Continuous Advances in QCD 2002

The following sections are included:

• FOREWORD

• CONTENTS

This talk contains a short overview of the history of the interplay of the weak and the strong interaction and CP-violation. It describes the phenomenology and the basic physics mechanisms involved in the Standard Model calculations of K → ππ decays with an emphasis on the evaluation of Penguin operator matrix-elements.

The Standard Model prediction for the magnetic moment of the muon requires a determination of the electromagnetic form factor of the pion at high precision. It is shown that the recent progress in ππ scattering allows us to obtain an accurate representation of this form factor on the basis of the data on e⁺e^- → π⁺π^-. The same method also applies to the form factor of the weak vector current, where the data on the decay τ → π^-π⁰ν_τ are relevant. Unfortunately, however, the known sources of isospin breaking do not explain the difference between the two results. The discrepancy implies that the Standard Model prediction for the magnetic moment of the muon is currently subject to a large uncertainty.

In spite of very general title, this is not a mini-review on instantons, but a sum of two unrelated new developments. The first deals with the pion and nucleon formfactors which were found to be calculable in a simple single-instanton approximation. The second is summary of several recent papers on production of the topological sphaleron-type gluomagnetic clusters in high energy reactions, which clarified their properties and production cross section. The paper ends with some estimates claiming that the latter process can be important for heavy ion collisions at RHIC energies.

QCD sum rules are overviewed with an emphasize on the practical applications of this method to the physics of light and heavy hadrons.

The large asymmetry between the cross sections for charm hadrons and their antiparticles in charm hadroproduction is referred to as the leading particle effect. Heavy quark recombination is a new mechanism for heavy hadron production that generates charm asymmetries by a hard-scattering parton process. Using this mechanism, the E791 data on the D^- - D⁺ asymmetry in π^- N collisions can be fit reasonably well by adjusting a single multiplicative nonperturbative constant.

The lifetime splitting between the B⁺ and mesons has recently been calculated in the next-to-leading order of QCD. These corrections are necessary for a reliable theoretical prediction, in particular for the meaningful use of hadronic matrix elements computed with lattice QCD. Using results from quenched lattice QCD we find , where the uncertainties from unquenching and 1/m_b, corrections are not included. The lifetime difference of heavy baryons and is also discussed.

The Standard Model contribution to mixing is dominated by the contributions of light s and d quarks. Neglecting the tiny effects due to b quark, both mass and lifetime differences vanish in the limit of SU(3)_F symmetry. Thus, the main challenge in the Standard Model calculation of the mass and width difference in the system is to estimate the size of SU(3) breaking effects. We prove that D meson mixing occurs in the Standard Model only at second order in SU(3) violation. We consider the possibility that phase space effects may be the dominant source of SU(3) breaking. We find that y = (ΔΓ)/(2Γ) of the order of one percent is natural in the Standard Model, potentially reducing the sensitivity to new physics of measurements of D meson mixing. We also discuss the possibility of observing lifetime differences and CP violation in charmed mesons both at the currently operating and proposed facilities.

Power corrections to differential cross sections near a kinematic threshold are analysed by Dressed Gluon Exponentiation. Exploiting the factorization property of soft and collinear radiation, the dominant radiative corrections in the threshold region are resummed, yielding a renormalization-scale-invariant expression for the Sudakov exponent. The interplay between Sudakov logs and renormalons is clarified, and the necessity to resum the latter whenever power corrections are non-negligible is emphasized. The presence of power-suppressed ambiguities in the exponentiation kernel suggests that power corrections exponentiate as well. This leads to a non-perturbative factorization formula with non-trivial predictions on the structure of power corrections, which can be contrasted with the OPE. Two examples are discussed. The first is event-shape distributions in the two-jet region, where a wealth of precise data provides a strong motivation for the improved perturbative technique and an ideal situation to study hadronization. The second example is deep inelastic structure functions. In contrast to event shapes, structure functions have an OPE. However, since the OPE breaks down at large x, it does not provide a practical framework for the parametrization of power corrections. Performing a detailed analysis of twist 4 it is shown precisely how the twist-2 renormalon ambiguity eventually cancels out. This analysis provides a physical picture which substantiates the non-perturbative factorization conjecture.

Effective theories based on experimental data provide powerful probes and tests of underlying theories in elementary particle physics. Examples within and beyond the Standard Model are discussed, including a specific model for supersymmetry breaking within the context of the weakly coupled heterotic string.

The past leaves the surprising experimental successes of the simple constituent quark model to be expained by QCD. The future opens the way to new insight into QCD from heavy flavor experiments

For an unpolarized target, the generalized parton distribution H_q(x,0,t) is related to the distribution of partons in impact parameter space. The transverse distortion of this distribution for a transversely polarized target is described by E_q(x,0,t).

There are two sources of the factorial large-order behavior of a typical perturbative series. First, the number of the different Feynman diagrams may be large; second, there are abnormally large diagrams known as renormalons. It is well known that the large combinatorial number of diagrams is described by instanton-type solutions of the classical equations. We demonstrate that from the functional-integral viewpoint the renormalons do not correspond to a particular configuration but manifest themselves as dilatation modes in the functional space.

QCD in a strong magnetic field yields an example of a rich, sophisticated and controllable dynamics.

We review recent advances in the light-front quantization of gluodynamics. A definition is given to the DLCQ Hamiltonian for SU(2) gludynamics. In particular, it is explained that a global contribution to the Wilson loop along the compactified light-like direction features this Hamiltonian as a degree of freedom.

In many gauge theories at different values of parameters entering Lagrangian, the vacuum is dominated by coherent condensates of different mutually non-local fields (for instance, by condensates of electric or magnetic charges, or by various dyons). It is argued that the transition between these "dual to each other" phases proceeds through an intermediate "mixed phase", having qualitatively different features. The examples considered include: ordinary YM, N = 1 SYM, N = 1 SQCD, and broken N = 2 SYM and SQCD.

A generalization of the operator product expansion for Euclidean correlators of gauge invariant QCD currents is presented. Each contribution to the modified expansion, which is based on a delocalized multipole expansion of a perturbatively determined coefficient function, sums up an infinite series of local operators. On a more formal level the delocalized operator expansion corresponds to an optimal choice of basis sets in the dual spaces which are associated with the interplay of perturbative and nonperturbative N-point correlations in a distorted vacuum. A consequence of the delocalized expansion is the running of condensates with the external momentum. Phenomenological evidence is gathered that the gluon condensate, often being the leading nonperturbative parameter in the OPE, is indeed a function of resolution. Within a model calculation of the nonperturbative corrections to the ground state energy of a heavy quarkonium system it is shown exemplarily that the convergence properties are better than those of the OPE. Potential applications of the delocalized operator expansion in view of estimates of the violation of local quark-hadron duality are discussed.

I discuss why QCD is our most perfect physical theory and visit a few of its current frontiers. Finally I draw some appropriate conclusions.

We show that QCD Dirac spectra well below Λ_QCD, both at zero and at nonzero chemical potential, can be obtained from a chiral Lagrangian. At nonzero chemical potential Goldstone bosons with nonzero baryon number condense beyond a critical value. Such superfluid phase transition is likely to occur in any system with a chemical potential with the quantum numbers of the Goldstone bosons. We discuss the phase diagram for one such system, QCD with two colors, and show the existence of a tricritical point in an effective potential approach.

The thermal conductivity of the color-flavor locked phase of dense quark matter is calculated. The dominant contribution to the conductivity comes from photons and Nambu-Goldstone bosons associated with the breaking of baryon number, both of which are trapped in the quark core. Because of their very large mean free path the conductivity is also very large. The cooling of the quark core arises mostly from the heat flux across the surface of direct contact with the nuclear matter. As the thermal conductivity of the neighboring layer is also high, the whole interior of the star should be nearly isothermal. Our results imply that the cooling time of compact stars with color-flavor locked quark cores is similar to that of ordinary neutron stars.

Using flow equations, we derive an effective quark-quark interaction and obtain the coupled set of gap equations for the condensates of the CFL phase of massless N_f = 3 dense QCD. We find two different sources of the infrared cutoff in magnetic interaction. When the penetration depth of the magnetic field inside the superconductor is less than the coherence length of quark-quark bound state, our results for the gap agree with those of Son ⁴. In the other case, we obtain parametric enhancement of the gap on the coupling constant.

I discuss several types of domain walls and global strings which occur in colour superconducting quark matter due to the spontaneous violation of relevant U(1) and discrete symmetries. These include the baryon U(1)_B, approximate axial U(1)_A symmetries as well as an approximate U(1)_Y symmetry arising from kaon condensation in colour-flavour locking phase. In this talk I concentrate on discussions of K strings due to their interesting internal structures. Specifically, I demonstrate that under some conditions the global U(1)_Y symmetry may not be restored inside the string, in contrast with the standard expectations. Instead, K⁺ condensation occurs inside the core of the string if a relevant parameter is larger than some critical value θ_K⁰ ≥ θ_crit. If this phenomenon happens, the U(1)_Y strings become superconducting and may considerably influence the magnetic properties of dense quark matter, in particular in neutron stars.

(2+1)-dimensional Georgi-Glashow model and its SU(N)-generalization are explored at nonzero temperatures and in the regime when the Higgs boson is not infinitely heavy. The finiteness of the Higgs-boson mass leads to various novel effects. Those include the appearance of two separate phase transitions and of the upper bound on the parameter of the weak-coupling approximation, necessary to maintain the stochasticity of the Higgs vacuum. The modification of the finite-temperature behavior of the model emerging due to the introduction of massless quarks is also discussed.

Many supersymmetric theories which possess BPS states exhibit co-dimension one curves of marginal stability (CMS) in parameter or moduli space across which the BPS spectrum changes discontinuously. It follows that to obtain a global picture of the spectrum we require control over aspects of the near-CMS dynamics. Fortunately, the questions of interest concerning the spectrum simplify in this regime to tractable problems in nonrelativistic quantum mechanics. In this talk, we review the features of this system focusing on the interaction potential between BPS states and the delocalization mechanism via which states are removed from the spectrum. We discuss two examples in detail; kink states in theories in D = 2, and dyonic states in theories in D = 4.

Three closely related issues will be discussed. Magnetic quarks having non-Abelian charges have been found recently to appear as the dominant infrared degrees of freedom in some vacua of softly broken supersymmetric QCD with SU(n_c) gauge group. Their condensation upon perturbation causes confinement and dynamical symmetry breaking. We argue that these magnetic quarks can be naturally related to the semiclassical non-Abelian monopoles of the type first discussed by Goddard, Nuyts, Olive and E. Weinberg. We discuss also general properties of non-Abelian vortices and discuss their relevance to the confinement in QCD. Finally, calculation by Douglas and Shenker of the tension ratios for vortices of different N-alities in the softly broken supersymmetric SU(N) Yang-Mills theory, is carried to the second order in the adjoint multiplet mass. A correction to the ratios violating the sine formula is found, showing that the latter is not a universal quantity.

I describe the framework my collaborators and I have developed for the study of one-loop quantum corrections to extended field configurations in renormalizable quantum field theories. I then present a few of the applications of these methods to problems ranging from quantum stabilization of solitons to the "classic" Casimir effect.

The Seiberg-Witten map for noncommutative Yang-Mills theories is studied and methods for its explicit construction are discussed which are valid for any gauge group. In particular the use of the evolution equation is described in some detail and its relation to the cohomological approach is elucidated. Cohomological methods which are applicable to gauge theories requiring the Batalin-Vilkoviskii antifield formalism are briefly mentioned. Also, the analogy of the Weyl-Moyal star product with the star product of open bosonic string field theory and possible ramifications of this analogy are briefly mentioned.

In the present review we show that renormalizations in a softly broken SUSY gauge theory are not independent but directly follow from those of an unbroken or rigid theory. This is a consequence of a treatment of a softly broken theory as a rigid one in external spurion superfield. This enables one to get the singular part of effective action in a broken theory from a rigid one by a simple modification of the couplings. Substituting the modified couplings into renormalization constants, RG equations, solutions to these equations, approximate solutions, fixed points, etc., one can get corresponding relations for the soft terms by a simple Taylor expansion over the Grassmannian variables. Some examples including the MSSM in low and high tan β regime, SUSY GUTs and the N=2 Seiberg-Witten model are considered.

We notice that the renormalization of the effective charge in a 4–dimensional (supersymmetric) gauge theory is determined by the same graphs and is rigidly connected to the renormalization of the metric on the moduli space of the classical vacua of the corresponding reduced quantum mechanical system. Supersymmetry provides constraints for possible modifications of the metric, and this might give an alternative simple proof of nonrenormalization theorems for the original 4-dimensional theory.

Recent work on the numerical solution of supersymmetric gauge theories is described. The method used is SDLCQ (supersymmetric discrete light-cone quantization). An application to N = 1 supersymmetric Yang–Mills theory in 2+1 dimensions at large N_c is summarized. The addition of a Chern–Simons term is also discussed.

Wilson loops in the context of AdS/CFT correspondence are reviewed with emphasis on Wilson loops protected or partially protected by supersymmetry.

On the occasion of this ArkadyFest, celebrating Arkady Vainshtein's 60^th birthday, I review some selected aspects of the connection between perturbative and nonperturbative physics, a subject to which Arkady has made many important contributions. I first review this connection in quantum mechanics, which was the subject of Arkady's very first paper. Then I discuss this issue in relation to effective actions in field theory, which also touches on Arkady's work on operator product expansions. Finally, I conclude with a discussion of a special quantum mechanical system, a quasi-exactly solvable model with energy-reflection duality, which exhibits an explicit duality between the perturbative and nonperturbative sectors, without invoking supersymmetry.

I give a pedagogical and historical introduction to axion physics, and briefly review the present status of axions in our understanding of particle physics and cosmology.

A deeper understanding of the vacuum structure in QCD invites one to rethink certain aspects of the axion physics. The recent advances are mostly due to developments in supersymmetric gauge theories and the brane theory, in which QCD can be embedded. They include, but are not limited to, the studies of metastable vacua in multicolor gluodynamics, and the domain walls. We briefly review basics of the axion physics and then present a modern perspective on a rich interplay between the QCD vacuum structure and axion physics.

We review a solution (Ref. 1) of the cosmological constant problem in a brane-world model with infinite-volume extra dimensions. The solution is based on a nonlinear generally covariant theory of a metastable graviton that leads to a large-distance modification of gravity. ¿From the extra-dimensional standpoint the problem is solved due to the fact that the four-dimensional vacuum energy curves mostly the extra space. The four-dimensional curvature is small, being inversely proportional to a positive power of the vacuum energy. The effects of infinite-volume extra dimensions are seen by a brane-world observer as nonlocal operators. ¿From the four-dimensional perspective the problem is solved because the zero-mode graviton is extremely weakly coupled to localized four-dimensional sources. The observable gravity is mediated not by zero mode but, instead, by a metastable graviton with a lifetime of the order of the present-day Hubble scale. Therefore, laws of gravity are modified in the infrared above the Hubble scale. Large wave-length sources, such as the vacuum energy, feel only the zero-mode interaction and, as a result, curve space very mildly. Shorter wave-length sources interact predominantly via exchange of the metastable graviton. Because of this, all standard properties of early cosmology, including inflation, are intact.

Particle physics arguments suggest that the H -dibaryon – a state consisting of two u, two d, and two s quarks – may have a mass ≈ 1.5 ± 0.2 MeV, and that r_H ≲ ¼ r_N. Remarkably, the observed stability of nuclei and other experimental limits not exclude this scenario at present, as discussed here. If they are present in sufficient abundance, relic H's would be the cold dark matter. Tests of this scenario are discussed

These are random recollections on the "middle years" of Arkady's life in science, from the late 1960's to late 1980's. One cannot write about Arkady in Siberia without first describing a general atmosphere in the Budker Institute of Nuclear Physics and Akademgorodok, Novosibirsk, in the 1960's and 1970's. I guess it may be interesting for our international friends and colleagues to learn about it, and to those who were there at the time, to recall Akademgorodok once again…

To me Arkady always seemed to be a striking and extremely impressive sample of a human breed, an evidence for the existence of a person who very naturally reached a summit of human abilities…

It is somewhat strange but, in spite of my quite vivid memory of Arkady's excellent personality and many conversations and discussions I had with him, I cannot recall anything reasonably coherent. There were very few amusing or funny incidents since he was always wise and did everything so well. Still it is my feeling that, being very certain and resolute in his scientific judgments, he may look rather indecisive in everyday life and sometimes just sinks in all those "from the one hand…, but from the other…"

The following sections are included:

• Glimpses of ITEP

• A few touches on Arkady's portrait

The Theoretical Physics Institute at the University of Minnesota is a direct result of the interest and generosity of Bill Fine. It was roughly 20 years ago that he and I became acquainted, and I discovered that Bill had a deep interest in physics, specifically High Energy physics…

Perturbation theory is the most common tool applied for calculations in quantum mechanics and, especially, field theory. In weakly coupled theories, such as quantum electrodynamics or electroweak model, calculations based on the Feynman graphs (which represent a particular order in the perturbative series) are innumerable. This approach has a solid theoretical foundation, and its remarkable success is no surprise…