Alan R. White

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.

The Past and Future of S-Matrix Theory

The “diagrammatic” framework of S -matrix theory is provided by the unitarity equations. In its purest form, the S -matrix theory establishes those analyticity properties of the S matrix that can be based on physical principles clearly formulated separately from the field theory. The chapter presents a heuristic way to develop a diagrammatic expansion that is connected to the Feynman diagram expansion. It is required to write the S matrix as S = 1 + R + and its Hermitian conjugate as S + = 1 - R - . Scattering processes can be described by a Landau diagram. The Landau equations for a given Landau diagram are the set of conditions for all internal loops of the diagram. The set of external momenta that satisfies the complete set of equations provides the Landau singularity corresponding to the diagram. The set of all physical region (+α) Landau diagram thresholds is the minimal set of singularities that an analytic scattering amplitude must have.

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.

The current status of high energy elastic scattering

The recent total cross section, σtot, and ρ-value results from the Fermilab Tevatron Collider experiments,1,2 presented at the 4th “Blois” Workshop on Elastic and Diffractive Scattering, held at Elba in May 1991, provide a natural springboard from which to launch a focused review of the field.

COULD A WEAK COUPLING MASSLESS SU(5) THEORY UNDERLY THE STANDARD MODEL S-MATRIX?

The unitary Critical Pomeron connects to a unique massless left-handed SU(5) theory that, remarkably, might provide an unconventional underlying unification for the Standard Model. Multi-regge theory suggests the existence of a {\it bound-state high-energy S-Matrix} that replicates Standard Model states and interactions via massless fermion anomaly dynamics. Configurations of anomalous wee gauge boson reggeons play a vacuum-like role. All particles, including neutrinos, are bound-states with dynamical masses (there is no Higgs field) that are formed (in part) by anomaly poles. The contributing zero-momentum chirality transitions break the SU(5) symmetry to vector SU(3)xU(1) in the S-Matrix. The high-energy interactions are vector reggeon exchanges accompanied by wee boson sums (odd-signature for the strong interaction and even-signature for the electroweak interaction) that strongly enhance couplings. The very small SU(5) coupling, ~ 1/120, should be reflected in small (Majorana) neutrino masses. A color sextet quark sector, still to be discovered, produces both Dark Matter and Electroweak Symmetry Breaking. Anomaly color factors imply this sector could be produced at the LHC with large cross-sections, and would be definitively identified in double pomeron processes.

The O(g4) Lipatov kernels

Abstract Leading plus next-to leading log results for the Regge limit of massless Yang-Mills theories are reproduced by reggeon diagrams in which the Regge slope α′ → 0 and reggeon amplitudes satisfy Ward identify constraints at zero transverse momentum. Using reggeon unitarity together with multiple discontinuity theory a complete set of such diagrams can be constructed. The resulting two-two, one-three and two-four kernels which generalise the Lipatov equation at O ( g 4 ) are determined uniquely.

Properties of the scale invariant O(g4) Lipatov kernel

Abstract We study the scale-invariant O(g4) kernel which appears as an infra-red contribution in the BFKL evolution equation and is constructed via multiparticle t-channel unitarity. We detail the variety of Ward identity constraints and infra-red cancellations that characterize its infrared behaviour. We give an analytic form for the full non-forward kernel. For the forward kernel controlling parton evolution at small x, we give an impact parameter representation, derive the eigenvalue spectrum, and demonstrate a holomorphic factorisation property related to conformal invariance. The present results indicate that, at next-to-leading order, the transverse momentum infra-red region may produce a significant reduction of the BFKL small-x behavior.

Gauge theory high-energy behavior from J-plane unitarity

Abstract In a non-abelian gauge theory the t-channel multiparticle unitarity equations continued in the complex j -plane can be systematically expanded around j = 1 and t = 0. The combination of Ward identity constraints with unitarity is sufficient to produce directly many of the results obtained by Regge limit leading-log and next-to-leading log momentum-space calculations. The O ( g 2 ) BFKL kernel is completely determined. O ( g 4 ) infrared contributions to this kernel are also obtained, including the leading contribution of a new partial-wave amplitude—previously identified as a separate forward component with a holomorphically factorizable spectrum. For this amplitude the only scale ambiguity is the overall normalization and it is anticipated to be a new conformally invariant kernel. While scale-dependent non-leading reggeon interactions can not be derived by the techniques developed, it is conjectured that all conformally invariant interactions may be determined by t -channel unitarity.

A unique SU(5) and SO(10) unification with complete dynamical symmetry breaking

A unique asymptotically free, anomaly-free, SU(5) gauge theory is proposed as a possible complete unification of the standard model in which all symmetry-breaking is dynamical. The asymptotic freedom constraint is saturated, removing renormalon divergences and leaving well-defined instanton interactions as the only nonperturbative ingredient of the theory. Consequently, it is argued, topological vacuum polarization of a very heavy, unconventional quantum number, quark sector dominates the dynamics, producing SU(5) symmetry breaking and a three generation low energy spectrum. Electroweak symmetry breaking is due to a chiral condensate of color sextet quarks. The embedding of the theory in a single SO(10) representation is used for the dynamical analysis and may also have physical significance.

INFRARED ANOMALOUS INTERACTIONS AS A SIGNAL FOR ELECTROWEAK SYMMETRY BREAKING BY COLOR SEXTET QUARKS

We study the possibility that electroweak symmetry breaking occurs dynamically as a consequence of a chiral condensate of color sextet quarks. New (but conventional) leptons are used to cancel gauge anomalies. An effective Lagrangian with a Wess-Zumino term is used to describe “sextet pion” interactions and associated chiral anomalies. We show that the gauge-invariant effective Lagrangian which describes infrared interactions of the physical W± and Z0 vector bosons contain axial-vector chiral anomalies generated by lepton loops. Lepton-induced anomalous interactions would therefore be a signal of this form of dynamical symmetry breaking.