Gribov Memorial Volume

PREFACE.

CONTENTS.

No abstract received.

No abstract received.

No abstract received.

I describe through a few anecdotes, Gribov's work on the high energy limit of strong interactions.

Studies of the small x dynamics at HERA energies allow to quantify the range of momentum transfers and energies for which the strength of the interaction approaches the maximum strength allowed by unitarity in the gluon channel (black disk limit - BDL). Implications for the proton-proton interactions at collider energies (Tevatron, LHC) include a dominance of BDL up to transverse momenta of hadrons (jets) in the final state ~ few GeV for collision at small impact parameters, and explanation of the proximity of the impact factor of pp interaction to one at small impact parameters, leading to universality of cross sections at super-high energies. We discuss briefly the theoretical challenges in the applications of pQCD to small x phenomena, the similarity between small x physics and critical phenomena, and new QCD phenomena related to this puzzle.

Numerically large QCD scales were discussed first in connection with a number of phenomena mostly related to vacuum quantum numbers and 0^± glueball and quark channels. We present arguments regarding the possible role of the larger scale in diquarks important for low-energy hadron phenomenology. Good diquarks, i.e. the 0⁺ states of two quarks, are argued to have a two-component structure with one of the components peaking at distances several times shorter than a typical hadron size (a short-range core).

I summarize the present status of the AGK cutting rules in perturbative QCD. Particular attention is given to the application of the AGK analysis to diffraction and multiple scattering in DIS at HERA and to pp collisions at the LHC. I also discuss the bootstrap conditions which appear in pQCD.

After some brief personal recollections about V.N. Gribov, I demonstrate that his results and ideas on complex angular momenta may be applied in unfamiliar directions. As an example, it is shown, that any strong interaction amplitude, satisfying dispersion relation (in momentum transfer), has infinite number of energy-plane poles, both for exotic and non-exotic quantum numbers. This result ensures the necessary condition for existence of exotic hadrons. However, without more detailed knowledge of dynamics one cannot secure sufficient conditions for the exotics existence.

No abstract received.

The MC@NLO program combines the precision of next-to-leading-order (NLO) perturbative QCD with the detailed final-state modelling of the HERWIG Monte Carlo (MC) event generator, without double counting. After a toy model exposition of the underlying method, results on a number of hadron collider processes, including vector boson pair, heavy flavour and associated and unassociated Higgs production, are reviewed.

I review recent results on soft gluon radiation at large angles.

The large single-spin asymmetries found in hard semi-inclusive reactions involving a transversely polarized nucleon remained unexplained for several decades, until the advent of the Collins mechanism, which provides a non-perturbative explanation. However, the mechanism vanishes in the naive parton model, where a quark is regarded as an essentially "free" particle. We give an intuitive analysis which highlights the difference between the naive picture and the realistic one and show how the Collins mechanism arises when the quark is described as an off-shell particle by a field in interaction.

We consider diffractive processes which can be measured at the LHC. Analysis of diffractive events will give unique information about the high energy asymptotics of the hadron scattering. In semihard diffraction one may study the partonic structure of the Pomeron. Central Exclusive Diffractive production provides a possibility to investigate the new particles (Higgs bosons, SUSY particles,…) in an exceptionally clean environment.

We stress the importance of testing dispersion relations at the LHC. A violation might be a sign for new physics.

We show that the addition of detectors to tag the outgoing forward protons, at the LHC, will significantly enlarge the potential of studying New Physics. A topical example is Higgs production by the exclusive double-diffractive process, pp → p + H + p. We discuss the production of Higgs bosons in both the SM and MSSM. We show how the predicted rates may be checked at the Tevatron by observing the exclusive double-diffractive production of dijets, or χ_c or χ_b mesons, or γγ pairs.

I summarize some recent developments in the issue of planar equivalence between supersymmetric Yang-Mills theory and its orbifold/orientifold daughters. This talk is based on works carried out in collaboration with Adi Armoni, Sasha Gorsky and Gabriele Veneziano.

Energy conservation is a large part of the NLO corrections to BFKL. A formalism is presented which includes effects of energy-momentum conservation in the dipole formalism in transverse coordinate space. Energy conservation gives a very strong suppression at small x, which implies that the effects of multi-pomeron exchange and saturation are pushed to very small x-values or very high energies. Perturbative QCD and PDFs from HERA can describe jets and E_⊥-flow in high energy pp collisions, but the multiplicity distributions are much more sensitive to non-perturbative effects. Analyses of minimum bias and underlying events at the Tevatron show that colours appear to combine to give strings which are as short as possible, in a way very different from e⁺e^--annihilation. This leads to important questions about the properties of the pomeron, the relation between high multiplicity events and diffraction, and the applicability of the AGK cutting rules.

The quantum vacuum becomes unstable in the presence of an event horizon; a famous example of that is quantum evaporation of black holes. In this talk I speculate that the universal and apparently thermal character of hadron production in various processes may originate in the decay of the QCD vacuum induced by a pulse of strong chromo–electric field.

In this talk we discuss the BFKL Pomeron Calculus and its interrelation with the colour dipole approach. The two key problems we consider are the probabilistic interpretation of the FKL Pomeron Calculus and the possible scenario for the asymptotic behaviour of the scattering amplitude at high energy in QCD.

The approach to interaction of hadrons and virtual photons with nuclei, proposed by Gribov, is reviewed and applied to description of nuclear structure functions in the small x region. The problem of saturation of parton densities in deep inelastic scattering (DIS) in the limit x → 0 is discussed and its relation to heavy ion collisions at very high energies is investigated in the framework of reggeon theory. It is emphasized that the shadowing effects are important in a definite kinematic region. It is shown how the prediction of the Glauber model for the density of hadrons produced in the central rapidity region in nucleus–nucleus interactions are modified due to shadowing of small-x-partons. Calculations show that shadowing effects are important at RHIC energies, but the "saturation" at these energies is not achieved yet. Production of particles with large transverse momenta and jets both in AuAu and dAu collisions is discussed.

We review the Regge description of high energy hadron interactions. It is shown, that gluon in QCD belongs to a Regge family. Pomeron and Odderon are composite states of reggeized gluons. The BFKL equation for the Pomeron wave function is discussed. In the multi-colour QCD the BKP equations for composite states of several gluons turn out to be integrable. To construct the Gribov reggeon calculus we formulate an effective lagrangian for the interaction of QCD partons with reggeized gluons. The effective vertices satisfy recurrent relations and are constructed explicitly in the momentum representation. We discuss the BFKL and DGLAP equations in N=4 SUSY. The intercept of the Pomeron at large couplings is calculated in the framework of the AdS/QFT correspondence.

We review the origin, and salient features, of the breaking of the conventional linear k_⊥ factorization for an in-nucleus hard pQCD processes. A realization of the nonlinear k_⊥-factorization which emerges instead is shown to depend on color properties of the underlying pQCD subprocesses. We discuss the emerging universality classes and extend nonlinear k_⊥-factorization to AGK unitarity rules for the excitation of the target nucleus.

We reanalyze an old recombination model of hadron production in proton - proton interactions. We start with comparing the results with data on hadron production in pp interactions. The model shows reasonable agreement with data on the production of non - strange hadrons. The model also reasonably describes the production of pairs, but it has problems with describing the ratio of strange baryons to strange mesons. We also make first attempts to extend the model to proton - nucleus collisions.

For particles emerging from a second order QCD phase transition, we show that a recently introduced shape parameter of the Bose-Einstein correlation function, the Lévy index of stability equals to the correlation exponent - one of the critical exponents that characterize the behavior of the matter in the vicinity of the second order phase transition point. Hence the shape of the Bose-Einstein/HBT correlation functions, when measured as a function of bombarding energy and centrality in various heavy ion reactions, can be utilized to locate experimentally the second order phase transition and the critical end point of the first order phase transition line in QCD.

The equation of state (EOS) of neutron-rich matter plays many important roles in both nuclear physics and astrophysics. However, it is still very poorly known, especially its isospin dependent part, namely the symmetry energy. Nuclear reactions with neutron-rich nuclei, stable and/or radioactive, provide a great opportunity to pin down the EOS of isospin asymmetric nuclear matter. In this talk, we report some recent theoretical progress in this field within an isospin and momentum dependent transport model (IBUU04). Using in-medium nucleon-nucleon cross sections consistent with the nuclear mean field used in the transport model, a symmetry energy of E_sym(ρ) ≈ 31.6(ρ/ρ₀)^0.69 was found most acceptable compared with both the MSU isospin diffusion data and the presently acceptable neutron-skin thickness in ²⁰⁸Pb. The isospin dependent part K_asy(ρ₀) of isobaric nuclear incompressibility was further narrowed down to -500 ± 50 MeV. Predictions on several observables sensitive to the density dependence of the symmetry energy at supranormal densities accessible at GSI and the planned Rare Isotope Accelerator (RIA) are also made.

Gribov's theory of light quark confinement implies the existence of two kinds of scalar bound states. The phase diagram of the three-flavor QCD is mapped out in the (m_π - m_K)–plane with help of the SU_L(3) × SU_R(3) linear sigma model supplemented with the assumption that the masses of the so-called superbound scalars do not change under the variation of the pion and kaon mass. The phase boundary along the m_π = m_K line is found in the interval 15 MeV < m_crit < 25 MeV, irrespective which f₀ - σ linear combination is identified with the pure superbound state.

No abstract received.

We discuss the problem of how to preserve the chiral symmetry of the continuum theory by a lattice regularization of QCD – a goal which was thought to be impossible to achieve for a long time. We also discuss the amazing properties of the corresponding lattice Dirac operator.

We briefly review and comment on the lattice data which indicate that confining vacuum fields are fine tuned, exhibiting non-trivial dependences both on the infrared and ultraviolet scales.

Bosonic string formation in gauge theories is reviewed with particular attention to the confining flux in lattice QCD and its string theory description. Recent results on the Casimir energy of the ground state and the string excitation spectrum are analyzed in the Dirichlet string limit of large separation between static sources. The closed string-soliton (torelon) with electric flux winding around a compact dimension is also discussed.

In the framework of the dispersion relation N/D-method we restore the low–energy ππ (IJ^PC = 00⁺⁺)-wave amplitude sewing it with the previously obtained K-matrix solution for the region 450–1900 MeV. The restored N/D-amplitude has a pole on the second sheet of the complex-s plane, near the ππ threshold. We discuss the hypothesis that this low–mass pole, or the low-mass σ-meson, corresponds to the dynamical state related to the confinement forces, that is the eyewitness of confinement.

As a non-perturbative and gauge invariant regularization the lattice became a powerful tool for a deeper understanding of vector and chiral gauge theories. Exact chiral symmetry on the lattice is a prerequisite of these developments. I will discuss briefly the history of chiral symmetry on the lattice which was long and troubled and had an amazingly nice upshot. Then an unexpected feature of lattice regularized chiral gauge theories will be discussed: although CPT remains intact, CP and T are violated at any finite resolution. It is not yet understood whether and under what conditions this symmetry breaking disappears in the continuum limit and whether a lattice formulation exists where these symmetries are explicit from the start.

Gribov's scenario of confinement caused by supercritical charges is described and the present status of Gribov's equation for the Green function of light quarks is discussed.

The general iteration solution (i.e., when the relevant skeleton loop integrals, contributing into the gluon self-energy, have to be iterated, which means that no any truncations/approximations have been made) of the Schwinger-Dyson equation of motion for the full gluon propagator unavoidably becomes the exact sum of the two terms. The first term is the Laurent expansion in the inverse powers of the gluon momentum squared, starting necessarily from the simplest one 1/(q²)². Each power-type severe (i.e., more singular than 1/q²) IR singularity is accompanied by the corresponding powers of the mass squared parameter (the mass gap) multiplied by the corresponding residues. The mass gap is responsible for the large scale structure of the true QCD vacuum. The standard second term is always as much singular as 1/q² and otherwise remaining undetermined. The inevitable existence of the first term makes just the principal difference between the nonlinear dynamics of non-Abelian QCD and the linear one of Abelian QED. Moreover, the infrared renormalization program of the theory leads to the gluon confinement criterion in a gauge-invariant way.

It is pointed out that inhomogeneous condensates or spinodal instabilities suppress the propagation of elementary excitations due to the absorptive zero mode dynamics. This mechanism is shown to be present in the scalar ϕ⁴ model and in Quantum Gravity. It is conjectured that the plane wave states of color charges have vanishing scattering amplitude owing to the color condensate in the vacuum.

We discuss new methods for non-compact sigma models with and without RR fluxes. The methods include reduction to one dimensional supermagnets, super-coset constructions and supertwistors. This work is a first step towards the solution of these models, which are important in several areas of physics. I dedicate it to the memory of Volodya Gribov.

High-energy unitarity is argued to select a special version of QCD as the strong interaction. Electroweak symmetry breaking has to be due to a new sextet quark sector — that will produce large cross-section effects at the LHC. The sextet sector embeds, uniquely, in a massless SU(5) theory that potentially generates the states and interactions of the Standard Model within a bound-state S-Matrix. Infra-red chirality transitions of the massless Dirac sea play an essential dynamical role.

We argue that the fundamental Theory of Everything is a conventional field theory defined in the flat multidimensional bulk. Our Universe should be obtained as a 3-brane classical solution in this theory. The renormalizability of the fundamental theory implies that it involves higher derivatives (HD). It should be supersymmetric (otherwise one cannot get rid of the huge induced cosmological term) and probably conformal (otherwise one can hardly cope with the problem of ghosts). We present arguments that in conformal HD theories the ghosts (which are inherent for HD theories) might be not so malignant. In particular, we present a nontrivial QM HD model where ghosts are absent and the spectrum has a well defined ground state. The requirement of superconformal invariance restricts the dimension of the bulk to be D ≤ 6. We suggest that the TOE lives in six dimensions and enjoys the maximum superconformal symmetry. Unfortunately, no renormalizable field theory with this symmetry is presently known. We construct and discuss an 6D supersymmetric gauge theory with four derivatives in the action. This theory involves a dimensionless coupling constant and is renormalizable. At the tree level, the theory enjoys conformal symmetry, but the latter is broken by quantum anomaly. The sign of the β function corresponds to the Landau zero situation.

The birefringence of a neutrino sea is discussed in the Standard Model. We demonstrate that the optical activity of a neutrino sea in the SM is dominated by the contribution of the two-loop diagrams that are five order of magnitudes larger than one-loop diagrams.

The "famous formula" E = mc² and the concept of "relativistic mass" increasing with velocity, which follows from it, are historical artifacts, contradicting the basic symmetry of Einstein's Special Relativity, the symmetry of 4-dimensional space-time. The relation discovered by Einstein is not E = mc², but E₀ = mc², where E₀ is the energy of a free body at rest introduced by Einstein in 1905. The source of the longevity of the "famous formula" is the irresponsible attitude of relativity theory experts to the task of explaining it to the non-experts.

The notion of "relativistic mass" presents a kind of pedagogical virus which very effectively infects new generations of students and professors and shows no signs of decline. Moreover in the Year of Physics it threatens to produce a real pandemia.

Under quite natural general assumptions, the following results are obtained. The maximum entropy of a quantized surface is demonstrated to be proportional to the surface area in the classical limit. The general structure of the horizon spectrum is found. The discrete spectrum of thermal radiation of a black hole fits the Wien profile. The natural widths of the lines are much smaller than the distances between them. The total intensity of the thermal radiation is estimated. In the special case of loop quantum gravity, the value of the Barbero – Immirzi parameter is found. Other values for this parameter, obtained under an additional assumption that the horizon is described by a U(l) Chern – Simons theory, are demonstrated to be in conflict with the firmly established holographic bound.

We give an elementary discussion of the asymptotic correspondence between highly excited strings and (mini)-black holes. A highly excited string can be assigned a temperature: the Hagedorn temperature, even though it is an isolated system. Some consequences of this result are discussed.

Previous results on trans-Planckian collisions in superstring theory are rewritten in terms of an explicitly unitary S-matrix whose domain of validity in energy–impact-parameter space borders with the black hole production threshold. Properties of the final state are analyzed by applying the famous AGK (Abramovskij–Gribov–Kancheli) rules and, as the region's boundary is approached, are found to resemble those expected from Hawking's evaporation process.

After a brief discussion of dimensional reductions leading to the 1+1 dimensional dilaton gravity theory we consider general properties of these theories and identify problems that arise in its further reductions to one dimensional theories – cosmological models, static states (in particular, black holes) and gravity-matter waves. To bypass shortcomings of the standard ('naive') reduction we propose to exploit more general ideas: 1. separating the space and time variables in generic models, 2. reductions of the moduli spaces in integrable models that may also be viewed as dimensional reductions. This allows us to clearly see a duality between static and cosmological solutions (that we call 'SC-duality') and to demonstrate a close relation of these objects to gravity-matter waves.

I review some of the salient points of the construction of a perturbative quantum theory of the dimensionally reduced pure Einstein gravity from 4 to 2 dimensions assuming that the 4 dimensional (4D) metrics admit two commuting Killing vectors. The dimensionally reduced theory corresponds to an O(1,2) symmetric σ-model coupled to two scalar fields in flat spacetime. It inherits the lack of standard perturbative renormalizability from 4D gravity, however, it turns out that strict cutoff independence can be achieved to all loop orders in a space of Lagrangians differing only by a field dependent conformal factor. The renormalization group flow possesses a unique non-Gaussian fixed point at which the trace anomaly vanishes. The existence of this non-Gaussian fixed point is compatible with Weinberg's "asymptotic safety" scenario.

As a concluding remark to the Memorial Budapest Conference Gribov–75 I recall the peculiar atmosphere in which in 1973 certain physical issues have been discussed that did not lose their actuality 30+ years later.

LIST OF PARTICIPANTS.