Gluon cascades and amplitudes in light-front perturbation theory

We construct the gluon wave functions, fragmentation functions and scattering amplitudes within the light-front perturbation theory. Recursion relations on the light-front are constructed for the wave functions and fragmentation functions, which in the latter case are the light-front analogs of the Berends–Giele recursion relations. Using general relations between wave functions and scattering amplitudes it is demonstrated how to obtain the maximally-helicity violating amplitudes, and explicit verification of the results is based on simple examples.     

An introduction to on-shell recursion relations

This article provides an introduction to on-shell recursion relations for calculations of tree-level amplitudes. Starting with the basics, such as spinor notations and color decompositions, we expose analytic properties of gauge-boson amplitudes, BCFW-deformations, the large z-behavior of amplitudes, and on-shell recursion relations of gluons. We discuss further developments of on-shell recursion relations, including generalization to other quantum field theories, supersymmetric theories in particular, recursion relations for off-shell currents, recursion relation with nonzero boundary contributions, bonus relations, relations for rational parts of one-loop amplitudes, recursion relations in 3D and a proof of CSW rules. Finally, we present samples of applications, including solutions of split helicity amplitudes and of N = 4 SYM theories, consequences of consistent conditions under recursion relation, Kleiss-Kuijf (KK) and Bern-Carrasco-Johansson (BCJ) relations for color-ordered gluon tree amplitudes, Kawai-Lewellen-Tye (KLT) relations.     

Compact multigluonic scattering amplitudes with heavy scalars and fermions

Combining the Berends-Giele and on-shell recursion relations we obtain an extremely compact expression for the scattering amplitude of a complex massive scalar-antiscalar pair and an arbitrary number of positive helicity gluons. This is one of the basic building blocks for constructing other helicity configurations from recursion relations. We also show explicitly that the scattering amplitude of massive fermions to gluons, all with positive helicity, is proportional to the scalar one, confirming in this way the recently advocated SUSY-like Ward identities relating both amplitudes.     

Off-shell πN amplitudes via a multichannel separable potential

The off-shell pion-nucleon transition matrix is a basic ingredient in theories of pion-nuclear interactions which, in the absence of fundamental theory of πN dynamics, must be obtained by a phenomenological extrapolation from the available on-shell data. As one means of performing such an extrapolation, we explore a multichannel separable potential model with the property that the off-shell elastic scattering amplitude is generated directly from the measured elastic-channel phase shifts. The off-shell πN partial-wave transition amplitudes determined by this procedure are compared with those calculated by Landau and Tabakin using a one-channel absorptive separable potential. We find that the absorptive separable potential approach provides a physically unreasonable off-shell extrapolation at energies where the on-shell amplitude is highly inelastic, and show that the difficulty is a direct consequence of the one-channel nature of that method. The multichannel extrapolation is free of these difficulties.     

On-shell methods for form factors in N = 4 SYM and their applications

Form factors are quantities that involve both asymptotic on-shell states and gauge invariant operators. They provide a natural bridge between on-shell amplitudes and off-shell correlation functions of operators, thus allowing us to use modern on-shell amplitude techniques to probe into the off-shell side of quantum field theory. In particular, form factors have been successfully used in computing the cusp(soft) anomalous dimensions and anomalous dimensions of general local operators. This review is intended to provide a pedagogical introduction to some of these developments. We will first review some amplitudes background using four-point amplitudes as main examples. Then we generalize these techniques to form factors, including(1) tree-level form factors,(2) Sudakov form factor and infrared singularities, and(3) form factors of general operators and their anomalous dimensions. Although most examples we consider are inN= 4 super-Yang-Mill theory, the on-shell methods are universal and are expected to be applicable to general gauge theories.     

General N-Body Theory of Nonrelativistic Quantum Scattering

 The two-Hilbert-space theory of scattering is reviewed with particular reference to its application to nonrelativistic multichannel quantum- mechanical scattering theory. In Part I the abstract assumptions of the theory are collected, transition operators (both on- and off-energy-shell) are defined, the dynamical equations that determine the off-shell transition operators are presented and their real-energy limits examined, and the convergence of sequences of approximate transition operators is established. A section on how to incorporate group symmetries into the formalism reports new work. The material of Part I is relevant to a variety of both classical and quantum scattering systems. In Part II attention is directed specifically to N-body nonrelativistic quantum scattering systems in which the particles interact via short-range pair potentials. A method of constructing approximate transition operators is presented and shown to satisfy all the abstract assumptions of Part I. The dynamical equations that determine the half-on-shell approximate transition operators are shown to be coupled one-dimensional integral equations that have compact kernels and unique solutions when considered as operators on a Hilbert space of H?lder continuous functions. Moreover, the on-shell parts of those approximate transition amplitudes are shown to converge to the exact on-shell amplitudes as the order of the approximation increases. Detailed formulas for the kernels of the integral equations are written down for systems of particles that are distinguishable and for systems containing identical particles. Finally, some important open problems are described. Received July 2, 1999; accepted in final form October 27, 1999     

Three applications of a bonus relation for gravity amplitudes

Arkani-Hamed et al. have recently shown that all tree-level scattering amplitudes in maximal supergravity exhibit exceptionally soft behavior when two supermomenta are taken to infinity in a particular complex direction, and that this behavior implies new non-trivial relations amongst amplitudes in addition to the well-known on-shell recursion relations. We consider the application of these new ‘bonus relations’ to MHV amplitudes, showing that they can be used quite generally to relate (n−2)!$(n-2)!$-term formulas typically obtained from recursion relations to (n−3)!$(n-3)!$-term formulas related to the original BGK conjecture. Specifically we provide (1) a direct proof of a formula presented by Elvang and Freedman, (2) a new formula based on one due to Bedford et al., and (3) an alternate proof of a formula recently obtained by Mason and Skinner. Our results also provide the first direct proof that the conjectured BGK formula, only very recently proven via completely different methods, satisfies the on-shell recursion.     

J/gy suppression as evidence for high densities in nuclear collisions

It is shown that the scattering amplitudes of some degenerate massive string states can be expressed in terms of that of higher spin states at the same mass level. This phenomenon is discussed from σ-model point of view and demonstrated explicitly by using massive Ward identities generated by zero-norm states atD=26. The subtlety of the scalar propagating state is briefly pointed out. We also compare our on-shell gauge symmetry derived from σ-model with off-shell gauge symmetry of covariant string field theory.     

Off-shell effects in quasielastic electron nucleus scattering

Using the Ward-Takahashi identity, on-shell condition, bound Dirac equation and off-shell expansion, a reduced version of half off-shell virtual photon nucleon vertex has been suggested. The vertex are decomposed into several different order terms: the on-shell terms, first and second off-shell terms. The off-shell behaviour of the form factors is discussed in the one meson loop model. Using the reduced vertex and parametrized off-shell form factors the quasielastic response functions are calculated for several nuclei at ¦q¦–k_f and for⁵⁶Fe at large ¦q¦ up to 1.14 GeV/c and at ?q²=0.9 (GeV/c)². The Coulomb sums are evaluated and a comparison of the theoretical prediction with data is given. The off-shell electron nucleon cross section is calculated and compared with the “cc1” off-shell extrapolation.     

Generalized optical theorems for the reconstruction of Green's function of an inhomogeneous elastic medium

This paper investigates the reconstruction of elastic Green's function from the cross-correlation of waves excited by random noise in the context of scattering theory. Using a general operator equation-the resolvent formula-Green's function reconstruction is established when the noise sources satisfy an equipartition condition. In an inhomogeneous medium, the operator formalism leads to generalized forms of optical theorem involving the off-shell T-matrix of elastic waves, which describes scattering in the near-field. The role of temporal absorption in the formulation of the theorem is discussed. Previously established symmetry and reciprocity relations involving the on-shell T-matrix are recovered in the usual far-field and infinitesimal absorption limits. The theory is applied to a point scattering model for elastic waves. The T-matrix of the point scatterer incorporating all recurrent scattering loops is obtained by a regularization procedure. The physical significance of the point scatterer is discussed. In particular this model satisfies the off-shell version of the generalized optical theorem. The link between equipartition and Green's function reconstruction in a scattering medium is discussed.     

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.     

动量空间中能质子-12C弹性散射截面和自旋量的研究

在KMT理论框架下，应用微观的动量空间一级光学势，包括了库仑修正，自旋关联，NN振幅反对称，离壳效应，核子反冲和结合能转换，Lorentz不变的角变换.在整个中能区域系统地计算了质子-¹²C弹性散射微分截面和自旋观测量，并与实验数据及Glauber理论框架下或已有的其他理论计算结果做了比较，其结果显示，在200—1000MeV，该理论与实验结论符合程度较好.     

Dimensional renormalization and factorization

The problem of formulating a high-energy factorization explicitly in terms of dimensionally renormalized operators and coefficient functions is analyzed in the context of deep-inelastic scattering in renormalizable scalar theories. The coefficient functions that emerge are found to be the finite parts of dimensionally continued on-shell amplitudes, and are readily amenable to explicit computation. As a byproduct, an explicit forest formula emerges for the mass-singularity poles of on-shell amplitudes in renormalizable theories. The extension to gauge theories is briefly discussed at the leading twist level. The method is compared to the alternative approach to factorization whereby a finite hard part is defined by factorizing off mass-singularities.     

The 2H(p, 2p)n reaction at Einc = 45 MeV and its sensitivity to various separable S-wave N-N potentials

This paper presents and analyses the data for the ²H(p, pp)n reaction at E_inc = 44.9 MeV. Kinematic conditions including the quasi-free scattering region and the regions far from quasi-two-body processes are considered. The experimental results are compared with the predictions of several separable S-wave models of the N-N interaction. Potential models that differ only off-shell, as well as models that predict different N-N scattering results are included to help to isolate aspects of the break-up reaction sensitive to off-shell and on-shell differences. The regions far from quasi-free scattering are generally much more sensitive to the off-shell features of the interaction than are quasi-free scattering results. On-shell differences in the potential affect predictions in all regions of phase space with the potentials best representing the free N-N data giving the best overall fit to the data over most regions of phase space.     

Dispersion relations for elastic n-d scattering in the Amado model

The formulation of rigorous, dispersion relations for on-shell three-body amplitudes in a separable model is reported. The results of approximate $\text{N}\text{D}$ calculations of s-wave n-d elastic scattering are compared with exact, numerical solutions of the Faddeev equations.     

Compact QED tree-level amplitudes from dressed BCFW recursion relations

We construct a modified on-shell BCFW recursion relation to derive compact analytic representations of tree-level amplitudes in QED. As an application, we study the amplitudes of a fermion pair coupling to an arbitrary number of photons and give compact formulae for the NMHV and N²MHV case. We demonstrate that the new recursion relation reduces the growth in complexity with additional photons to be exponential rather than factorial.     

Weak coupling expansions fully off the energy shell

This paper contains off-shell generalizations of the standard (on-shell) Born series. Both Fredholm and Volterra integral equations are derived for the half-off-shell wave functions. Fully off-shell matrix elements of the transition operator are then developed by iteration. Convergence and truncation problems are also discussed. An alternative approach via the explicit form of the T-operator is also indicated.