We highlight the progress, current status, and open challenges of QCD-driven physics, in theory and in experiment. We discuss how the strong interaction is intimately connected to a broad sweep of physical problems, in settings ranging from astrophysics and cosmology to strongly coupled, complex systems in particle and condensed-matter physics, as well as to searches for physics beyond the Standard Model. We also discuss how success in describing the strong interaction impacts other fields, and, in turn, how such subjects can impact studies of the strong interaction. In the course of the work we offer a perspective on the many research streams which flow into and out of QCD, as well as a vision for future developments.

The infrared behavior of the quark-gluon vertex of quenched Landau gauge QCD is studied by analyzing its Dyson-Schwinger equation. Building on previously obtained results for Green functions in the Yang-Mills sector we analytically derive the existence of power-law infrared singularities for this vertex. We establish that dynamical chiral symmetry breaking leads to the self-consistent generation of components of the quark-gluon vertex forbidden when chiral symmetry is forced to stay in the Wigner-Weyl mode. In the latter case the running strong coupling assumes an infrared fixed point. If chiral symmetry is broken, either dynamically or explicitely, the running coupling is infrared divergent. Based on a truncation for the quark-gluon vertex Dyson-Schwinger equation which respects the analytically determined infrared behavior numerical results for the coupled system of the quark propagator and vertex Dyson-Schwinger equation are presented. The resulting quark mass function as well as the vertex function show only a very weak dependence on the current quark mass in the deep infrared. From this we infer by an analysis of the quark-quark scattering kernel a linearly rising quark potential with an almost mass independent string tension in the case of broken chiral symmetry. Enforcing chiral symmetry does lead to a Coulomb type potential. Therefore we conclude that chiral symmetry breaking and confinement are closely related. Furthermore we discuss aspects of confinement as the absence of long-range van-der-Waals forces and Casimir scaling. An examination of experimental data for quarkonia provides further evidence for the viability of the presented mechanism for quark confinement in the Landau gauge.

We employ a functional approach to investigate the confinement problem in quenched Landau gauge QCD. We demonstrate analytically that a linear rising potential between massive quarks is generated by infrared singularities in the dressed quark-gluon vertex. The selfconsistent mechanism that generates these singularities is driven by the scalar Dirac amplitudes of the full vertex and the quark propagator. These can only be present when chiral symmetry is broken. We have thus uncovered a novel mechanism that directly links chiral symmetry breaking with confinement.PACS numbers: 12.38. Aw, 12.38.Lg, 14.70.Dj, 11.30.Rd More than thirty years after the identification of nonAbelian gauge theory as the appropriate framework to describe the strong interactions we still lack a satisfactory understanding of the confinement phenomenon. Isolated particles with nonvanishing colour charges have not been observed in nature. This fact is supposed to be encoded in the infrared structure of QCD. In the quenched theory a gauge invariant signature of confinement is the area law of the Wilson loop at large distances. This behaviour corresponds to a linear rising potential between static colour charges in the fundamental representation of the gauge group. This signature has been unambiguously verified in lattice gauge QCD, see e.g. ref.[1]. However, the dynamical mechanism that generates the Wilson potential is still elusive. Since the underlying long range interaction is provided by gauge dependent objects, this mechanism may have a different appearance in different gauges. In this letter we present such a mechanism for covariant Landau gauge QCD.The idea of 'infrared slavery', i.e. the notion that infrared singularities generate confinement, dates back to the early seventies [2]. Speculations about the infrared behaviour of the running coupling at that time distinguish two cases: (A) the coupling develops an infrared fixed point and (B) the coupling diverges at small or zero momenta. The last possibility has been considered as the driving mechanism for the generation of infrared singularities and quark confinement. Today there is ample evidence from functional approaches that the first possibility is realised in the Yang-Mills sector of Landau gauge QCD: the running coupling freezes out at small momenta [3,4,5,6]. However, this does not imply that the Green's functions of Yang-Mills theory are finite in the infrared: Instead, depending on the number of ghost and gluon legs, many of the one-particle irreducible Green's functions are indeed singular in the limit that all external momenta vanish [6]. In this letter we demonstrate that these singularities also induce a corresponding singularity in the dressed quark-gluon vertex. As a consequence the running coupling defined from this vertex diverges at vanishing renormalization scale, and a linear potential between massive quarks is generated thereby realizing infrared slavery via an infrared singular quark-gluon vertex.Besides confinement the other fundamental property of infrared Q...

The infrared behaviour of vertex functions in an SU (N ) Yang-Mills theory in Landau gauge is investigated employing a skeleton expansion of the Dyson-Schwinger equations. The three-and four-gluon vertices become singular if and only if all external momenta vanish while the dressing of the ghost-gluon vertex remains finite in this limit. The running coupling as extracted from either of these vertex functions possesses an infrared fixed point. In general, diagrams including ghost-loops dominate in the infrared over purely gluonic ones.

We compute the mean free path and shear viscosity in the color-flavor locked (CFL) phase of dense quark matter at low temperature T , when the contributions of mesons, quarks and gluons to the transport coefficients are Boltzmann suppressed. CFL quark matter displays superfluid properties, and transport phenomena in such cold regime are dominated by phonon-phonon scattering. We study superfluid phonons within thermal field theory and compute the mean free path associated to their most relevant collision processes. Small-angle processes turn out to be more efficient in slowing transport phenomena in the CFL matter, while the mean free path relevant for the shear viscosity is less sensitive to collinear scattering due to the presence of zero modes in the Boltzmann equation. In analogy with superfluid He 4 , we find the same T power law for the superfluid phonon damping rate and mean free path. Our results are relevant for the study of rotational properties of compact stars, and correct wrong estimates existing in the literature.

Results from an extensive relativistic many-body analysis utilizing a realistic effective QCD Hamiltonian are presented for the meson spectrum. A comparative numerical study of the BCS, Tamm-Dancoff (TDA), and RPA treatments provides new, significant insight into the condensate structure of the vacuum, the chiral symmetry governance of the pion, and the meson spin, orbital, and flavor mass splitting contributions. In contrast to a previous glueball application, substantial quantitative differences are computed between TDA and RPA for the light quark sector with the pion emerging as a Goldstone boson only in the RPA.PACS numbers: 12.39. Pn, 11.10.St, 12.39.Ki, 12.39.Mk Common to the diverse areas of condensed matter, molecular, atomic, and nuclear physics is the routine implementation of many-body techniques such as the Bardeen, Cooper, Schrieffer (BCS), Tamm-Dancoff (TDA), and random phase approximation (RPA) methods. Particle physics, with an inherent few-body nature, has generally been devoid of such applications even though hadronic structure, requiring a relativistic QCD description, is an extremely challenging many-body problem. The purpose of the present Letter is to report a comparative study documenting the powerful utility of the above techniques for hadronic systems and to detail new, important meson structure results clarifying the nature of spin splittings and the role of chiral symmetry. The equations of motion, while numerically solvable, exhibit a richness and complexity beyond the simple two-body equations such as the generalized Schrödinger schemes. We find that both TDA and RPA solutions to an approximate QCD Hamiltonian with linear confinement reproduce the meson spectrum except for the pion, where only the RPA reasonably describes the mass and decay constant due to proper implementation of chiral symmetry.This work complements our previous many-body treatment [1] of the gluonic sector in which the lattice gauge "measurements" were reproduced. Our collaborative program seeks to develop a rigorous effective Hamiltonian from QCD and then to comprehensively investigate hadronic structure by systematic, accurate diagonalization utilizing controllable approximations. Reference [2] details our renormalization program, based upon a continuous cutoff regularization and similarity transformation. That work addressed only the gluon sector but a similar effort is currently in progress for the quark sector. Accordingly, this paper presents many-body solutions for only the unrenormalized effective Hamiltonian. The starting point is the approximate QCD quark Hamiltonian in the Coulomb gaugeinvolving the quark field C q ͑ x͒, current quark mass m q , and color density r a ͑ x͒ C y q ͑ x͒T a C q ͑ x͒. Coupling to the gluonic sector is omitted and the Faddeev-Popov determinant is replaced by its lowest order unit value. Consistent with our previous work [1], the confining potential is a linear interaction, V sj x 2 yj, rather than the harmonic oscillator [3,4] since lattice gauge theory generates this form ...