Continuous Advances in QCD 2008

following sections are included:

• FOREWORD

• CONTENTS

The small-x deep inelastic scattering in the saturation region is governed by the non-linear evolution of Wilson-line operators. In the leading logarithmic approximation it is given by the BK equation for the evolution of color dipoles. I discuss recent calculation of the next-to-leading order evolution of color dipoles in QCD and SYM.

We present new results for heavy quark decays at next-to-next-to-leading order. In particular, we discuss the calculation of the charm-quark mass effects and the expansion in the intermediate recoil limit in semi-leptonic bottom-quark decays and the evaluation of the helicity fractions of the W boson from top-quark decays.

I review some classic results and recent progress in the resummation of leading and nonleading singularities in QCD cross sections and dimensionally-regularized hard-scattering amplitudes.

Recursion relations are succinctly obtained for (++⋯+) and (-++⋯+) amplitudes in the context of the space-cone gauge in QCD. We rely on the helicity symmetry of the problems to dictate our choices of reference twistors and the momentum shifts used to analytically continue the amplitudes. Of great importance is the power of Lorentz invariance, which is enough to determine the soft factors in the latter cases.

A surprising number of new mesons with masses above the threshold have been discovered at the B factories. Some of them are ordinary charmonium states, but others are definitely exotic mesons. The current theoretical status of the new mesons is summarized.

We present the current status of the search for new physics effects in the mixing quantities ΔM_s, ΔΓ_s and ɸ_s of the neutral B_s-system.

I review constraints on possible New Physics interactions from mixing measurements. I consider the most general low energy effective Hamiltonian and include leading order QCD running of effective operators. I discuss constraints from an extensive list of popular New Physics models, each of which could be discovered at the LHC, that can generate these operators. In most of the scenarios, strong constraints that surpass those from other search techniques could be placed on the allowed parameter space using the existent evidence for observation of D meson mixing.

In this contribution two recent analyses for the extraction of the charm quark mass are discussed. Although they rely on completely different experimental and theoretical input the two methods provide the same final results for the charm quark mass and have an uncertainty of about 1%.

In this talk I review the recent discovery of a crystalline condensate solution to the gap equation for the (massless) chiral Gross-Neveu model. This work is motivated by the search for the complete phase diagram, in the temperature and chemical potential plane, of this well-known 1+1 dimensional quantum field theory that exhibits continuous chiral symmetry, asymptotic freedom and dynamical mass generation. We are also motivated by the recent solution [by M. Thies et al] of the phase diagram for the non-chiral Gross-Neveu model, which has instead a discrete chiral symmetry. The key technical advance in our work is the observation that a suitable ansatz for the Gorkov resolvent reduces the functional gap equation, for the inhomogeneous condensate, to a nonlinear Schrödinger equation, which is exactly soluble. The resulting general crystalline solution includes as special cases all previously known real and complex condensate solutions to the gap equation.

Recent results for the cross section of electron-positron annihilation into hadrons and for the decay rates of the Z boson and the τ lepton into hadrons including corrections of order are reviewed. The consistency between two values of α_s measured at vastly different energies constitutes a striking test of asymptotic freedom and requires the proper matching conditions at charm and bottom thresholds. Combining the results from Z and τ decays leads to α_s(M_Z) = 0.1198 ± 0.0015 as one of the most precise and presently only NNNLO result for the strong coupling constant. We report a recent determination of α_s which is based on a lattice evaluation of the pseudoscalar correlator for the charm quarks combined with continuum perturbation theory.

Quarkyonic matter is a new phase of QCD at finite temperature and density which is distinct from the confined and de-confined phases. Its existence is unambiguously argued in the large numbers of colors limit, N_c → ∞, of QCD. Hints of its existence for QCD, N_c = 3, are shown in lattice Monte-Carlo data and in heavy ion experiments.

In this talk we discuss the microscopic limit of QCD at nonzero chemical potential. In this domain, where the QCD partition function is under complete analytical control, we uncover an entirely new link between the spectral density of the Dirac operator and the chiral condensate: violent complex oscillations on the microscopic scale give rise to the discontinuity of the chiral condensate at zero quark mass. We first establish this relation exactly within a random matrix framework and then analyze the importance of the individual modes by Fourier analysis.

We summarize recent results regarding the equilibrium and non-equilibrium behavior of cold dilute atomic gases in the limit in which the two body scattering length a goes to infinity. In this limit the system is described by a Galilean invariant (non-relativistic) conformal field theory. We discuss the low energy effective lagrangian appropriate to the limit a → ∞, and compute low energy coefficients using an ϵ-expansion. We also show how to combine the effective lagrangian with kinetic theory in order to compute the shear viscosity, and compare the kinetic theory predictions to experimental results extracted from the damping of collective modes in trapped Fermi gases.

In this lecture we discuss various aspects of QCD at nonzero chemical potential, including its phase diagram and the Dirac spectrum, and summarize what chiral random matrix theory has contributed to this subject. To illustrate the importance of the phase of the fermion determinant, we particularly highlight the differences between QCD and phase quenched QCD.

Linear confinement in holographic QCD can be obtained with a soft-wall quadratic dilaton background. We present a solution to the five-dimensional Einstein's equations which dynamically realizes the soft-wall model. We discuss aspects of the solution and comment on the possible relation to a noncritical string theory.

A simple holographic model, derived from the AdS/CFT Correspondence, is described that displays many features of QCD's dynamics. The geometry has a non-trivial dilaton flow that breaks supersymmetry but preserves the SO(6) R-symmetry of Yang Mills. We speculate that this flow describes the super-Yang Mills theory with a scalar mass term (which is highly irrelevant and would enter as a sharp UV cut off). The geometry describes confinement and chiral symmetry breaking at low temperatures and a first order phase transition to a deconfined plasma with melted mesons at a finite critical temperature.

Several key problems of QCD sum rules in the spin-0 glueball channels are resolved by implementing nonperturbative short-distance physics from direct instantons and topological charge screening. A lattice-based instanton size distribution and the IR renormalization of the nonperturbative Wilson coefficients are also introduced. Results of a comprehensive quantitative sum rule analysis are reviewed and their implications discussed.

Holographic QCD provides a unique framework in which to compute QCD observables. In this talk we summarize recent numerical work on computing the pion electromagnetic form factor using an AdS/QCD action that includes both spontaneous and explicit chiral symmetry breaking. We consider both hard- and soft-wall model results and develop an intermediate background that supports the best features of both. We also begin to see possible evidence in the fit for the presence of 1/N_c corrections.

Holographic techniques are used to study the dispersion relation of meson quasiparticles moving through a thermal plasma in N = 2 super-Yang-Mills theory with N_c colours and coupled to N_f flavours of fundamental matter in the regime N_f/N_c ≪ 1. The meson states are destabilized by introducing a small quark density n_q. Holographic spectral functions are used to investigate the dispersion relations and widths of these quasiparticles. In a low momentum regime q < q_max, the quasiparticles approach a limiting velocity that can be significantly less than the speed of light. In this regime, the widths of the quasiparticles also rise dramatically as the momentum approaches q_max. The spectral functions do not display isolated resonances for q > q_max. However, by studying the dual quasinormal modes one can extend the dispersion relation into this regime. We give a qualitative argument suggesting that the group velocity rises to the speed of light for q ≫ q_max. This contribution provides a summary of the results in [1].

We give a brief summary of our recent works^1,2 on the baryons in holographic QCD.³ In the holographic description, meson effective action is given by the five dimensional Yang-Mills - Chern-Simons theory in a certain curved background. The baryon is described as a soliton carrying an instanton number on the four dimensional space. By quantizing the soliton, we obtain various baryon states and calculate static quantities such as charge radii, magnetic moments, axial coupling, etc.

We present general results about the chiral ring of quiver gauge theories, arising on the world-volume of D3-branes at conical Calabi-Yau singularities. We discuss the structure of the moduli space and the computation of generating functions for the chiral operators in the theory. The paper summarizes results from published work in Refs 1–5.

Dynamics of SU(N_c) Yang-Mills theories with N_f adjoint Weyl fermions is quite different from that of SU(N_c) gauge theories with fundamental quarks. The symmetry breaking pattern is SU(N_f) → SO(N_f). The corresponding sigma model supports Skyrmions whose microscopic identification is not immediately clear. We address this issue as well as the issue of the Skyrmion stability. We discuss the coupling between the massless Goldstone bosons and massive composite fermions (with mass ) from the standpoint of the low-energy chiral sigma model. We derive the Wess-Zumino-Novikov-Witten term and then determine Skyrmion statistics. We also determine their fermion number (mod 2) and observe an abnormal relation between the statistics and the fermion number. This explains the Skyrmion stability.

We study a mechanism that induces confinement inside domain walls. Condensates on the two vacua separated by the wall, if they are equivalent, can tunnel from one side to the other. They can create a current and trap a confining string inside the domain wall. Strings in the two vacua are attracted toward the domain wall and form a bound state with it.

We consider a simple toy model that realizes this mechanism. We also provide an example from the Seiberg-Witten theory where everything can be studied in the strong coupling regime using the dual effective action. We finally compare our findings with the previously studied wall with two different quark flavors and explain why here the discussed mechanism of confinement does not act.

Interactions between non-BPS non-Abelian vortices are studied in non-Abelian U(1) × SU(N) extensions of the Abelian-Higgs model in four dimensional space-time. In addition to the usual type I/II Abelian superconductors, we find two new regime which we call type I*/II*.

After briefly reviewing the problems associated with non-Abelian monopoles, we turn our attention to the development in our understanding of non-Abelian vortices in the last several years. In the U(N) model with N_f = N flavors in which they were first found, the fluctuations of the orientational modes along the vortex length and in time become strongly coupled at long distances. They effectively reduce to Abelian ANO vortices. We discuss then a very recent work on non-Abelian vortices with CP^n-1 × CP^r-1 orientational moduli, which, unlike the ones so far extensively studied, do not dynamically Abelianize completely. The surviving vortex orientational moduli, fluctuating along the vortex length and in time, gets absorbed by the monopoles at the ends, turning into the dual gauge degrees of freedom for the latter.

We construct the general vortex solution in a fully-Higgsed, color-flavor locked vacuum of a non-Abelian gauge theory, where the gauge group is taken to be the product of an arbitrary simple group and U(1), with a Fayet-Iliopoulos term. The strict correspondence between vortices and lumps in the associated NLσM which arise in the limit of strong coupling is pointed out. The construction of the vortex moduli space is derived here as a consequence of this correspondence.

The conjectured all-loop integrability of the planar maximally supersymmetric Yang-Mills theory offers an efficient way to compute the cusp anomalous dimension at any value of the 't Hooft coupling constant through its relation with the logarithmic scaling of anomalous dimensions of high-spin Wilson operators. In this talk, I report on calculation of the cusp anomalous dimension in this theory at strong coupling.

The properties of supersymmetric gauge theories in the Higgs phase at low energies can appropriately be studied by means of a non-linear σ model, which has the target space being Kähler for supersymmetric models and hyperKähler for models. By construction of the Kähler and hyperKähler quotients for the gauge theories with SO and USp gauge symmetries, we obtain the explicit metrics on their respective manifolds. Furthermore, we study the lumps in the non-linear σ models and their effective description, using the Kähler quotients.

We report preliminary results of lattice super-Yang-Mills computations using domain wall fermions, performed at an actual rate of 1000 Gflop/s, over the course of six months, using two BlueGene/L racks at Rensselaer's CCNI supercomputing center. This has allowed us to compute the gluino condensate and string tension over a wide range of lattice parameters, setting the stage for continuum, chiral extrapolations.

Baryon Regge trajectories are discussed in the light of the 1/N_c expansion. The approximate dynamical symmetry SU(6) × O(3) is used to identify the spin-flavor singlet component of baryon masses. By fitting to the known baryon spectrum, this component is shown to produce distinct Regge trajectories for the SU(6) 56- and 70-plets which are remarkably linear.

Infrared behavior of the fermion propagator in QED3 is analysed by dispersion method with dressed photon spectral function. Propagator has no one-partcle states. Finite threshold effects of fermion pair cause oscillation of the propagator. However this does not affect the order parameter. Screening effect is large for small N and the N dependence of the order parameter is not significant.

Quantized fields in accelerated frames (Rindler spaces) with emphasis on gauge fields are investigated. Important properties of the dynamics in Rindler spaces are shown to follow from the scale invariance of the corresponding Hamiltonians. Origin and consequences of this extraordinary property of Hamiltonians in Rindler spaces are elucidated. Characteristics of the Unruh radiation, the appearance of a photon condensate and the interaction energy of vector and scalar static charges are discussed and implications for Yang-Mills theories and QCD in Rindler spaces are indicated.

We discuss the relationship between the large order behavior of the perturbative series for the average plaquette in pure gauge theory and singularities in the complex coupling plane. We discuss simple extrapolations of the large order for this series. We point out that when these extrapolated series are subtracted from the Monte Carlo data, one obtains (naive) estimates of the gluon condensate that are significantly larger than values commonly used in the continuum for phenomelogical purpose. We present numerical results concerning the zeros of the partition function in the complex coupling plane (Fisher's zeros). We report recent attempts to solve this problem using the density of states. We show that weak and strong coupling expansions for the density of states agree surprisingly well for values of the action relevant for the crossover regime.

In this talk I argue that dark matter in the form of dense matter/antimatter nuggets could provide a natural and unified explanation for several distinct bands of diffuse radiation from the core of the galaxy spanning over 13 orders of magnitude in frequency. It includes: SPI/INTEGRAL observations of 511 keV gamma rays; detection by the CHANDRA satellite of diffuse X-ray emission; COMPTEL observation of the flux of gamma rays in the 1-20 MeV range; finally, the so-called "WMAP- haze" which is a diffuse microwave excess observed from the core of our galaxy. If correct, our proposal identifies the nature of the dark matter, explains baryogenesis, and provides a means to directly probe the matter distribution in our Galaxy by analyzing several different types of diffuse emissions.

The following sections are included:

• Pictures

• LIST OF THE PARTICIPANTS OF CAQCD-08