Applications of the reggeon calculus to dual models

Physics Reports, 1971

THE OPERATOR APPROACH TO DUAL MU LTIPARTICLE TIIEOR 271 5.5. The zero mode 5.6. An alternative notation 5.7. Diagtmaltzatlon of C matrices mzd traces of canonical forms 6. Single loop amplitudes 6,1. CalculAtion of the plaz~r-loop amplitude 6. 2. Rules for arbitrary single-loop diagrams 6°$. Properties of ortentable non-planar one-loop amplitudes 7. Renormalization 7.1. Definition of the counter-term 7. 2. Properties of the counter-term 7.3. Discussion of the renormallzation 8. Duality and unitartty properties of the single loop amphtu~i,,s 8.1. Duality properties of the twisted propagator 8.2. Duality properties of orlontable single loops 8.3. Non-orientable diagrams 8.4. Unitarity 9. General vertices 9.1. The symmetric vertex 9.2. Canonical H-vertices 9.3. MObius N-vertices 9.4. The N-Reggeon vertex 9.5. Some simple properties 9.6. The bootstrap or tactorization property 9.7. The operatortal duality conditions and ~e connection with the previous formalism 9.8. The Lovelace vertex Appendix: Some properties of coherent states References

Nuclear Physics B, 1977

We present a detailed study of the bare pomeron graph in two-dimensional QCD in the 1IN c approximation. The absence of a new singularity unrelated to quark parameters is derived. The "cylinder" graph is shown to induce renormalization of the vertex and intercept associated with quark andti-quark exchange in the vacuum channel.

Modern Physics Letters A, 2017

The technique of one-loop calculations for the processes involving Reggeized quarks is described in the framework of gauge invariant effective field theory for the Multi-Regge limit of QCD, which has been introduced by Lipatov and Vyazovsky. The rapidity divergences, associated with the terms enhanced by log(s), appear in the loop corrections in this formalism. The covariant procedure of regularization of rapidity divergences, preserving the gauge invariance of effective action is described. As an example application, the one-loop correction to the propagator of Reggeized quark and [Formula: see text]-scattering vertex are computed. Obtained results are used to construct the Regge limit of one-loop [Formula: see text] amplitude. The cancellation of rapidity divergences and consistency of the EFT prediction with the full QCD result is demonstrated. The rapidity renormalization group within the EFT is discussed.

Physical Review D, 2000

In order to check the compatibility of the gluon Reggeization in QCD with the s-channel unitarity, the one-loop correction to the Reggeon-Reggeon-gluon vertex must be known at arbitrary space-time dimension D. We obtain this correction from the gluon production amplitude in the multi-Regge kinematics and present an explicit expression for it in terms of a few integrals over the transverse momenta of virtual particles. The one-gluon contribution to the non-forward BFKL kernel at arbitrary D is also obtained. * Work supported in part by the Ministero italiano dell'Università e della Ricerca Scientifica e Tecnologica, in part by INTAS and in part by the Russian Fund of Basic Researches.

Journal of High Energy Physics, 2009

We derive the evolution equation for hadronic scattering amplitude at high energy. Our derivation includes the nonlinear effects of finite partonic density in the hadronic wave function as well as the effect of multiple scatterings for scattering on dense hadronic target. It thus includes Pomeron loops. It is based on the evolution of the hadronic wave function derived in . The kernel of the evolution equation defines the second quantized Hamiltonian of the QCD Reggeon Field Theory, H RF T beyond the limits considered so far. The two previously known limits of the evolution: dilute target (JIMWLK limit) and dilute projectile (KLWMIJ limit) are recovered directly from our final result. The Hamiltonian H RF T is applicable for the evolution of scattering amplitude for arbitrarily dense hadronic projectiles/targets -from "dipole-dipole" to "nucleus-nucleus" scattering processes.

Suplemento de la Revista Mexicana de Física

The three-gluon vertex is a fundamental ingredient of the intricate QCD dynamics, being inextricably connected to key nonperturbative phenomena, such as the emergence of a mass scale in the gauge sector of the theory. In this presentation, we review the main theoretical properties of the three-gluon vertex in the Landau gauge, obtained from the fruitful synergy between functional methods and lattice simulations. We pay particular attention to the manifestation and origin of the infrared suppression of its main form factors and the associated zero crossing. In addition, we discuss certain characteristic phenomenological applications that require this special vertex as input.

2006

The Reggeon field theory with zero transverse dimensions is studied in the Hamiltonian formulation for both sub-and supercritical pomeron. Mathematical aspects of the model, in particular the scalar products in the space of quantum states, are discussed. Relation to reaction-diffusion processes is derived in absence of pomeron merging. Numerical calculations for different parameters of the models, α(0) − 1 = µ and the triple pomeron coupling constant λ, show that the triple pomeron interaction always makes amplitudes fall with rapidity irrespective of the value of the intercept. The smaller the values of the ratio λ/µ the higher are rapidities y at which this fall starts, so that at small values of λ it begins at asymptotically high rapidities (for λ/µ < 1/4 the fall is noticeable only at µy > 100). No visible singularity is seen for the critical pomeron. A perturbative treatment is proposed which may be useful for more realistic models.

Nuclear Physics B, 2000

The complete two-loop correction to the quark propagator, consisting of the spider, rainbow, gluon bubble and quark bubble diagrams, is evaluated in the noncovariant light-cone gauge (lcg), n•A a (x) = 0, n 2 = 0. (The overlapping self-energy diagram had already been computed.) The chief technical tools include the powerful matrix integration technique, the n * µ-prescription for the spurious poles of (q •n) −1 , and the detailed analysis of the boundary singularities in five-and six-dimensional parameter space. It is shown that the total divergent contribution to the two-loop correction Σ 2 contains both covariant and noncovariant components, and is a local function of the external momentum p, even off the mass-shell, as all nonlocal divergent terms cancel exactly. Consequently, both the quark mass and field renormalizations are local. The structure of Σ 2 implies a quark mass counterterm of the form δm(lcg) = m α s C F (3 + α s W) + O(α 3 s), α s ≡ g 2 Γ(ǫ)(4π) ǫ−2 , with W depending only on the dimensional regulator ǫ, and on the numbers of colors and flavors. It turns out that δm(lcg) is identical to the mass counterterm in the general linear covariant gauge. Our results are in agreement with the Bassetto-Dalbosco-Soldati renormalization scheme.

2006

This paper is a brief survey of the Balitskii-Fadin-Kuraev-Lipatov (BFKL) approach for the description of hard or semi-hard processes in the so-called Regge limit of perturbative QCD. The starting point is a fundamental property of perturbative QCD, the gluon Reggeization. This property, combined with s-channel unitarity, allows to predict the growth in energy of the amplitude of hard or semi-hard processes with exchange of vacuum quantum numbers in the t-channel. When also the so-called impact factors of the colliding particles are known, then not only the behavior with the energy, but the complete amplitude can be determined. This was recently done, for the first time with next-to-leading order accuracy and for a process with colorless external particles, in the case of the electroproduction of two light vector mesons.

Developing an approach defined in previous papers a correspondence between elementary particles and elements of a particular set of directed graphs said "glyphs" is made explicit. These can, in turn, be put in correspondence with a particular set of biquaternions. Charge conjugation and weak isospin inversion then become both topological (on glyphs) and algebraic (on biquaternions) symmetries. The formalism describes leptons and quarks, the latter successfully combined into mesons and baryons. The derivation is possible of both a de Sitter interior spacetime of particles and the usual external Minkowski spacetime. The biquaternions can be related to creation and annihilation operators of the corresponding fermionic fields in Quantum Field Theory (QFT). The base states of QFT and their mutual interactions are thus constrained by their common emergence from logically antecedent structures. This result appears of great importance for the understanding of the elementary particles spectrum.