The (LATTICE) QCD Potential and Running Coupling: How to Accurately Interpolate between Multi-Loop QCD and the String Picture

We present a simple parameterization of a running coupling constant, defined via the static potential, that interpolates between 2-loop QCD in the UV and the string prediction in the IR. Besides the usual \Lam-parameter and the string tension, the coupling depends on one dimensionless parameter, determining how fast the crossover from UV to IR behavior occurs (in principle we know how to take into account any number of loops by adding more parameters). Using a new Ansatz for the LATTICE potential in terms of the continuum coupling, we can fit quenched and unquenched Monte Carlo results for the potential down to ONE lattice spacing, and at the same time extract the running coupling to high precision. We compare our Ansatz with 1-loop results for the lattice potential, and use the coupling from our fits to quantitatively check the accuracy of 2-loop evolution, compare with the Lepage-Mackenzie estimate of the coupling extracted from the plaquette, and determine Sommer's scale $r_0$ much more accurately than previously possible. For pure SU(3) we find that the coupling scales on the percent level for $\beta\geq 6$.Comment: 47 pages, incl. 4 figures in LaTeX [Added remarks on correlated vs. uncorrelated fits in sect. 4; corrected misprints; updated references.

Heavy baryons in the large Nc limit

It is shown that in the large N-c limit heavy baryon masses can be estimated quantitatively in a 1/N-c expansion using the Hartree approximation. The results are compared with available lattice calculations for different values of the ratio between the square root of the string tension and the heavy quark mass root sigma/m(Q). These estimates implement important 1/N-c corrections and assume a string tension independent of N-c. Using a potential adjusted to agree with the one obtained in lattice QCD, a variational analysis of the ground state spin averaged baryon mass is performed using Gaussian Hartree wave functions. Relativistic corrections through the quark kinetic energy are included. The results provide good estimates for the first sub-leading in 1/N-c corrections.Open Access funded by SCOAP³ - Sponsoring Consortium for Open Access Publishing in Particle Physics.This work was supported in part by DOE Contract No. DE-AC05-06OR23177 under which JSA operates the Thomas Jefferson National Acceler- ator Facility (J.L.G.), by the National Science Foundation through grant PHY-1307413 (I.P.F. and J.L.G.) and the Spanish Mineco (grant FIS2014-59386-P) and Junta de Andalucía (grant FQM225) (C.A.T. and E.R.A.). C.A.T. acknowledges a contract from the CPAN

Effective String Theory of Vortices and Regge Trajectories

Starting from a field theory containing classical vortex solutions, we obtain an effective string theory of these vortices as a path integral over the two transverse degrees of freedom of the string. We carry out a semiclassical expansion of this effective theory, and use it to obtain corrections to Regge trajectories due to string fluctuations.Comment: 27 pages, revtex, 3 figures, corrected an error with the cutoff in appendix E (was previously D), added more discussion of Fig. 3, moved some material in section 9 to a new appendi

Coulomb Gauge QCD, Confinement, and the Constituent Representation

Quark confinement and the genesis of the constituent quark model are examined in nonperturbative QCD in Coulomb gauge. We employ a self-consistent method to construct a quasiparticle basis and to determine the quasiparticle interaction. The results agree remarkably well with lattice computations. They also illustrate the mechanism by which confinement and constituent quarks emerge, provide support for the Gribov-Zwanziger confinement scenario, clarify several perplexing issues in the constituent quark model, and permit the construction of an improved model of low energy QCD.Comment: 43 pages, 14 figures, revtex, uses psfig.st

Spin Effects in Two Quark System and Mixed States

Based on the numeric solution of a system of coupled channels for vector mesons ($S$- and $D$-waves mixing) and for tensor mesons ($P$- and $F$-waves mixing) mass spectrum and wave functions of a family of vector mesons $q\bar{q}$ in triplet states are obtained. The calculations are performed using a well known Cornell potential with a mixed Lorentz-structure of the confinement term. The spin-dependent part of the potential is taken from the Breit-Fermi approach. The effect of singular terms of potential is considered in the framework of the perturbation theory and by a configuration interaction approach (CIA), modified for a system of coupled equations. It is shown that even a small contribution of the $D$-wave to be very important at the calculation of certain characteristics of the meson states.Comment: 12 pages, LaTe

The light sigma meson

In the framework of the dispersion relation N/D-approach, we restore the low-energy pi-pi (IJ^{PC}=00^{++})-wave amplitude sewing it with the previously obtained K-matrix solution for the region 450-1900 MeV. The restored N/D-amplitude has a pole on the second sheet of the complex-s plane near the pi-pi threshold, that is the light sigma meson.Comment: 5 pages, LaTeX, 3 EPS figures, epsfig.st

QCD strings with spinning quarks

We construct a consistent action for a massive spinning quark on the end of a QCD string that leads to pure Thomas precession of the quark's spin. The string action is modified by the addition of Grassmann degrees of freedom to the string such that the equations of motion for the quark spin follow from boundary conditions, just as do those for the quark's position.Comment: REVTeX4, 10 pages, no figure

Magnetic Catalysis: A Review

We give an overview of the magnetic catalysis phenomenon. In the framework of quantum field theory, magnetic catalysis is broadly defined as an enhancement of dynamical symmetry breaking by an external magnetic field. We start from a brief discussion of spontaneous symmetry breaking and the role of a magnetic field in its a dynamics. This is followed by a detailed presentation of the essential features of the phenomenon. In particular, we emphasize that the dimensional reduction plays a profound role in the pairing dynamics in a magnetic field. Using the general nature of underlying physics and its robustness with respect to interaction types and model content, we argue that magnetic catalysis is a universal and model-independent phenomenon. In support of this claim, we show how magnetic catalysis is realized in various models with short-range and long-range interactions. We argue that the general nature of the phenomenon implies a wide range of potential applications: from certain types of solid state systems to models in cosmology, particle and nuclear physics. We finish the review with general remarks about magnetic catalysis and an outlook for future research.Comment: 37 pages, to appear in Lect. Notes Phys. "Strongly interacting matter in magnetic fields" (Springer), edited by D. Kharzeev, K. Landsteiner, A. Schmitt, H.-U. Yee. Version 2: references adde