Bethe Ansatz for QCD Pomeron,

Abstract

The equivalence is found between high-energy QCD in the generalized leading logarithmic approximation and the one-dimensional Heisenberg magnet. According to Regge theory, the high energy asymptotics of hadronic scattering amplitudes are related to singularities of partial waves in the complex angular momentum plane. In QCD, the partial waves are determined by nontrivial two-dimensional dynamics of the transverse gluonic degrees of freedom. The "bare" gluons interact with each other to form a collective excitation, the Reggeon. The partial waves of the scattering amplitude satisfy the Bethe-Salpeter equation whose solutions describe the color singlet compound states of Reggeons -- Pomeron, Odderon and higher Reggeon states. We show that the QCD Hamiltonian for reggeized gluons coincides in the multi-color limit with the Hamiltonian of XXX Heisenberg magnet for spin s=0 and spin operators the generators of the conformal SL(2,C) group. As a result, the Schrodinger equation for the compound states of Reggeons has a sufficient number of conservation laws to be completely integrable. A generalized Bethe ansatz is developed for the diagonalization of the QCD Hamiltonian and for the calculation of hadron-hadron scattering. Using the Bethe Ansatz solution of high-energy QCD we investigate the properties of the Reggeon compound states which govern the Regge behavior of the total hadron-hadron cross sections and the small-x behavior of the structure functions of deep inelastic scattering.

43 pages, LaTeX style, (one reference added)

References in corpus (3)

• High energy QCD as a completely integrable model
• Nonperturbative Corrections in Resummed Cross Sections
• Anomalous Dimensions of High Twist Operators in QCD at $N\to 1$ and large $Q^2

Cited by in corpus (74)

• The Bethe-Ansatz for N=4 Super Yang-Mills
• The Uses of Conformal Symmetry in QCD
• Conformal Regge theory
• Baryon Distribution Amplitudes in QCD
• Dressing and Wrapping
• Logarithmic scaling in gauge/string correspondence
• Noncompact Heisenberg spin magnets from high-energy QCD: I. Baxter Q-operator and Separation of Variables
• Integrability in QCD and beyond
• Odderon in the Color Glass Condensate
• Renormalization of twist-three operators and integrable lattice models
• Fine structure of spectrum of twist-three operators in QCD
• Solution of the Odderon Problem
• N=2 Supersymmetric QCD and Integrable Spin Chains: Rational Case N_f < 2N_c
• Integrability and WKB solution of twist-three evolution equations
• Exciting the GKP string at any coupling
• Evolution equations for quark-gluon distributions in multi-color QCD and open spin chains
• Quasiclassical QCD Pomeron
• Dilatation operator in (super-)Yang-Mills theories on the light-cone
• Quantum spectral curve as a tool for a perturbative quantum field theory
• Superconformal operators in N=4 super-Yang-Mills theory
• Separation of variables for the quantum SL(2,R) spin chain
• Odderon and seven Pomerons: QCD Reggeon field theory from JIMWLK evolution
• Interaction of Reggeized Gluons in the Baxter-Sklyanin Representation
• Embedding nonlinear O(6) sigma model into N=4 super-Yang-Mills theory
• Sum rules and dualities for generalized parton distributions: is there a holographic principle?
• Noncompact Heisenberg spin magnets from high-energy QCD: II. Quantization conditions and energy spectrum
• Solution of the multi-reggeon compound state problem in multi-colour QCD
• Anomalous Dimensions from Crossing Kernels
• Tailoring Non-Compact Spin Chains
• Long-range SL(2) Baxter equation in N=4 super-Yang-Mills theory
• Solution of the odderon problem for arbitrary conformal weights
• Reggeon Field Theory for Large Pomeron Loops
• Onium-Onium scattering at fixed impact parameter: exact equivalence between the color dipole model and the BFKL Pomeron
• Integrability of two-loop dilatation operator in gauge theories
• Integrable Fishnet from $\gamma$-Deformed $\mathcal{N}=2$ Quivers
• Three loop anomalous dimensions of twist-3 gauge operators in N=4 SYM
• Nonperturbative scales in AdS/CFT
• Integrable structures and duality in high-energy QCD
• The full spectrum of AdS5/CFT4 I: Representation theory and one-loop Q-system
• Q-operators in the six-vertex model
• Solitons in high-energy QCD
• QCD Reggeon Calculus From KLWMIJ/JIMWLK Evolution: Vertices, Reggeization and All
• From bubbles to foam: dilute to dense evolution of hadronic wave function at high energy
• Review of AdS/CFT Integrability, Chapter IV.4: Integrability in QCD and N<4 SYM
• ${\eta }_c$ production in photon - induced interactions at the AFTER@LHC experiment as a probe of the Odderon
• Universal R-matrix as integral operator
• On the Integrability of Planar N=2 Superconformal Gauge Theories
• Non-compact quantum spin chains as integrable stochastic particle processes
• Duality and hidden equilibrium in transport models
• High Energy QCD: Stringy Picture from Hidden Integrability
• Fusion hierarchies for N = 4 superYang-Mills theory
• Probing the Odderon in coherent hadron - hadron interactions at CERN LHC
• Universality of three gaugino anomalous dimensions in N=4 SYM
• The odderon and spin-flip dependence of high energy proton-proton scattering
• Universal R operator with deformed conformal symmetry
• Uncovering the triple pomeron vertex from Wilson line formalism
• Liouville field theory for gluon saturation in QCD at high energy
• Large spin expansion of the long-range Baxter equation in the sl(2) sector of N=4 SYM
• Regge spectroscopy of higher twist states in $\mathcal{N}=4$ supersymmetric Yang-Mills theory
• Anomalous dimensions of finite size field strength operators in N=4 SYM
• A Collinear Perspective on the Regge Limit
• Direct Calculations of the Odderon Intercept in the Perturbative QCD
• Integrability and the AdS/CFT correspondence
• Amplitudes in the N=4 SYM from Quantum Geometry of the Momentum Space
• Reciprocity and integrability in the sl(2) sector of N=4 SYM
• The Soft Pomeron and Nonperturbative Corrections in Quark-Quark Scattering
• Regge amplitudes in Generalized Fishnet and Chiral Fishnet Theories
• Inside looking out: probing JIMWLK with BFKL calculations
• Analytic continuation of Bethe energies and application to the thermodynamic limit of the $SL(2,\mathbb{C})$ non-compact spin chains
• New Effective Feynman-like Rules for the Multi-Regge QCD Asymptotics of Inclusive Multijet Production
• Eikonal but not: a complementary view of high energy evolution
• From QCD Strings to WZW
• Jet Physics from Static Charges in AdS
• Baryon wave functions in QCD and integrable models