the cross section. The production of longitudinally polarized vector mesons by longitudinally polarized virtual photons is predicted to be the dominant component, yielding a cross section behaving as [ital Q][sup [minus]6]. The nuclear dependence of the diffractive cross sections, which follows from a factorization theorem in perturbative QCD, provides important tests of color transparency as well as constraints on the shadowing of the gluon structure functions and the longitudinal structure functions of nuclei.

Hadronic spectrum of a holographic dual of QCD

We compute the spectrum of light hadrons in a holographic dual of QCD defined on AdS5 x S5 which has conformal behavior at short distances and confinement at large interquark separation. Specific hadrons are identified by the correspondence of string modes with the dimension of the interpolating operator of the hadrons valence Fock state. Higher orbital excitations are matched quanta to quanta with fluctuations about the AdS background. Since only one parameter, the QCD scale Lambda(QCD), is used, the agreement with the pattern of physical states is remarkable. In particular, the ratio of delta to nucleon trajectories is determined by the ratio of zeros of Bessel functions.

Light-Front Dynamics and AdS/QCD Correspondence: The Pion Form Factor in the Space- and Time-Like Regions

at large distances. The AdS/CFT correspondence also provides insights into the inherently non-perturbative 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 fth-dimensional coordinate of anti{de Sitter (AdS) space z and a specic light-front impact variable 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 fth-dimensional theory. As specic examples we compute the pion coupling constant f , the pion charge radius r 2 and examine the propagation of the electromagnetic current in AdS space, which determines the space and time-like behavior of the pion form factor and the pole of the meson.

Hadronic spectra and light-front wave functions in holographic QCD.

We show how the string amplitude phi(z) defined on the fifth dimension in AdS5 space can be precisely mapped to the light-front wave functions of hadrons in physical space-time. We find an exact correspondence between the holographic variable z and an impact variable zeta, which represents the measure of transverse separation of the constituents within the hadrons. In addition, we derive effective four dimensional Schrödinger equations for the bound states of massless quarks and gluons which exactly reproduce the anti-de Sitter conformal field theory results and give a realistic description of the light-quark meson and baryon spectrum as well as the form factors for space-like Q2. Only one parameter which sets the mass scale, lambda(QCD), is introduced.

Large Transverse Momentum Processes

Abstract We present a comprehensive survey of experimental and theoretical work on large transverse momentum processes. Exclusive data and single particle inclusive measurements are summarized and some discussion of multiparticle inclusive data is included. We review many of the predictions of nonparton models including the geometrical, statistical, eikonal and bootstrap approaches. A more detailed discussion is given of the structure of models based on the hard scattering of constituents. The predictions for hadronic and electromagnetic processes based on quark counting rules and the constituent interchange model (CIM) are summarized. We present numerous comparisons with experiment and indicate the framework for the comparison with new experimental data. Recent theoretical progress in the problem of relating short distance structure of hadrons with the asymptotic behavior of form factors and fixed angle amplitudes is also reviewed. We include a brief discussion of the possible influence of new hadronic degrees of freedom on large- p T phenomena. Finally, we attempt to anticipate the type of experiments which will prove decisive in the understanding of this subject.