Gribov-80 Memorial Volume

The following sections are included:

• PREFACE

• CONTENTS

Note from Publisher - Please refer to full text.

Note from Publisher - Please refer to full text.

It is really hard to write about Volodya. There are no words that can express my admiration for his talent and the charm of his outstanding personality. Time can not soothe the pain of his untimely death. It only makes it worse, especially for the scientific world…

We remind the Gribov approach to the hadron high energy scattering. It was based on the effective field theory for the Pomeron interactions. In QCD and in gravity the gluons and gravitons are reggeized and therefore at high energies one should reformulate these theories in terms of the reggeons and their interactions. We review the basic ideas of the BFKL approach in QCD and in supersymmetric models and generalize them in the framework of the gauge-invariant effective theory for the reggeized gluon interactions. The similar generally covariant action for the reggeized graviton interactions is formulated in terms of the effective currents satisfying a non-linear evolution equation.

The low lying spectrum of QCD in a special environment (δ-regime) can be obtained in chiral perturbation theory (ChPT). The NNL order result predicts the spectrum in terms of the low energy constants of ChPT: F, Λ₁, Λ₂ and a mass M. Since the size of the spatial box in the δ-regime is a few fermi, only numerical simulations can create the QCD data. The low lying stable spectrum in the box is a relatively simple numerical problem. Comparing the data with the predictions of ChPT will be a precise way to determine three of the low energy constants of chiral perturbation theory.

I give a brief review of advances in Yang–Mills theory at strong coupling. Analytical theory of quark (color) confinement on which Gribov worked non-stop in the last twenty years of his life seems closer now than ever before.

The dynamical Maxwell-cut, a degeneracy is shown to be a precursor of condensate in the ɸ⁴ and the sine-Gordon models. The difference of the way the Maxwell-cut is obtained is pointed out and quantum censorship, the generation of semiclassically looking phenomenon by loop-corrections is conjectured in the sine-Gordon model. It is argued that quantum censorship and gluon confinement exclude each other.

We describe a unified picture of confining and deconfined phases of Yang-Mills theories in terms of nonperturbative vacuum defects. The confinement is related to condensation of (magnetic) strings. The phase transition at T = T_c is viewed as change of dimensions, 4d → 3d. Namely, all the defects become time oriented. As a result, percolation of strings becomes percolation of 3d trajectories or, in field theoretic language, condensation of a 3d scalar field. The condensation, in turn, might signal superfluidity of the quark-gluon plasma. The notes are mostly a mini-review. A remark on entanglement and confinement is added.

We investigate a hypothesis according to which the sigma-meson is a remnant of the confinement singularity in the white channel.¹ Introducing the confinement singularity 1/s² into the ππ-interaction block, we observe a splitting of the white component of the confinement singularity (1/s²) into two poles which are diving on the second sheet of the complex-s plane. The poles correspond to states which are mixtures of gluonic, flavour-singlet , and π π components. The low-lying pole is located at the complex-M region (690 ± 160) - i(400 ± 150) MeV, the second one goes in the region of large masses: (Re M ≳ 1400, -Im M ≳ 500) MeV.

I discuss the calculation of QCD jet rates in e⁺e^- annihilation as a testing ground for parton shower simulations and jet finding algorithms.

Almost 40 years ago, Gribov and colleagues at the Leningrad Nuclear Physics Institute developed the ideas that led to the Dokhsitzer-Gribov-Lipatov-Altarelli-Parisi and the Balitsky-Fadin-Kuraev-Lipatov equations. These equations describe the evolution of the distributions for quarks and gluon inside a hadron to increased resolution scale of a probe or to smaller values of the fractional momentum of a hadronic constituent. I motivate and discuss the generalization required of these equations needed for high energy processes when the density of constituents is large. This leads to a theory of saturation realized by the Color Glass Condensate.

Non-perturbative production of quark-antiquarks is investigated in the early stage of heavy-ion collisions. The time-dependent study is based on a kinetic description of the fermion-pair production in strong non-Abelian fields. We introduce time-dependent chromo-electric external field with a pulse-like time evolution in order to simulate the overlap of two colliding heavy ions. Our investigation is performed with finite current quark masses and focus on heavy quark-pair production. We have found that the small inverse duration time of the field pulse determines the efficiency of the quark-pair production. Therefore, the expected suppression for heavy quark production, as follows from the Schwinger formula for a constant field, is not seen, but an enhanced heavy quark production appears at ultrarelativistic energies.

We summarize results of the Generalization of the Gribov picture of nuclear shadowing in high energy processes off nuclei for calculating shadowing of the parton distributions in nuclei and some properties of the final states in small x processes in DIS are described. It is explained how account of the restrictions due to the energy-momentum conservation allows to choose approximations effective for the description of small x phenomena. Estimates of proximity of the pQCD interaction of small dipoles to the black disk limit are provided and the phenomenon of post-selection suppression of leading parton spectrum (effective fractional energy losses) in the proximity of the black disk regime in DIS is described. We argue that the resulting suppression of the the leading hadron production provides one of the most sensitive signals of the onset of new QCD dynamics. Evidence for importance of the post-selection phenomenon in the production of the leading pions in the d - Au collisions studied at RHIC is presented. We also outline briefly impact of rapid increase of parton distributions within pQCD at small x on the interplay of soft and hard QCD dynamics at the LHC.

An updated formulation of the Pomeron, in which s and t-channel unitarity screenings are included, is reviewed. The consequent soft scattering features are explored and it is suggested that the soft and hard Pomerons can be effectively presented by a single Pomeron trajectory. The interplay between theory and and data analysis is discussed.

We study the case when the triple-Pomeron vertex is assumed to have a vectorial form, that is, the amplitude of high-mass diffractive dissociation vanishes as as . We find that the available data in the triple-Reggeon region may be well described in such a 'weak' coupling scenario, providing that absorptive effects are taken into account. We compare this weak (vector) coupling scenario with the strong and weak (scalar) coupling scenarios. Corresponding predictions are presented for an LHC energy of 14 TeV.

The proton has a substructure in terms of parton cascades, which in a high energy collision fills the whole rapidity range between projectile and target. In the Good–Walker formalism the fluctuations in the cascades will give rise to diffractive excitation. Within the Lund Dipole Cascade model, it is in this way possible to reproduce diffractive excitation in pp collisions and DIS. In central pp collisions the fluctuations, and thus diffractive excitation, is suppressed by saturation. This leads to factorization breaking when comparing pp scattering and DIS. The results shows a multi-regge behaviour, with a bare pomeron pole with α(0) = 1.21, α′ = 0.2 GeV^-2, and an almost constant triple-pomeron coupling g_3P ≈ 0.3 GeV^-1.

We have computed meson and muon polarized radiative decays. The undergoing dynamics giving rise to lepton and photon polarizations is examined and analyzed in the soft and hard region of momenta. The particular configurations made by right-handed leptons with accompanying photons are investigated and interpreted as a manifestation of the axial anomaly. The photon polarization asymmetry is evaluated. Finiteness of polarized amplitudes against infrared and collinear singularities is shown to take place with mechanisms distinguishing between right handed and left handed final leptons.

We explain how the Jaffe-Witten mass gap appears in QCD. It is responsible for the large-scale structure of its ground state.

It is demonstrated, that chirality violating condensates in massless QCD arise entirely from zero mode solutions of Dirac equations in arbitrary gluon fields. A model is suggested, where the zero mode solutions are the ones for quarks, moving in the instanton field. Based on this model the quark condensate magnetic susceptibilities of dimensions 3(χ) and 5 (κ and ξ) were calculated. The good coincidence of the values χ, κ and ξ, obtained in this approach, with those found from the hadronic spectrum is a serious argument in favour of the idea that instantons are the only source of chirality violating condensates in QCD. The temperature dependence of the quark condensate is discussed. It is shown that the phase transition, corresponding to the T-dependence of the quark condensate α(T) as an order parameter, is of the type of crossover.

The effects of nonperturbatively generated "quark sea" have been investigated to determine the flavor structure of the octet baryons. The chiral constituent quark model (χ^CQM), which is known to provide a satisfactory explanation of the proton spin and related issues in the nonperturbative regime, is able to explain the qualitative generation of the requisite amount of quark sea. The importance of quark sea has been studied at different values of the Bjorken scaling variable x by including it phenomenologically in the sea quark distribution functions. The results for the quark sea asymmetries like , and Gottfried integral for the octet baryons strengthen the significance of quark sea at lower values of x.

The analytic behaviour of θ-vacuum energy at θ = 0 and θ = π in QCD is related to the existence of phase transitions which might involve CP symmetry breaking. The appearance of cusp singularities is a signal of CP symmetry breaking by non-perturbative effects. The only cusp singularities that could arise in the vacuum energy density are due to the presence of Lee-Yang zeros but these singularities are always ⋀ cusp singularities and never ⋁ cusps, which in the case θ = 0 is incompatible with the Vafa-Witten diamagnetic inequality. The argument is very similar to that used in the derivation of Bank-Casher formula. In this case the topological charge condensate is proportional to the density of Lee-Yang zeros at the CP invariant points. The fact that this density is always positive provides a key missing link in the Vafa-Witten proof of parity symmetry conservation in vector-like gauge theories like QCD. However, this property does not exclude the existence of a first phase transition at θ = π with a ⋀ cusp singularity, or a second order phase transition at θ = 0, which might be very relevant for interpretation of the anomalous behavior of the topological susceptibility in the ℂP¹ sigma model.

The structure of matter is related to symmetries at every level of study. CPT symmetry is one of the most important laws of field theory: it states the invariance of measurable physical properties when one simultaneously changes the signs of the charges and of the spatial and time coordinates of free elementary particles. Although in general opinion CPT symmetry is not violated in Nature, there are theoretical attempts to develop CPT-violating models. The Antiproton Decelerator at CERN has been built to test CPT invariance. The ASACUSA experiment compares the properties of particles and antiparticles by studying the antiprotonic helium atom via laser spectroscopy and measuring the mass, charge and magnetic moment of the antiproton as compared to those of the proton.

I review a number of topics where conventional wisdom in hadron physics has been challenged. For example, hadrons can be produced at large transverse momentum directly within a hard QCD subprocess, rather than from jet fragmentation. Such "direct" higher-twist processes can explain the deviations from perturbative QCD predictions in measurements of inclusive hadron cross sections at fixed , as well as the "baryon anomaly, the anomalously large proton-to-pion ratio seen in high centrality heavy ion collisions. Initial-state and final-state interactions of the struck quark, soft-gluon rescattering associated with its Wilson line lead to Bjorken-scaling single-spin asymmetries, diffractive deep inelastic scattering, the breakdown of the Lam-Tung relation in Drell-Yan reactions, as well as nuclear shadowing and antishadowing. The Gribov-Glauber theory predicts that antishadowing of nuclear structure functions is not universal, but instead depends on the flavor quantum numbers of each quark and antiquark, thus explaining the anomalous nuclear dependence measured in deep-inelastic neutrino scattering. Since shadowing and antishadowing arise from the physics of leading-twist diffractive deep inelastic scattering, one cannot attribute such phenomena to the structure of the nucleus itself. It is thus important to distinguish "static" structure functions, the probability distributions computed from the square of the target light-front wavefunctions, versus "dynamical" structure functions which include the effects of the final-state rescattering of the struck quark. The importance of the J = 0 photon-quark QCD contact interaction in deeply virtual Compton scattering is also emphasized. The scheme-independent BLM method for setting the renormalization scale is discussed. The elimination of the renormalization scale ambiguity would greatly improve the precision of QCD predictions and increase the sensitivity of searches for new physics at the LHC. Other novel features of QCD are discussed, including the consequences of confinement for quark and gluon condensates.

Probably the most enticing observation in theoretical physics during the last decade was the discovery of the great amount of consequences obtained from the AdS/CFT conjecture put forward by Maldacena. In this work we review how this correspondence can be used to address hydrodynamic properties such as the viscosity of some strongly interacting systems. We also employ the Boltzmann equation for those systems closer to low-energy QCD, and argue that this kind of transport coefficients can be related to phase transitions, in particular the QGP/hadronic phase transition studied in heavy ion collisions.

We use the gauge/gravity correspondence to study the screening of a heavy quark-antiquark pair in various strongly coupled plasmas. Besides super Yang-Mills theory and the corresponding AdS₅ space we also study theories obtained as deformations of AdS₅, among them in particular a class of deformations solving supergravity equations of motion. We consider the dependence of the screening distance on the velocity and the orientation of the pair in the plasma. The value of the screening distance in SYM is found to be a minimum in the class of theories under consideration for all kinematic parameters.

It is shown that the screening of impurities in plasma with Bose-Einstein condensate of electrically charged bosons is drastically different from the usual Debye screening. The polarization operator of photons in plasma becomes infrared singular and the screened potential drops down as a power of distance and even has an oscillating behavior, similar to the Priedel oscillations in plasma with degenerate fermions. The properties of the cosmological plasma with condensed W-bosons are also studied and it is shown that W-bosons condense in ferromagnetic state. The spontaneously generated magnetic fields in such ferromagnetic state may seed the large scale magnetic fields observed in the present-day universe.

In the framework of the quasi-particle picture of diquark, the possibility of describing the baryons as a cluster of the quark and diquark has been explored. Different diquark masses have been estimated and these are used to estimate baryon masses. The results are found to be in reasonable agreement with experimental data. The model has been extended to describe the dibaryon masses such as Λ₆, , etc which are yet to be confirmed.

Gribov viewed the axial anomaly as a manifestation of the collective motion of Dirac fermions with arbitrarily high momenta in the vacuum. In the presence of an external magnetic field and a chirality imbalance, this collective motion becomes directly observable in the form of the electric current – this is the chiral magnetic effect (CME). I give an elementary introduction into the physics of CME, and discuss the experimental status and recent developments.

A reduction of the mass of the η′ (958) meson may signal restoration of the U_A(1) symmetry in a hot and dense hadronic matter, corresponding to the return of the 9th, "prodigal" Goldstone boson. We report on an analysis of a combined PHENIX and STAR data set on the intercept parameter of the two-pion Bose-Einstein correlation functions, as measuremed in collisions at RHIC. To describe this combined PHENIX and STAR dataset, an in-medium η′ mass reduction of at least 200 MeV is needed, at the 99.9% confidence level in a broad model class of resonance abundances.

A 1+3 dimensional solution of relativistic hydrodynamics is analyzed in this paper. Momentum distribution and other observables are calculated from the solution and compared to hadronic measurements from the Relativistic Heavy Ion Collider (RHIC). The solution is compatible with the data, but only the freeze-out point of the evolution is determined. Many equation of states and initial states (initial temperatures) are valid with the same freeze-out distribution, thus the same hadronic observables. The observable that would distinguish between these initial temperatures is momentum distribution of photons, as photons are created throughout the evolution of the fireball created in RHIC collisions. The PHENIX experiment at RHIC measures such data via low invariant mass e⁺e^- pairs. Average temperature from this data is T = 221 ± 23(stat)±18(sys) MeV, while a model calculation with initial temperature T_init = 370 MeV agree with the data.

Some exact and explicit solutions of the relativistic hydrodynamical equations are reviewed in context of high-energy heavy ion physics. Hydrodynamics is a powerful tool to describe the experimentally observed features (e.g. scaling laws) in the final state of high-energy collisions. Hydrodynamical solutions (both exact, analytic and numerical) can then be used to draw consequences on the initial state or the equation of state of the created matter. These findings can help to reach the ultimate goal of heavy-ion physics, the mapping of the phase structure of the strong interaction. In this paper we discuss exact and phenomenologically relevant solutions of hydrodynamics, and hint at some applications of them. We detail one important application: the estimation of the initial energy density from the observed final state.

It is demonstrated that the strong power-like scaling violation in the transverse momentum distribution of inclusive hadron production, observed by the CDF Collaboration in collisions at the Tevatron is caused by the contribution of weak interaction. The contribution of the weak interaction is increasing with energy at high energies.

There is an additional subprocess of hadron production in three quark strings in scattering. Its contribution is proportional to the logarithm of full energy squared so this subprocess is important at very high energies. It leads to a difference in multiplicity distributions in pp and interactions. Due to this effect the inclusive cross sections of scattering are larger than the inclusive cross sections of pp scattering. The difference in inclusive cross sections might be very evident in events with high multiplicities, and it is shown for energy .

Non-extensive thermodynamics is a novel approach in the field of high energy physics. The low and intermediate transverse momentum spectra are extremely well reproduced by a Tsallis–Pareto distribution. However, the derivation of the Tsallis parameter is still an unsolved question. Understanding hadronization processes in heavy-ion collisions requires more detailed tests, especially at high transverse momenta, where we are far from the thermal equilibrium state. Here we focus on parton fragmentation processes at the final state, we analyze whether standard power-law-tailed fragmentation functions do overlap with Tsallis–Pareto energy distributions, reproducing experimental data. Moreover, we investigated a possible QCD evolution of the parameters.

In this work, we study the production of a large-p_T photon in association with a jet in proton-proton collisions. We assess the sensitivity of various photon+jet correlation observables to the photon fragmentation functions, especially the photon-jet angular distribution.

Quantum mechanical and quantum field theoretical approaches to neutrino oscillations are discussed and compared.

The evolution of the entangled muon-neutrino system emerging from charged pion decay is explored both in vacuum and in matter. The study is based on a Weisskopf-Wigner type wave-packet description. Explicit formulae are derived displaying modulation and attenuation of the oscillations due to additional time scales characterising the production process. The case of neutrinos disentangled due to the detection of the muon is also considered.

The leading relativistic (nonrecoil and recoil) corrections to bound state g-factors of particles with an arbitrary spin are discussed. These corrections are universal for any spin and depend only on the free particle gyromagnetic ratios. The physical reasons behind this universality are explained.

Planar supersymmetric Yang–Mills theory appears to be perturbatively integrable. This work reviews integrability in terms of a Yangian algebra and compares the application to the problems of anomalous dimensions and scattering amplitudes.

This note is an attempt to explain in simple words why the famous relation E = mc² misrepresents the essence of Einstein's relativity theory. The note is addressed to high-school teachers, and a part of it – to those university professors who permit themselves to say that the mass of a body increases with its velocity or momentum and thus mislead the teachers and their students.

During the merging process of a binary system made of two neutron stars there should be a phase transition in the star, given that the superfluid is constrained by the crust to corotate on pinning sites. Two things should happen, neither of which is well-studied and that affect both the gravitational wave emission and the approach to the final structure. Even before the actual merger, the two neutron stars (or a neutron star and white dwarf or black hole, taking the former as the model system) have a tidal coupling that strongly affects the rotation. Due to tidal coupling, the interior should spin up, leading to strong glitching and dissipation. This is independent of the equation of state (for the core) but depends strongly on the superfluid and the superconductor state in the crust. So the problem is to look at how this affects the calculations of both the rate and timing of the mergers (the same issue for precession of distorted neutron stars). The same with heating and the magnetic field coupling. All of this is very schematic in the polytropic interior models now used.

The following sections are included:

• Introduction

• One Matrix Model

• The Method of Orthogonal Polynomials

• Evaluation of Z₀ and Z₁

• The Vicinity of the p-Critical Point

• Minimal Gravity

• Comparison of the Matrix Model and Liouville Gravity

• Resonance Transformations

• Finding the Liouville Coordinates

• Comparison of the Matrix Model and Topological Gravity

• Conclusion

• Acknowledgments

• References

We consider the capture of galactic dark matter by the Solar System, due to the gravitational three-body interaction of the Sun, a planet, and a dark matter particle. Closed (up to an overall numerical factor) analytical expression is derived for the capture cross-section. With this result we arrive at simple estimates for density and velocity distribution of captured dark matter particles close to the Earth.

We briefly discuss new models of an 'affine' theory of gravity in multidimensional space-times with symmetric connections. We use and generalize Einstein's proposal to specify the space-time geometry by use of the Hamilton principle to determine the connection coefficients from a geometric Lagrangian that is an arbitrary function of the generalized Ricci curvature tensor and of other fundamental tensors. Such a theory supplements the standard Einstein gravity with dark energy (the cosmological constant, in the first approximation), a neutral massive (or tachyonic) vector field (vecton), and massive (or tachyonic) scalar fields. These fields couple only to gravity and can generate dark matter and/or inflation. The concrete choice of the geometric Lagrangian determines further details of the theory. The most natural geometric models look similar to recently proposed brane models of cosmology usually derived from string theory.

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 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)⊗U(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, α_QUD ≲ 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.

We present selected new results on chiral symmetry breaking in nearly conformal gauge theories with fermions in the fundamental representation of the SU(3) color gauge group. We found chiral symmetry breaking (χSB) for all flavors between N_f = 4 and N_f = 12 with most of the results discussed here for N_f = 4, 8, 12 as we approach the conformai window. To identify χSB we apply several methods which include, within the framework of chiral perturbation theory, the analysis of the Goldstone spectrum in the p-regime and the spectrum of the fermion Dirac operator with eigenvalue distributions of random matrix theory in the ∈-regime. Chiral condensate enhancement is observed with increasing N_f when the electroweak symmetry breaking scale F is held fixed in technicolor language. Important finite-volume consistency checks from the theoretical understanding of the SU(N_f) rotator spectrum of the δ-regime are discussed. We also consider these gauge theories at N_f = 16 inside the conformal window.

We study the kinetics of chiral transitions in quark matter using a microscopic framework (Nambu-Jona-Lasinio model) and a phenomenological model (Ginzburg-Landau free energy). We focus on the coarsening dynamics subsequent to a quench from the massless quark phase to the massive quark phase. The morphology of the ordering system is characterized by the scaling of the order-parameter correlation function. The domain growth process obeys the Allen-Cahn growth law, L(t) ~ t^1/2. We also study the growth of bubbles of the stable massive phase from the metastable massless phase.

The progress on calorons (finite temperature instantons) is sketched. In particular there is some interest for confining temperatures, where the holonomy (the asymptotic value of the Polyakov loop) is non-trivial. In the last section I give more recent results by others.

Anomalous quark triangles with one axial and two vector currents are studied in special kinematics when one of the vector currents carries a soft momentum. According to the Adler-Bardeen theorem the anomalous longitudinal part of the triangle is not renormalized in the chiral limit. We show that perturbative corrections the transversal part of the triangle is also absent. This nonrenormalization, in difference with the longitudinal part, holds on only perturbatively.

The nature of the actual presentation that I gave in the "Concluding remarks" slot of the Gribov–80 Workshop does not make it suitable to be included into Proceedings. So, I use this opportunity to present you another essential part of the Gribov Memorial: his lectures on Strong Interactions of Hadrons at High Energies.

The following sections are included:

• LIST OF PARTICIPANTS AND CONTRIBUTORS