Non-perturbative determination of beta-functions and excited string states from lattices

We use lattice sum rules for the static quark potential to determine the beta-function for symmetric and asymmetric lattices non-perturbatively. We also study the colour field distributions in excited gluonic states.Comment: 9 pages, LATEX, 1 postscript figur

Gribov Copies in the Maximally Abelian Gauge and Confinement

We fix $SU(2)$ lattice gauge fields to the Maximally Abelian gauge in both three and four dimensions. We extract the corresponding $U(1)$ fields and monopole current densities and calculate separately the confining string tensions arising from these $U(1)$ fields and monopole `condensates'. We generate multiple Gribov copies and study how the $U(1)$ fields and monopole distributions vary between these different copies. As expected, we find substantial variations in the number of monopoles, their locations and in the values of the $U(1)$ field strengths. The string tensions extracted from `extreme' Gribov copies also differ but this difference appears to be no more than about 20\%. We also directly compare the fields of different Gribov copies. We find that on the distance scales relevant to confinement the $U(1)$ and monopole fluxes that disorder Wilson loops are highly correlated between these different Gribov copies. All this suggests that while there is indeed a Gribov copy problem the resulting ambiguity is, in this gauge and for the study of confinement, of limited importance.Comment: 31 pages LaTeX plus 5 PostScript figures. Uses epsf.sty. Self-unpacking, uuencoded tar-compressed fil

Observing Long Colour Flux Tubes in SU(2) Lattice Gauge Theory

We present results of a high statistics study of the chromo field distribution between static quarks in SU(2) gauge theory on lattices of volumes 16^4, 32^4, and 48^3*64, with physical extent ranging from 1.3 fm up to 2.7 fm at beta=2.5, beta=2.635, and beta=2.74. We establish string formation over physical distances as large as 2 fm. The results are tested against Michael's sum rules. A detailed investigation of the transverse action and energy flux tube profiles is provided. As a by-product, we obtain the static lattice potential in unpreceded accuracy.Comment: 66 pages, 29 figures, uuencoded latex file with epsfigures (450 K), supplementary full colour figures are available via ftp, CERN-TH.7413/94 (extended version

Heavy-quark condensate at zero- and nonzero temperatures for various forms of the short-distance potential

With the use of the world-line formalism, the heavy-quark condensate in the SU(N)-QCD is evaluated for the cases when the next-to-1/r term in the quark-antiquark potential at short distances is either quadratic, or linear. In the former case, the standard QCD-sum-rules result is reproduced, while the latter result is a novel one. Explicitly, it is UV-finite only in less than four dimensions. This fact excludes a possibility to have, in four dimensions, very short strings (whose length has the scale of the lattice spacing), and consequently the short-range linear potential (if it exists) cannot violate the OPE. In any number of dimensions, the obtained novel expression for the quark condensate depends on the string tension at short distances, rather than on the gluon condensate, and grows linearly with the number of colors in the same way as the standard QCD-sum-rules expression. The use of the world-line formalism enables one to generalize further both results to the case of finite temperatures. A generalization of the QCD-sum-rules expression to the case of an arbitrary number of space-time dimensions is also obtained and is shown to be UV-finite, provided this number is smaller than six.Comment: 11 pages, no figure

Nonperturbative hyperfine contribution to the b1b_1 and h1h_1 meson masses

Due to the nonperturbative contribution to the hyperfine splitting the mass of the $n^1P_1$ state is strongly correlated with the center of gravity $M_{\rm cog}(n^3P_J)$ of the $n^3P_J$ multiplet: $M(n^1P_1)$ is less than $M_{\rm cog}(n^3P_J)$ by about 40 MeV (20 MeV) for the 1P (2P) state. For $b_1(1235)$ the agreement with experiment is reached only if $a_0(980)$ belongs to the $1^3P_J$ multiplet. The predicted mass of $b_1(2^1P_1)$ is $\approx 1620$ MeV. For the isoscalar meson a correlation between the mass of $h_1$(1170) $(h_1(1380))$ and $M_{cog}(1^3P_J)$ composed from light (strange) quarks also takes place.Comment: 22 pages RevTe

Reduction of the QCD string to a time component vector potential

We demonstrate the equivalence of the relativistic flux tube model of mesons to a simple potential model in the regime of large radial excitation. We make no restriction on the quark masses; either quark may have a zero or finite mass. Our primary result shows that for fixed angular momentum and large radial excitation, the flux tube/QCD string meson with a short-range Coulomb interaction is described by a spinless Salpeter equation with a time component vector potential V(r) = ar - k/r.Comment: RevTeX4, 10 pages, 3 eps figure

Chiral shifts in heavy-light mesons

The mass shifts of the $P$-wave $D_s$ and $B_s$ mesons due to coupling to $DK$ and $BK$ channels are calculated in the coupling channel model without fitting parameters. The strong mass shifts down for $0^+$ and ${1^+}'$ states have been obtained, while ${1^+}"$ and $2^+$ states remain almost in situ. The masses of $0^+$ and ${1^+}'$ states of $B_s$ mesons have been predicted.Comment: to be published in the Proceedings of the 14th International QCD Conference, 7th-12th July 2008, Montpellier, Franc

The Matter and the Pseudoscalar Densities in Lattice QCD

The matter and the pseudoscalar densities inside a hadron are calculated via gauge-invariant equal-time correlation functions. A comparison is made between the charge charge and the matter density distributions for the pion, the rho, the nucleon and the $\Delta^+$ within the quenched theory, and with two flavours of dynamical quarks.Comment: Typos corrected; 13 pages, 16 figure

The glueball spectrum from an anisotropic lattice study

The spectrum of glueballs below 4 GeV in the SU(3) pure-gauge theory is investigated using Monte Carlo simulations of gluons on several anisotropic lattices with spatial grid separations ranging from 0.1 to 0.4 fm. Systematic errors from discretization and finite volume are studied, and the continuum spin quantum numbers are identified. Care is taken to distinguish single glueball states from two-glueball and torelon-pair states. Our determination of the spectrum significantly improves upon previous Wilson action calculations.Comment: 14 pages, 8 figures, uses REVTeX and epsf.sty (final version published in Physical Review D

Thermodynamics of SU(3) gauge theory on anisotropic lattices

Finite temperature SU(3) gauge theory is studied on anisotropic lattices using the standard plaquette gauge action. The equation of state is calculated on $16^{3} \times 8$, $20^{3} \times 10$ and $24^{3} \times 12$ lattices with the anisotropy $\xi \equiv a_s / a_t = 2$, where $a_s$ and $a_t$ are the spatial and temporal lattice spacings. Unlike the case of the isotropic lattice on which $N_t=4$ data deviate significantly from the leading scaling behavior, the pressure and energy density on an anisotropic lattice are found to satisfy well the leading $1/N_t^2$ scaling from our coarsest lattice, $N_t/\xi=4$. With three data points at $N_t/\xi=4$, 5 and 6, we perform a well controlled continuum extrapolation of the equation of state. Our results in the continuum limit agree with a previous result from isotropic lattices using the same action, but have smaller and more reliable errors.Comment: RevTeX, 21 pages, 17 PS figures. A quantitative test about the benefit of anisotropic lattices added, minor errors corrected. Final version for PR