Felipe J. Llanes-Estrada

QCD and strongly coupled gauge theories: challenges and perspectives

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 quark-gluon vertex in Landau gauge QCD: Its role in dynamical chiral symmetry breaking and quark confinement

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 powerlawinfrared singularities for this vertex.Weestablish 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, eitherdynamically orexplicitly, 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 quarkmass function aswell 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 analmostmass independent string tensionin the case of brokenchiral 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 derWaals 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.

Viscosity of meson matter

We report a calculation of the shear viscosity in a relativistic multicomponent meson gas as a function of temperature and chemical potentials. We approximately solve the Uehling-Uhlenbeck transport equation of kinetic theory, appropriate for a boson gas, with relativistic kinematics. Since at low temperatures the gas can be taken as mostly composed of pions, with a fraction of kaons and etas, we explore the region where binary elastic collisions with at least one pion are the dominant scattering processes. Our input meson scattering phase shifts are fits to the experimental data obtained from chiral perturbation theory and the inverse amplitude method. Our results take the correct nonrelativistic limit ~viscosity proportional to the square root of the temperature!, show a viscosity of the order of the cube of the pion mass up to temperatures somewhat below that mass, and then a large increase due to kaons and etas. Our approximation may break down at even higher temperatures, where the viscosity follows a temperature power law with an exponent near 3.

Chirally symmetric quark description of low-energy pi pi scattering

Weinberg’s theorem for π-π scattering, including the Adler zero at threshold in the chiral limit, is analyticall proved for microscopic quark models that preserve chiral symmetry. Implementing Ward-Takahashi identities, the isospin 0 and 2 scattering lengths are derived in exact agreement with Weinberg’s low energy results. Our proof applies to alternative quark formulations including the Hamiltonian and Euclidean space Dyson-Schwinger approaches. Finally, the threshold π-π scattering amplitudes are calculated using the Dyson- Schwinger equations in the rainbow-ladder truncation, confirming the formal derivation.

Y(4260) and possible charmonium assignment

The newly reported Y(4260) becomes the second most massive state in the charmonium family. We argue that it displaces the psi(4415) as the (largely) 4s vector charmonium state, recall s-d wave interference to explain the lack of a signal in e-e+ to hadrons and suggest some further study avenues that can exclude exotic meson assignments. The absence of a J/psi KK mode can be understood, beyond phase space suppression, to be a consequence of chiral symmetry. We also provide a model calculation in this sector showing that, although forcing the fit somewhat (which suggests a small sea quark wavefunction component), the state can be incorporated in a standard scheme.

Meson Structure in a Relativistic Many-Body Approach

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.

Shear viscosity in a CFL quark star

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 He4, 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.

One-loop W L W L and Z L Z L scattering from the electroweak Chiral Lagrangian with a light Higgs-like scalar

A bstractBy including the recently discovered Higgs-like scalar φ in the Electroweak Chiral Lagrangian, and using the Equivalence Theorem, we carry out the complete one-loop computation of the elastic scattering amplitude for the longitudinal components of the gauge bosons V = W, Z at high energy. We also compute φφ → φφ and the inelastic process VV → φφ, and identify the counterterms needed to cancel the divergences, namely the well known a4 and a5 chiral parameters plus three additional ones only superficially treated in the literature because of their dimension 8. Finally we compute all the partial waves and discuss the limitations of the one-loop computation due to only approximate unitarity.

DYNAMICALLY INDUCED SCALAR QUARK CONFINEMENT

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 self-consistent 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.

Relativistic many body Hamiltonian approach to mesons

Abstract We represent QCD at the hadronic scale by means of an effective Hamiltonian, H , formulated in the Coulomb gauge. As in the Nambu–Jona-Lasinio model, chiral symmetry is explicitly broken, however our approach is renormalizable and also includes confinement through a linear potential with slope specified by lattice gauge theory. This interaction generates an infrared integrable singularity and we detail the computationally intensive procedure necessary for numerical solution. We focus upon applications for the u , d , s and c quark flavors and compute the mass spectrum for the pseudoscalar, scalar and vector mesons. We also perform a comparative study of alternative many-body techniques for approximately diagonalizing H : BCS for the vacuum ground state; TDA and RPA for the excited hadron states. The Dirac structure of the field theoretical Hamiltonian naturally generates spin-dependent interactions, including tensor, spin–orbit and hyperfine, and we clarify the degree of level splitting due to both spin and chiral symmetry effects. Significantly, we find that roughly two-thirds of the π – ρ mass difference is due to chiral symmetry and that only the RPA preserves chiral symmetry. We also document how hadronic mass scales are generated by chiral symmetry breaking in the model vacuum. In addition to the vacuum condensates, we compute meson decay constants and detail the Nambu–Goldstone realization of chiral symmetry by numerically verifying the Gell-Mann–Oakes–Renner relation.