At The Frontier of Particle Physics

The following sections are included:

• FOREWORD

• NOTE FROM THE EDITOR

• CONTENTS

• General acknowledgments

• List of participants

The goal of this book is two-fold. First it was designed to present the full picture of the progress achieved in analytic quantum chromodynamics in the 1990's. QCD is the theory of hadrons which will stay with us forever, no matter what, unlike many recent theories whose relevance to Nature is still a big question mark. Every novel result in QCD, every new insight, has a special weight—it reflects our deepening understanding of the structure of matter…

I am honored to present Boris Lazarevich Ioffe to the readers of the Ioffe Festschrift, which is being published on the occasion of his 75-th birthday.

First, some basic biographical data. Boris Ioffe was born in Moscow on July 6, 1926, into a Jewish family. His father was a famous medical doctor, a urologist, and his mother was a librarian. During the second World War, Ioffe's father was the head of a large military hospital, and for some time, Boris worked in a hospital too…

It is difficult to imagine that Boris Lazarevich is turning 75 years old. He who is working actively and successfully in theoretical physics (which is well-known to be a science for mainly young people); he who is not only deeply interested in everything around him, but also participates actively in events; he who was only recently ascending Everest; he who was fighting severe illnesses bravely and has overcome them one by one.

The following sections are included:

• Pages of the Past

• On the history of the Soviet hydrogen bomb

• People and “the problem”

• Nuclear reactors: physics versus politics

The following sections are included:

• List of Names

• Abbreviations

• Geographical Names

It happened that our careers in physics – that of Boris Lazarevich Ioffe and mine – started almost simultaneously at the Institute of Theoretical and Experimental Physics (ITEP) in Moscow. Half a century later, my memories of this time are still vivid, and I'd like to share them with the readers of the Ioffe Festschrift…

I present comments on the history of the Yang-Mills field theory, with the emphasis on the covariant quantization worked out in 1966.

The following sections are included:

• Introduction

• The Theoretical Scene
  • Quantum field theory
  • The bootstrap
  • Symmetries
  • Experiment

• My Road to Asymptotic Freedom
  • From N/D to QCD
  • How to explain scaling?
  • The plan
  • The Discovery of asymptotic freedom

• Non-Abelian Gauge Theories of the Strong Interactions

• The Emergence and Acceptance of QCD

• Other Implications of Asymptotic Freedom
  • Consistency of quantum field theory
  • Unification

• References

Professor Juan José Giambiagi and I started working on divergent diagrams in different number of dimensions in 1970. We had a certain idea about the behavior in odd or even number of dimensions, but the most important factor in our work, I think, was the previous experience with an analytical regularization method. We had developed it a few years before. Within this method the amplitudes turned out to be analytic functions of the regularizing parameter, with poles at the physical value of that parameter…

Asymptotic freedom as the basic property of QCD was discovered by Gross, Wilczek, and Politzer in 1973. Personal recollections of David Gross which are being published in this Volume vividly describe the historical background and the chain of events which led to this fundamental breakthrough. Unfortunately, I failed to obtain Politzer's side of the story. Some details can be found in an interview which Prof. Politzer gave to R. Crease and C. Mann on February 21, 1985. Below I acquaint the reader with the pre-1973 appearances of asymptotic freedom which, unfortunately, were not recognized.

The study of nuclei predates by many years the theory of quantum chromodynamics. More recently, effective field theories have been used in nuclear physics to “cross the border” from QCD to a nuclear theory. We are now entering the second decade of efforts to develop a perturbative theory of nuclear interactions using effective field theory. This chapter describes the current status of these efforts.

The effective field theory relevant for the analysis of QCD at low energies is reviewed. The foundations of the method are discussed in some detail and a few illustrative examples are described.

We give a pedagogical review of implications of chiral symmetry in QCD. First, we briefly discuss classical textbook subjects such as the axial anomaly, spontaneous breaking of the flavor-nonsinglet chiral symmetry, formation of light pseudo-Goldstone particles, and their effective interactions. Then we proceed to other issues. We explain in some detail a recent discovery how to circumvent the Nielsen–Ninomiya's theorem and implement chirally symmetric fermions on the lattice. We touch upon such classical issues as the Vafa-Witten's theorem and 't Hooft's anomaly matching conditions. We derive a set of exact theorems concerning the dynamics of the theory in a finite Euclidean volume and the behavior of the Dirac spectral density. Finally, we discuss an imaginary world with a nonzero value of the vacuum angle θ.

In the limit of large number of colors N_c the nucleon consisting of N_c quarks is heavy, and one can treat it semiclassically, like the large-Z Thomas–Fermi atom. The role of the semiclassical field binding the quarks in the nucleon is played by the pion or chiral field; its saddle-point distribution inside the nucleon is called the chiral soliton. The old Skyrme model for this soliton is an over-simplification. One can do far better by exploiting a realistic and theoretically-motivated effective chiral lagrangian presented in this paper. As a result one gets not only the static characteristics of the nucleon in a fair accordance with the experiment (such as masses, magnetic moments and formfactors) but also much more detailed dynamic characteristics like numerous parton distributions. We review the foundations of the Chiral Quark-Soliton Model of the nucleon as well as its recent applications to parton distributions, including the recently introduced ‘skewed’ distributions, and to the nucleon wave function on the light cone.

I review the consequences of the chiral symmetry of QCD for the structure and dynamics of the low—lying baryons, with particular emphasis on the nucleon.

The properties of QCD hadrons are studied using an expansion in 1/N, where N is the number of colors. Meson properties are computed in this approach, and compared with experiment. The consequences of the large-N spin-flavor symmetry for baryons is developed in detail. The 1/N expansion is used to derive many features of the quark model of hadrons. The implications of the 1/N expansion for chiral perturbation theory is discussed.

In the following we briefly review exact QCD inequalities as derived from considerations of two-point correlators of color-singlet currents. We then apply these inequalities to a variety of fundamental issues such as the (non)breaking of (axial-vector) global symmetries. We also briefly discuss inequalities for n-point functions with n > 2 and for scattering, as well as try and understand/extend some of the inequalities by developing some intuition based on a Hamiltonian variational approach

Basic properties of Regge poles are reviewed. The Regge poles are considered from both t-channel and s-channel points of view. The main part of the review is devoted to the Regge poles in QCD. The method of the Wilson-loop path integral is used to calculate trajectories of the Regge poles for and gluonic states. The problem of the pomeron in QCD is discussed in detail. It is shown how to use the 1/N expansion for classification of the reggeon diagrams in QCD. The role of Regge cuts in reggeon theory is discussed and their importance for high-energy phenomenology is emphasized. Models based on the reggeon calculus, 1/N expansion in QCD, and string picture of interactions at large distances are reviewed and applied to a broad class of phenomena in strong interactions. It is shown how to apply the reggeon approach to small-x physics in deep inelastic scattering.

I describe why the small x problem is important for understanding QCD, and and speculations on how me might understand it.

I comment on possible relations of Gribov's ideas on mechanism of confinement with some phenomena in QCD and in supersymmetric gauge theories.

The following sections are included:

• APPENDIX Ioffe's Publications and Ph.D. Students

We will review our understanding of non-abelian gauge theories in finite physical volumes. It allows one in a reliable way to trace some of the non-perturbative dynamics. The role of gauge fixing ambiguities related to large field fluctuations is an important lesson that can be learned. The hamiltonian formalism is the main tool, partly because semiclassical techniques are simply inadequate once the coupling becomes strong. Using periodic boundary conditions, continuum results can be compared to those on the lattice. Results in a spherical finite volume will be discussed as well.

The subject of our investigations is QCD formulated in terms of physical degrees of freedom. Starting from the Faddeev-Popov procedure, the canonical formulation of QCD is derived for static gauges. Particular emphasis is put on obstructions occurring when implementing gauge conditions and on the concomitant emergence of compact variables and singular fields. A detailed analysis of nonperturbative dynamics associated with such exceptional field configurations within the Coulomb and axial gauges is described. We present evidence that compact variables generate confinement-like phenomena in both gauges and point out the deficiencies in achieving a satisfactory nonperturbative treatment concerning all variables. Gauge fixed formulations are shown to constitute also a useful framework for phenomenological studies. Phenomenological insights into the dynamics of Polyakov loops and monopoles in confined and deconfined phases are presented within axial gauge QCD.

The review starts with a few puzzles related to the scales at which the perturbative description should be replaced by a non-perturbative one. A number of various examples are considered, leading to different scales and eventually related to instantons (or confinement) effects. Then we discuss the QCD vacuum as an instanton liquid, and show that statistical models based on this picture work surprisingly well and quantitatively explain many properties of hadrons. Then we proceed to a wider range of questions, related to the phase diagram of QCD, at finite temperature and density, emphasizing recent progress in color superconductivity. Finally, we discuss a few recent application of instanton-induced effects in high energy processes.

This review consists of two parts: an introductory exposition of the foundation of perturbative QCD, which underpins the universally used QCD parton picture of high energy interactions; and a survey of recent progress on the parton structure of the nucleon – through global QCD analysis of a full range of hard scattering processes, using all available theoretical tools and experimental measurements. The three key features of perturbative QCD – asymptotic freedom, infrared safety, and factorization – are discussed in detail and highlighted by many illustrations. The review of global QCD analysis emphasizes the non-trivial underlying issues, current uncertainties, and the challenges which await due to the demands of precision standard model studies and new physics searches in the next generation of experiments.

Multiloop QCD corrections to the evolution of the QCD coupling consteint and quark masses are briefly reviewed.

We review progress that has been made over the last decade in calculating and understanding the structure of multi-leg amplitudes in QCD. Applications to QCD, gravity and their supersymmetric counterparts are reviewed. For special cases it is possible to obtain exact tree and one-loop n-parton scattering amplitudes. We also discuss the surprisingly close relationship of QCD amplitudes to those of Einstein gravity, pointing towards a much deeper relationship between the two theories than is apparent in their respective Lagrangians.

Applications of perturbative QCD to deeply virtual Compton scattering and hard exclusive electroproduction processes require a generalization of the usual parton distributions for the case when long-distance information is accumulated in non-diagonal matrix elements of quark and gluon light-cone operators. I describe two types of nonperturbative functions parametrizing such matrix elements: double distributions and skewed parton distributions. I discuss their general properties, relation to the usual parton densities and form factors, evolution equations for both types of generalized parton distributions (GPD), models for GPDs and their applications in virtual and real Compton scattering.

We review the perturbative approach to multiparticle production in hard collision processes. It is investigated to what extent parton level analytical calculations at low momentum cut-off can reproduce experimental data on the hadronic final state. Systematic results are available for various observables with the next-to-leading logarithmic accuracy (the so-called modified leading logarithmic approximation – MLLA). We introduce the analytical formalism and then discuss recent applications concerning multiplicities, inclusive spectra, correlations and angular flows in multijet events. In various cases the perturbative picture is surprisingly successful, even for very soft particle production.

We describe some aspects of soft high energy scattering in a space-time picture. A treatment based on path integrals is presented, it leads naturally to a separation of the scattering amplitude into an amplitude describing the scattering of quark-antiquark pairs and transverse densities of hadrons or photons. Several models are presented and compared, we especially discuss a nonperturbative model which relates high energy scattering with vacuum properties. Some typical results of the model calculation are compared with experimental data.

At high energies the particles move very fast so their trajectories can be approximated by straight lines collinear to their velocities. The proper degrees of freedom for the fast gluons moving along the straight lines are the Wilson-line operators – infinite gauge factors ordered along the straight line. I review the study of the high-energy scattering in terms of Wilson-line degrees of freedom.

Exclusive processes provide a window into the bound state structure of hadrons in QCD as well as the fundamental processes which control hadron dynamics at the amplitude level. The natural calculus for describing bound state structure of relativistic composite systems needed for describing exclusive amplitudes is the light-cone Fock expansion which encodes the multi-quark, gluonic, and color correlations of a hadron in terms of frame-independent wavefunctions. In hard exclusive processes in which hadrons receive a large momentum transfer, perturbative QCD leads to factorization theorems which separate the physics of bound state structure from that of the relevant quark and gluonic hard-scattering reactions which underlie these reactions. At leading twist, the bound state physics is encoded in terms of universal “distribution amplitudes,” the fundamental theoretical quantities which describe the valence quark substructure of hadrons as well as nuclei. The combination of discretized light-cone quantization and transverse lattice methods are now providing nonperturbative predictions for the pion distribution amplitude. A basic feature of the gauge theory formalism is “color transparency,” the absence of initial and final state interactions of rapidly-moving compact color-singlet states. Other applications of the factorization formalism are briefly discussed, including semileptonic B decays, deeply virtual Compton scattering, and dynamical higher twist effects in inclusive reactions. A new type of jet production reaction, “selfresolving diffractive interactions” provide empirical constraints on the light-cone wavefunctions of hadrons in terms of their quark and gluon degrees of freedom as well as the composition of nuclei in terms of their nucleon and mesonic degrees of freedom.

I review the notion of the quark-hadron duality from the modern perspective. Both, the theoretical foundation and practical applications are discussed. The proper theoretical framework in which the problem can be formulated and treated is Wilson's operator product expansion (OPE). Two models developed for the description of duality violations are considered in some detail: one is instanton-based, another resonance-based. The mechanisms they represent are complementary. Although both models are rather primitive (their largest virtue is their simplicity) they hopefully capture important features of the phenomenon. Being open for improvements, they can be used “as is” for orientation in the studies of duality violations in the processes of practical interest.

An introduction to the method of QCD sum rules is given for those who want to learn how to use this method. Furthermore, we discuss various applications of sum rules, from the determination of quark masses to the calculation of hadronic form factors and structure functions. Finally, we explain the idea of the light-cone sum rules and outline the recent development of this approach.

Achievements in the heavy quark theory over the last decade are reviewed, with the main emphasis put on dynamical methods which quantify nonperturbative effects via application of the Operator Product Expansion. These include the total weak decay rates of heavy flavor hadrons and nonperturbative corrections to heavy quark sum rules. Two new exact superconvergent sum rules are derived; they differ from the known ones in that they are finite and normalization point independent in perturbation theory. A new hadronic parameter is introduced which is a spinnonsinglet analogue of it is expected to be about 0.25 GeV. The first sum rule implies the bound ϱ² > 3/4 for the slope of the Isgur-Wise function. The heavy quark potential is discussed and along with its connection to the infrared contributions in the heavy quark mass. I address, among other applications, the determination of |V_cb| from the total semileptonic rate and from the B → D* zero recoil rate, as well as extracting |V_ub| from Γ_sl(b → u). Practical aspects of local quark-hadron duality are briefly discussed.

We review some aspects of weak decays of hadrons containing one heavy quark. The main emphasis is on B physics, in particular in the framework of the Heavy Quark Effective Theory.

Even for short-distance dominated observables the QCD perturbation expansion is never complete. The divergence of the expansion through infrared renormalons provides formal evidence of this fact. In this article we review how this apparent failure can be turned into a useful tool to investigate power corrections to hard processes in QCD.

In this review I explain the idea how one could understand confinement by studying the low-energy effective dynamics of non-Abelian gauge theories. I argue that under some mild assumptions, the low-energy dynamics is determined universally by the spontaneous breaking of the magnetic symmetry introduced by 't Hooft more than 20 years ago. The degrees of freedom in the effective theory are magnetic vortices. Their role in confining dynamics is similar to that played by pions and σ in the chiral symmetry breaking dynamics. I give an explicit derivation of the effective theory in (2+1)-dimensional weakly coupled confining models and argue that it remains qualitatively the same in strongly coupled (2+1)-dimensional gluodynamics. Confinement in this effective theory is a very simple classical statement about the long range interaction between topological solitons, which follows (by virtue of a simple direct classical calculation) from the structure of the effective Lagrangian. I discuss elements of this picture which generalize to 3+1 dimensions and point out remaining open questions.

The confinement scenario in N = 2 supersymmetric gauge theory at the monopole point is reviewed. Basic features of this U(1) confinement are contrasted with those we expect in QCD. In particular, extra states in the hadron spectrum and non-linear Regge trajectories are discussed. Then another confinement scenario arising on Higgs branches of the theory with fundamental matter is also reviewed. Peculiar properties of the Abrikosov–Nielsen–Olesen flux tubes on the Higgs branch lead to a new confining regime with the logarithmic suppression of the linear rising potential. Motivations for a search for tensionless strings (flux tubes) are proposed.

Supersymmetric gauge theories have had a significant impact on our understanding of QCD and of field theory in general. The phases of supersymmetric QCD (SQCD) are discussed, and the possibility of similar phases in non-supersymmetric QCD is emphasized. It is described how duality in SQCD links many previously known duality transformations that were thought to be distinct, including OliveMontonen duality of supersymmetric gauge theory and quark-hadron duality in (S)QCD. A connection between Olive-Montonen duality and the confining strings of Yang-Mills theory is explained, in which a picture of confinement via nonabelian monopole condensation — a generalized dual Meissner effect — emerges explicitly. Similarities between supersymmetric and ordinary QCD are discussed, as is a non-supersymmetric QCD-like “orbifold” of Yang-Mills theory. I briefly discuss the recent discovery that gauge theories and string theories are more deeply connected than ever previously realized. Specific questions for lattice gauge theorists to consider are raised in the context of the first two topics.

The Euclidean action of non-Abelian gauge theories with adjoint dynamical charges (gluons or gluinos) at non-zero temperature T is invariant against topologically non-trivial gauge transformations in the Z(N)_c center of the SU(N) gauge group. The Polyakov loop measures the free energy of fundamental static charges (infinitely heavy test quarks) and is an order parameter for the spontaneous break-down of the center symmetry. In SU(N) Yang-Mills theory the Z(N)_c symmetry is unbroken in the low-temperature confined phase and spontaneously broken in the high-temperature deconfined phase. In 4-dimensional SU(2) Yang-Mills theory the deconfinement phase transition is of second order and is in the universality class of the 3-dimensional Ising model. In the SU(3) theory, on the other hand, the transition is first order and its bulk physics is not universal. When a chemical potential μ is used to generate a non-zero baryon density of test quarks, the first order deconfinement transition line extends into the (μ, T)-plane. It terminates at a critical endpoint which also is in the universality class of the 3-dimensional Ising model. At a first order phase transition the confined and deconfined phases coexist and are separated by confined-deconfined interfaces. Similarly, the three distinct high-temperature phases of SU(3) Yang-Mills theory are separated by deconfined-deconfined domain walls. As one approaches the deconfinement phase transition from the high-temperature side, a deconfined-deconfined domain wall splits into a pair of confined-deconfined interfaces and becomes completely wet by the confined phase. Complete wetting is a universal interface phenomenon that arises despite the fact that the bulk physics is non-universal. In supersymmetric SU(3) Yang-Mills theory, a Z(3)_χ chiral symmetry is spontaneously broken in the confined phase and restored in the deconfined phase. As one approaches the deconfinement phase transition from the low-temperature side, a confined-confined domain wall splits into a pair of confined-deconfined interfaces and thus becomes completely wet by the deconfined phase. This allows a confining string to end on a confined-confined domain wall as first suggested by Witten based on M-theory. Deconfined gluons and static test quarks are sensitive to spatial boundary conditions. For example, on a periodic torus the Gauss law forbids the existence of a single static quark. On the other hand, on a C-periodic torus (which is periodic up to charge conjugation) a single static quark can exist. As a paradoxical consequence of the presence of deconfined-deconfined domain walls, in very long C-periodic cylinders quarks are “confined” even in the deconfined phase.

In certain 1 + 1 dimensional field theoretic toy models, one can go all the way from microscopic quarks via the hadron spectrum to the properties of hot and dense baryonic matter in an essentially analytic way. This “miracle” is illustrated through case studies of two popular large N models, the Gross-Neveu and the 't Hooft model — caricatures ofthe Nambu—Jona-Lasinio model and real QCD, respectively. The main emphasis will be on aspects related to spontaneous symmetry breaking (discrete or continuous chiral symmetry, translational invariance) and confinement.

We give a brief review of modern theoretical understanding of physics of QCD at finite temperature and density. We concentrate on discussing “hot” systems with zero baryon number density. We consider, first, lukewarm pion gas and, in particular, dwell on kinetic properties of hadron collective excitations. Next, we discuss physics of the chiral restoration phase transition and confront theoretical expectations with available lattice data and with perspective heavy-ion experiments. We proceed then to the high-temperature QCD phase, the quark-gluon plasma. We notice that the temperatures one can expect to reach at the heavy-ion collider at RHIC are not yet high enough for perturbation theory in the QCD coupling constant to work well. Lastly, we discuss systems with nonzero baryon number density. We argue that, though the phase transition in temperature is probably absent, it can appear with vengeance when finite density effects are taken into account. An interesting color superconductivity phase is expected to show up at large densities.

Important progress in understanding the behavior of hadronic matter at high density has been achieved recently, by adapting the techniques of condensed matter theory. At asymptotic densities, the combination of asymptotic freedom and BCS theory make a rigorous analysis possible. New phases of matter with remarkable properties are predicted. They provide a theoretical laboratory within which chiral symmetry breaking and confinement can be studied at weak coupling. They may also playa role in the description of neutron star interiors. We discuss the phase diagram of QCD as a function of temperature and density, and close with a look at possible astrophysical signatures.