239 research outputs found
Discretization Errors and Rotational Symmetry: The Laplacian Operator on Non-Hypercubical Lattices
Discretizations of the Laplacian operator on non-hypercubical lattices are
discussed in a systematic approach. It is shown that order errors always
exist for discretizations involving only nearest neighbors. Among all lattices
with the same density of lattice sites, the hypercubical lattices always have
errors smaller than other lattices with the same number of spacetime
dimensions. On the other hand, the four dimensional checkerboard lattice (also
known as the Celmaster lattice) is the only lattice which is isotropic at order
. Explicit forms of the discretized Laplacian operators on root lattices
are presented, and different ways of eliminating order errors are
discussed.Comment: 30 pages in REVTe
Liquid-gas and other unusual thermal phase transitions in some large-N magnets
Much insight into the low temperature properties of quantum magnets has been
gained by generalizing them to symmetry groups of order N, and then studying
the large N limit. In this paper we consider an unusual aspect of their finite
temperature behavior--their exhibiting a phase transition between a perfectly
paramagetic state and a paramagnetic state with a finite correlation length at
N = \infty. We analyze this phenomenon in some detail in the large ``spin''
(classical) limit of the SU(N) ferromagnet which is also a lattice
discretization of the CP^{N-1} model. We show that at N = \infty the order of
the transition is governed by lattice connectivity. At finite values of N, the
transition goes away in one or less dimension but survives on many lattices in
two dimensions and higher, for sufficiently large N. The latter conclusion
contradicts a recent conjecture of Sokal and Starinets, yet is consistent with
the known finite temperature behavior of the SU(2) case. We also report closely
related first order paramagnet-ferromagnet transitions at large N and shed
light on a violation of Elitzur's theorem at infinite N via the large q limit
of the q-state Potts model, reformulated as an Ising gauge theory.Comment: 27 pages, 7 figures. Added clarifications requested by a refere
Two-loop QCD corrections of the massive fermion propagator
The off-shell two-loop correction to the massive quark propagator in an
arbitrary covariant gauge is calculated and results for the bare and
renormalized propagator are presented. The calculations were performed by means
of a set of new generalized recurrence relations proposed recently by one of
the authors. From the position of the pole of the renormalized propagator we
obtain the relationship between the pole mass and the \bar{MS} mass. This
relation confirms the known result by Gray et al.. The bare amplitudes are
given for an arbitrary gauge group and for arbitrary space-time dimensions.Comment: 18 pages LaTeX, misprints in formula (12) are correcte
Complete Renormalization Group Improvement-Avoiding Factorization and Renormalization Scale Dependence in QCD Predictions
For moments of leptoproduction structure functions we show that all
dependence on the renormalization and factorization scales disappears, provided
that all the ultraviolet logarithms involving the physical energy scale Q are
completely resummed. The approach is closely related to Grunberg's method of
Effective Charges. A direct and simple method for extracting the universal
dimensional transmutation parameter of QCD from experimental data is advocated.Comment: 16 pages, no figure
Exact mass dependent two--loop in the background MOM renormalization scheme
A two-loop calculation of the renormalization group --function in a
momentum subtraction scheme with massive quarks is presented using the
background field formalism. The results have been obtained by using a set of
new generalized recurrence relations proposed recently by one of the authors
(O.V.T.). The behavior of the mass dependent effective coupling constant is
investigated in detail. Compact analytic results are presented.Comment: 20 pages, 5 figures, LaTeX, uses axodraw.sty, revised version, Sec. 5
(numerical results) changed (quark masses were not set properly) and enhance
The random lattice as a regularization scheme
A semi-analytic method to compute the first coefficients of the
renormalization group functions on a random lattice is introduced. It is used
to show that the two-dimensional non-linear -model regularized
on a random lattice has the correct continuum limit. A degree of
``randomness'' in the lattice is introduced and an estimate of the ratio
for two rather opposite values of
in the -model is also given. This ratio turns out to depend on
.Comment: PostScript file. 22 pages. Revised and enlarged versio
condensate for light quarks beyond the chiral limit
We determine the condensate for quark masses from zero up to
that of the strange quark within a phenomenologically successful modelling of
continuum QCD by solving the quark Schwinger-Dyson equation. The existence of
multiple solutions to this equation is the key to an accurate and reliable
extraction of this condensate using the operator product expansion. We explain
why alternative definitions fail to give the physical condensate.Comment: 13 pages, 8 figure
Perturbative Strong Interaction Corrections to the Heavy Quark Semileptonic Decay Rate
We calculate the part of the order correction to the
semileptonic heavy quark decay rate proportional to the number of light quark
flavors, and use our result to set the scale for evaluating the strong coupling
in the order term according to the scheme of Brodsky, Lepage and
Mackenzie. Expressing the decay rate in terms of the heavy quark pole mass
, we find the scale for the strong coupling to be . If the decay rate is expressed in terms of the heavy
quark mass then the scale is . We use these
results along with the existing calculations for hadronic decay to
calculate the BLM scale for the nonleptonic decay width and the semileptonic
branching ratio. The implications for the value of extracted from
the inclusive semileptonic meson decay rate are discussed.Comment: 7 pages in Latex plus 1 uuencoded figure, uses epsf, UTPT-94-24,
CMU-HEP 94-29, CALT-68-1950 (previous results unchanged; we add a short
discussion of nonleptonic decays
Quark-gluon vertex in arbitrary kinematics
We compute the quark-gluon vertex in quenched lattice QCD, in the Landau
gauge using an off-shell mean-field O(a)-improved fermion action. The complete
vertex is computed in two specific kinematical limits, while the Dirac-vector
part is computed for arbitrary kinematics. We find a nontrivial and rich tensor
structure, including a substantial infrared enhancement of the interaction
strength regardless of kinematics.Comment: 6 pages, 8 figures, talk by JIS at QCD Down Under, Adelaide, 10-19
March 200
Static Quark Potentials in Quantum Gravity
We present potentials between static charges from simulations of quantum
gravity coupled to an SU(2) gauge field on and
simplicial lattices. The action consists of the gravitational term given by
Regge's discrete version of the Euclidean Einstein action and a gauge term
given by the Wilson action, with coupling constants and
respectively. In the well-defined phase of the gravity sector where geometrical
expectation values are stable, we study the correlations of Polyakov loops and
extract the corresponding potentials between a source and sink separated by a
distance . We compare potentials on a flat simplicial lattice with those on
a fluctuating Regge skeleton. In the confined phase, the potential has a linear
form while in the deconfined phase, a screened Coulombic behavior is found. Our
results indicate that quantum gravitational effects do not destroy confinement
due to non-abelian gauge fields.Comment: 8 pages, to be published in Phys. Lett. B, uuencoded compressed
postscript file
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