Light cone and mass shells

We propose a hypothesis which generalizes the notion of duality to off-mass-shell current matrix elements. The hypothesis, referred to as strong light-cone dominance, is formulated in terms of the light-cone sum rules, which reflect causality and the light-cone structure of current commutators: We postulate that these sum rules are saturated quasilocally by individual resonance peaks, in a similar manner as duality requires resonances to saturate the FESR for the hadronic on-shell amplitudes. This reconstitutes scaling in an average sense in regions where the leading light-cone singularity does not dominate. In coordinate space this hypothesis implies that the leading light-cone singularity regulates (tames) the entire light-cone expansion in a neighbourhood of the surface of the light-cone, whose extension is of the order of an inverse mass difference between consecutive resonances. We investigate the hypothesis of strong light-cone dominance in the framework of narrow resonance models for the vertex and show that the leading light-cone singularity indeed normalizes the single particle contributions by means of a relation of the Drell-Yan-West type. A simple Veneziano-like vertex model is exhibited, which is strongly light-cone dominated. Furthermore, we show how to exploitthe hypothesis in a rather model-independent way. We present some applications to the non-forward four-point function and show in particular that strong light-cone dominancerequires scaling for exclusive electroproduction processes like $\text{γ}{}^1\text{+}\text{N}\text{→ π +}\text{N}$.     

Light-cone expansion of matrix elements of current commutators

On the basis of general quantum field theory the existence of the light-cone expansion is shown for matrix elements of the current commutator. Mathematically, the problem consists of proving the expansion of entire functions in four complex variables in terms of harmonic polynomials.     

Heavy-to-light correlators beyond the light cone

We present the first systematic analysis of the off-light-cone effects in correlators relevant for the extraction of the heavy-to-light form factors within the method of light-cone sum rules. In a model with scalar constituents, the correlator is calculated in two different ways: (i) by performing the expansion of the Bethe-Salpeter amplitude of the light meson near the light cone x ² = 0 and (ii) by adopting the known solution for the Bethe-Salpeter amplitude which allows one to calculate the correlator without invoking any expansion. We demonstrate that the contributions to the correlator from the off-light-cone terms x ² ≠ 0 are not suppressed by any large parameter compared to the contribution of the light-cone term x ² = 0. For decays of heavy particles of mass in the range 1.5–5 GeV, the light-cone correlator is shown to systematically overestimate the full correlator, numerically the difference being 10–20%. The text was submitted by the authors in English.     

Wk structure of A SU(2)-level k from covariant construction of Kac-Moody algebras

The W_k structure underlying the transverse realization of affine SU(2) at level k is analyzed. The extension of the equivalence existing between the covariant and light-cone gauge realization of an affine Kac-Moody algebra to W_k algebras is given. Higher spin generators are extracted by the less singular terms in the operator product expansion of the parafermions constructed by means of the projection of the covariant on the light-cone gauge. These fields can be written in terms of only one free boson compactified on a circle.     

Constraints on light-cone expansions due to the asymptotic fall-off of the elastic form factors

Using a technique developed by Deser, Gilbert and Sudarshan, we express the elastic form factors and the scaling functions in terms of the same weight functions. Sum rules for the different terms appearing in the light-cone expansion follow from the asymptotic fall-off of the elastic form factors. We also write a set of sufficient conditions for the Drell-Yan-West relation to be valid.     

Path integral approach to the large-N expansion of the two-dimensional U(N) QCD

We use path integral method for the large-N expansion of the two-dimensional U(N) QCD in the light-cone gauge. We derive the 't Hooft equation for the quark-antiquark bound states from the quadratic part of the expansion. We also derive the effective interactions of the mesons from the higher-order terms of the expansion.     

Nonlocal light-cone operators describing hadrons in processes with large momentum transfer

The application of a special version of the nonlocal light-cone expansion to hadron processes with large momentum transfer is reviewed. The light-cone operators introduced in this approach may be considered as the relevant hadron operators: Their matrix elements between the vacuum and a one-hadron state coincide with the quark distribution amplitude, and their anomalous dimensions are unique extensions of the well known Brodsky-Lepage evolution kernels having also a simple relation to the Altarelli-Parisi kernels.     

Improved light-cone expansion

An improved light-cone expansion is obtained by explicitly summing up towers of derivative operators which transform irreducibly under the conformal algebra. The improved expansion explicitly exhibits the causality restrictions and conformal invariance on the light cone.     

String dynamics in QCD

Recent works of the authors on string interpretation of the Wilson loop operators in QCD are reviewed in a self-contained fashion. Although most of the results have already appeared in print, some new materials is presented on renormalization of the Wilson loop operator and on the use of light-cone expansion to derive a linear string-like equation in light-cone formalism.     

On the Light-Cone Expansion in Gauge Field Theories (QED)

The techniques for the derivation of light-cone expansions in scalar field theories are generalized to nonscalar, especially gauge field theories. For this reason the smallness of the remainder is proved in an arbitrary renormalizable theory provided an infrared regularization is present. Then we apply the formalism to derive a light-cone expansion for the product of two scalar currents in Quantum Electrodynamics in leading order. Thereby the gauge-invariance of the underlying theory is used from the very beginning by the application of the known solutions of the Ward identities. As a result of that, one obtains two gauge-invariant light cone operators, and the corresponding coefficient functions are independent one from another.     

Light-cone physics,current algebra and PCAC

It is shown that the light-cone operator expansion of the product of two SU(3) ? SU(3) currents or divergences, the requirement of maximal analyticity of the second kind, and the mathematical method of analytic continuation can be used to shed light on the validity and meaning of the Ward-Takahashi identities, of the Bjorken-Johnson-Low limit and in general of sum rules derived from current algebra either at equal time or on the light cone. In particular we give a definite content to the PCAC hypothesis in terms of the ‘dimension’ of the axial divergence and suggest some specific values for this ‘dimension’. It is also shown that the requirement of maximal analyticity of the second kind and gauge invariance impose a non-trivial condition on the Cornwall-Corrigan-Norton sum rule.     

Form factors of γ * ρ → π and γ * γ → π 0 transitions and light-cone sum rules

The method of light-cone QCD sum rules is applied to the calculation of the form factors of and transitions. We consider the dispersion relation for the amplitude in the variable . At large virtualities and , this amplitude is calculated in terms of light-cone wave functions of the pion. As a next step, the light-cone sum rule for the form factor is derived. This sum rule, together with the quark-hadron duality, provides an estimate of the hadronic spectral density in the dispersion relation. Finally, the form factor is obtained taking the limit in this relation. Our predictions are valid at and have a correct asymptotic behaviour at large . Received: 16 January 1998 / Revised version: 14 May 1998 / Published online: 26 August 1998     

Contact interactions in superstring theory

Contact interactions are shown to be required in superstring theory in order to ensure either world-sheet supersymmetry in a covariant formalism or spacetime supersymmetry in the light-cone gauge. These interactions only contribute for specific ranges of the momenta of the emitted particles. Their rôle is to ensure analyticity of S-matrix elements in much the same way as with contact terms in ordinary field theories with point particles. For tree diagrams the usual functional calculations, performed at sufficiently spacelike momentum transfer, give correct results. For other values of the momenta the correct answer is obtained either by analytic continuation or by adding the contribution of the contact interactions. In certain loop calculations the effect of the contact interactions must be taken into account. In the light-cone gauge formalism the contact terms ensure positivity of the hamiltonian.     

Tensor representations of conformal algebra and conformally covariant operator product expansion

A conformally covariant formulation of operator product expansion is discussed as an expansion of the product of two representations into a direct sum of irreducible representations. The basic irreducible representations are analyzed and classified. The isomorphism between the conformal algebra and the O(4, 2) algebra is used to obtain a manifestly covariant formalism. The implications of the isomorphism in the derivation of the representations is discussed. The covariant O(4, 2) formalism directly relates dominant terms to nondominant terms in the light-cone limit. The essential coincidence of the problem of a conformal covariant operator product expansion to the problem of determining the form of the three-point function is stressed, together with the relevance of a selection rule for two-point functions following from exact (not spontaneously broken) conformal covariance. The role of Ward identities in a conformal covariant scheme is pointed out, and the mathematical implications on the n-point functions from causality are described.     

Nonlocal quark condensate and photon distribution amplitude

The magnetic susceptibility of the quark condensate and the light-cone photon distribution amplitude of the leading twist is studied in the leading order of the perturbative expansion within the nonlocal condensates framework.     

Type IIB Green-Schwarz superstrings in AdS 5 × S 5 from the supercoset approach

We consider superstrings moving in the AdS ₅ × S ⁵ space-time and find their Green-Schwarz action using the supercoset approach based on the supergroup PSU(2, 2|4). We describe several parametrizations of the relevant supercoset and present the action in different κ-symmetry gauges. In particular, we discuss a gauge where all the fermionic coordinates corresponding to the conformal (S) supercharges are gauged away and also a light-cone type gauge where half of the Q and S supercoordinates are gauged away. The resulting action contains terms that are quadratic and quartic in fermions. In the flat-space limit, it reduces to the standard light-cone Green-Schwarz action. We comment on the possibility of fixing the bosonic light-cone gauge and of reformulating the action in terms of two-dimensional Dirac spinors.     

Light-cone expansion for a product of two gauge-invariant currents in QCD

A light-cone expansion for a product of two gauge-invariant currents is obtained in quantum chromodynamics. The coefficient functions in the expansion are derived from the Green functions. This has resulted in the establishment of gauge invariance and in the possibility of estimating the coefficient functions in any order of the perturbation theory. A new way of presenting the most singular part of the expansion in gauge-invariant form has been invented.     

A POSSIBLE FORM OF THE PION'S STRUCTURE FUNCTION

The pion's structure function behaviour is discussed by using the Fock state expansion of the hadronic wavefunction in QCD in this paper. As an example, we employ a model wavefunction of the Fock state in the light-cone and assume a Regge behaviour of a weight function for higher Fock states, and we get a possible form of the pion's structure function. This form is consistent with experimental data of the pion's structure function.     

Mass corrections to scaling in deep inelastic processes

We study subasymptotic hadron target and quark-parton mass corrections to scaling in deep inelastic scattering, ignoring interactions. The results can be summarized using a modified scaling variable common to parton, light-cone and short-distance operator product expansion formalisms, but with model-dependent spectral conditions. The analysis is expected to break down near the kinematic boundaries because of the bound state nature of hadrons. Related effects probably also dominate mass corrections due to very light quarks, but the analysis should be applicable to the production of new heavy quarks in neutrino production. Experimental deviations from scaling in deep inelastic electroproduction do not seem to be describable in terms of mass corrections alone, suggesting that interaction effects may be important at large momentum transfers as suggested by the renormalization group.