multi-Regge Amplitudes Research Articles

A KLT-like construction for multi-Regge amplitudes

Inspired by the calculational steps originally performed by Kawai, Lewellen and Tye, we decompose scattering amplitudes with single-valued coefficients obtained in the multi-Regge-limit of N=4 super-Yang–Mills theory into products of scattering amplitudes with multi-valued coefficients. We consider the simplest non-trivial situation: the six-point remainder function complementing the Bern–Dixon–Smirnov ansatz for multi-loop amplitudes.Utilizing inverse Mellin transformations, all single-valued amplitude components can indeed be decomposed into multi-valued amplitude components. Although the final expression is very similar in structure to the Kawai–Lewellen–Tye construction, moving away from the highly symmetric string scenario comes with several imponderabilities, some of which become more pronounced when considering more than six external legs in the remainder function.

Regge vertex for quark production in the central rapidity region in the next-to-leading order

The effective vertex for quark production in the interaction of a Reggeized quark and a Reggeized gluon is calculated in the next-to-leading order (NLO). The resulting vertex is the missing component of the NLO multi-Regge amplitude featuring quark and gluon exchanges in the t channels. This calculation will make it possible to develop in future the bootstrap approach to proving quark Reggeization in the next-to-leading logarithmic approximation.

The Multi-Regge limit of NMHV amplitudes in N=4 SYM theory

We consider the multi-Regge limit for N=4 SYM NMHV leading color amplitudes in two different formulations: the BFKL formalism for multi-Regge amplitudes in leading logarithm approximation, and superconformal N=4 SYM amplitudes. It is shown that the two approaches agree to two-loops for the 2->4 and 3->3 six-point amplitudes. Predictions are made for the multi-Regge limit of three loop 2->4 and 3->3 NMHV amplitudes, as well as a particular sub-set of two loop 2 ->2 +n N^kMHV amplitudes in the multi-Regge limit in the leading logarithm approximation from the BFKL point of view.

Confinement and the supercritical Pomeron in QCD

Deep-inelastic diffractive scaling violations have provided fundamental insight into the QCD pomeron, suggesting a single gluon inner structure rather than that of a perturbative two-gluon bound state. This paper derives a high-energy, transverse momentum cut-off, confining solution of QCD. The pomeron, in first approximation, is a single reggeized gluon plus a ``wee parton'' component that compensates for the color and particle properties of the gluon. This solution corresponds to a supercritical phase of Reggeon Field Theory. Beginning with the multi-regge behavior of massive quark and gluon amplitudes, reggeon unitarity is used to derive a reggeon diagram description of a wide class of multi-regge amplitudes, including those describing the formation and scattering of bound-state Regge poles. When quark and gluon masses are taken to zero, a logarithmic divergence is produced by helicity-flip reggeon interactions containing the infra-red quark triangle anomaly. With the gauge symmetry partially broken, this divergence selects the bound states and amplitudes of a confining theory. Both the pomeron and hadrons have an anomalous color parity wee-parton component. For the pomeron the wee parton component determines that it carries negative color charge parity and that the leading singularity is an isolated Regge pole.

ANALYTIC MULTI-REGGE THEORY AND THE POMERON IN QCD II: GAUGE-THEORY ANALYSIS

The high-energy Regge behavior of gauge theories is studied via the formalism of analytic multi-Regge theory. Perturbative results for spontaneously broken theories are first organized into Reggeon diagrams. Unbroken gauge theories are studied via a Reggeon-diagram infrared analysis of symmetry restoration. Massless fermions play a crucial role and the case of QCD involves the supercritical Pomeron as an essential intermediate stage. An introductory review of the buildup of transverse-momentum diagrams and Reggeon diagrams from leading-log calculations in gauge theories is presented first. It is then shown that the results closely reproduce the general structure for multi-Regge amplitudes derived in Part I of the article, allowing the construction of general Reggeon diagrams for spontaneously broken theories. Next it is argued that, with a transverse-momentum cutoff, unbroken gauge theories can be reached through an infrared limiting process which successively decouples fundamental-representation Higgs fields. The first infrared limit studied is the restoration of SU(2) gauge symmetry. The analysis is dominated by the exponentiation of divergences imposed by Reggeon unitarity and the contribution of massless quarks to Reggeon interactions. Massless quarks also produce “triangle anomaly” transverse-momentum divergences which do not exponentiate but instead are absorbed into a Reggeon condensate — which can be viewed as a “generalized winding-number condensate.” The result is a Reggeon spectrum consistent with confinement and chiral-symmetry breaking, but there is no Pomeron. The analysis is valid when the gauge coupling does not grow in the infrared region, i.e. when a sufficient number of massless quarks is present. An analogy is drawn between the confinement produced by the Reggeon condensate and that produced by regularization of the fermion sea, in the presence of the anomaly, in the two-dimensional Schwinger model. When the analysis is extended to the case of QCD with the gauge symmetry restored to SU(2), the Reggeon condensate can be identified with the Pomeron condensate of supercritical Pomeron theory. In this case, the condensate converts an SU(2) singlet Reggeized gluon to a Pomeron Regge pole — which becomes an SU(3) singlet when the full gauge symmetry is restored, The condensate disappears as SU(3) symmetry is recovered, and in general this limit gives the critical Pomeron at a particular value of the transverse cutoff. If the maximal number of fermions consistent with asymptotic freedom is present, no transverse-momentum cutoff is required. For SU (N) gauge theory it is argued that, when the theory contains many fermions, there are N–2 Pomeron Regge poles of alternating signature. This spectrum of Pomeron trajectories is in direct correspondence with the topological properties of transverse flux tubes characterized by the center ZN of the gauge group. The corresponding Reggeon-field-theory solution of s-channel unitarity should include a representation of ZN in the cutting rules. Finally, the implications of the results for the phenomenological study of the Pomeron as well as for the construction of QCD with a small number of flavors are discussed. Also discussed is the attractive possibility that a flavor doublet of color-sextet quarks could both produce the critical Pomeron in QCD and be responsible for electroweak dynamical-symmetry breaking.

ANALYTIC MULTI-REGGE THEORY AND THE POMERON IN QCD I: THE SUPER-CRITICAL POMERON

The formalism of analytic multi-Regge theory is developed as a basis for the study of abstract critical and super-critical pomeron high-energy behavior and for related studies of the Regge behavior of spontaneously broken gauge theories and the pomeron in QCD. Asymptotic domains of analyticity for multiparticle amplitudes are shown to follow from properties of field theory and S-matrix theory. General asymptotic dispersion relations are then derived for such amplitudes in which the spectral components are described by the graphical formalism of hexagraphs. Further consequences are distinct Sommerfeld-Watson representations for each hexagraph spectral component, together with a complete set of angular momentum plane unitarity equations which control the form of all multi-Regge amplitudes. Because of this constraint of “reggeon unitarity” the critical pomeron solution of the reggeon field theory gives the only known “non-trivial” unitary high-energy S-matrix. By exploiting the full structure of multi-Regge amplitudes as the pomeron becomes super-critical, one can study the simultaneous modification of hadrons and the pomeron. The result is a completely consistent description of the super-critical pomeron appearing in hadron scattering. Reggeon unitarity is satisfied in the super-critical phase by the appearance of a massive “gluon” (Reggeized vector particle) coupling pair-wise to the pomeron.

Factorization of the six-particle multi-Regge amplitude

It is shown that factorization of the multi-Regge contribution to the six-particle amplitude follows from the complex-helicity-plane structure, the Steinmann relations, and extended unitarity. The six-particle multi-Regge amplitude also satisfies some new discontinuity relations which are interpreted as resulting from the interplay of singularities required by the Gram-determinant constraint in four-dimensional space-time. (AIP)

Factorization of discontinuities of multi-Regge amplitudes

It is shown that an arbitrary discontinuity of an arbitrary multi-Regge amplitude factorizes in a large class of models which encompasses the dual resonance model. It is argued that multiple discontinuities also factorize and that the factorization of discontinuities is expexted to hold on very general grounds as a result of the singularity structure of multiparticle amplitudes. These results allow the full amplitude as well as its discontinuities to be written as a product of Regge propagators, single-, double- and triple-Regge vertices and their discontinuities.

Rules for multi-Regge amplitudes and their discontinuities

It is argued that an arbitrarary discontinuity of an arbitrary multi-Regge amplitude factorizes just as does the full amplitude itself. A set of rules is given for writing down the behavior of the full amplitude or any discontinuity as a product of Regge propagators, single-, double-, and triple-Regge vertices and their discontinuities. This result has numerous applications; e.g., in the consistency of the multiperipheral model and the Mueller analysis of inclusive cross sections.

Signature, factorisation and unitarity in the multi-Regge model

It is shown, by continuation from the Symanzik region that the 2→4 multi-Regge amplitude in φ 3 perturbation theory factorises into signature terms and vertex terms. By using the implied normal threshold structure we show how the 2 → 4 particle unitarity equation becomes an identity if the 2 → 4 and 2 → 3 unitarity equations are satisfied at high energies. This solves a long standing problem in the multi-peripheral bootstrap.

Application of multi-Regge theory to production processes

This paper describes and reviews both kinematic (phase space) and dynamical aspects of production processes within the framework of multi-Regge theory. Those techniques that rely on additional theoretical assumptions are not treated. As an illustrative example, the case of three-body final states is developed in considerable detail. A simplified multi-Regge amplitude is assumed and formulae for the resulting differential cross sections are given. The emphasis of this work is the analysis of experimental data containing potential multi-Regge events.

A remark on the Toller ω dependence of two-Reggeon-one-particle vertex functions

It is pointed out that a two-Reggeon-one-particle vertex function in a multi-Regge amplitude is independent of the associated Toller angle ω if the trajectory of one of the Reggeons is zero.