551 research outputs found
The continuum limit of the quark mass step scaling function in quenched lattice QCD
The renormalisation group running of the quark mass is determined
non-perturbatively for a large range of scales, by computing the step scaling
function in the Schroedinger Functional formalism of quenched lattice QCD both
with and without O(a) improvement. A one-loop perturbative calculation of the
discretisation effects has been carried out for both the Wilson and the
Clover-improved actions and for a large number of lattice resolutions. The
non-perturbative computation yields continuum results which are regularisation
independent, thus providing convincing evidence for the uniqueness of the
continuum limit. As a byproduct, the ratio of the renormalisation group
invariant quark mass to the quark mass, renormalised at a hadronic scale, is
obtained with very high accuracy.Comment: 23 pages, 3 figures; minor changes, references adde
Quantum Evolution of Inhomogeneities in Curved Space
We obtain the renormalized equations of motion for matter and semi-classical
gravity in an inhomogeneous space-time. We use the functional Schrodinger
picture and a simple Gaussian approximation to analyze the time evolution of
the model, and we establish the renormalizability of this
non-perturbative approximation. We also show that the energy-momentum tensor in
this approximation is finite once we consider the usual mass and coupling
constant renormalizations, without the need of further geometrical
counter-terms.Comment: 22 page
The phase diagram of twisted mass lattice QCD
We use the effective chiral Lagrangian to analyze the phase diagram of
two-flavor twisted mass lattice QCD as a function of the normal and twisted
masses, generalizing previous work for the untwisted theory. We first determine
the chiral Lagrangian including discretization effects up to next-to-leading
order (NLO) in a combined expansion in which m_\pi^2/(4\pi f_\pi)^2 ~ a \Lambda
(a being the lattice spacing, and \Lambda = \Lambda_{QCD}). We then focus on
the region where m_\pi^2/(4\pi f_\pi)^2 ~ (a \Lambda)^2, in which case
competition between leading and NLO terms can lead to phase transitions. As for
untwisted Wilson fermions, we find two possible phase diagrams, depending on
the sign of a coefficient in the chiral Lagrangian. For one sign, there is an
Aoki phase for pure Wilson fermions, with flavor and parity broken, but this is
washed out into a crossover if the twisted mass is non-vanishing. For the other
sign, there is a first order transition for pure Wilson fermions, and we find
that this transition extends into the twisted mass plane, ending with two
symmetrical second order points at which the mass of the neutral pion vanishes.
We provide graphs of the condensate and pion masses for both scenarios, and
note a simple mathematical relation between them. These results may be of
importance to numerical simulations.Comment: 13 pages, 5 figures, small clarifying comments added in introduction,
minor typos fixed. Version to be published in Phys. Rev.
A Kaluza-Klein Model with Spontaneous Symmetry Breaking: Light-Particle Effective Action and its Compactification Scale Dependence
We investigate decoupling of heavy Kaluza-Klein modes in an Abelian Higgs
model with space-time topologies and
. After integrating out heavy KK
modes we find the effective action for the zero mode fields. We find that in
the topology the heavy modes do not decouple in
the effective action, due to the zero mode of the 5-th component of the 5-d
gauge field . Because is a scalar under 4-d Lorentz
transformations, there is no gauge symmetry protecting it from getting mass and
interaction terms after loop corrections. In addition, after
symmetry breaking, we find new divergences in the mass that did not
appear in the symmetric phase. The new divergences are traced back to the
gauge-goldstone mixing that occurs after symmetry breaking. The relevance of
these new divergences to Symanzik's theorem is discussed. In order to get a
more sensible theory we investigate the
compactification. With this kind of compact topology, the zero mode
disappears. With no , there are no new divergences and the heavy modes
decouple. We also discuss the dependence of the couplings and masses on the
compactification scale. We derive a set of RG-like equations for the running of
the effective couplings with respect to the compactification scale. It is found
that magnitudes of both couplings decrease as the scale increases. The
effective masses are also shown to decrease with increasing compactification
scale. All of this opens up the possibility of placing constraints on the size
of extra dimensions.Comment: 35 pages, 6 figure
Scaling, asymptotic scaling and Symanzik improvement. Deconfinement temperature in SU(2) pure gauge theory
We report on a high statistics simulation of SU(2) pure gauge field theory at
finite temperature, using Symanzik action. We determine the critical coupling
for the deconfinement phase transition on lattices up to 8 x 24, using Finite
Size Scaling techniques. We find that the pattern of asymptotic scaling
violation is essentially the same as the one observed with conventional, not
improved action. On the other hand, the use of effective couplings defined in
terms of plaquette expectation values shows a precocious scaling, with respect
to an analogous analysis of data obtained by the use of Wilson action, which we
interpret as an effect of improvement.Comment: 43 pages ( REVTeX 3.0, self-extracting shell archive, 13 PostScript
figs.), report IFUP-TH 21/93 (2 TYPOS IN FORMULAS CORRECTED,1 CITATION
UPDATED,CITATIONS IN TEXT ADDED
Finite VEVs from a Large Distance Vacuum Wave Functional
We show how to compute vacuum expectation values from derivative expansions
of the vacuum wave functional. Such expansions appear to be valid only for
slowly varying fields, but by exploiting analyticity in a complex scale
parameter we can reconstruct the contribution from rapidly varying fields.Comment: 39 pages, 16 figures, LaTeX2e using package graphic
The numerical study of the solution of the model
We present a numerical study of the nonlinear system of equations
of motion. The solution is obtained iteratively, starting from a precise
point-sequence of the appropriate Banach space, for small values of the
coupling constant. The numerical results are in perfect agreement with the main
theoretical results established in a series of previous publications.Comment: arxiv version is already officia
Lattice energy-momentum tensor with Symanzik improved actions
We define the energy-momentum tensor on lattice for the and
for the nonlinear -model Symanzik tree-improved actions, using Ward
identities or an explicit matching procedure. The resulting operators give the
correct one loop scale anomaly, and in the case of the sigma model they can
have applications in Monte Carlo simulations.Comment: Self extracting archive fil
Ambiguities in the up quark mass
It has long been known that no physical singularity is encountered as up
quark mass is adjusted from small positive to negative values as long as all
other quarks remain massive. This is tied to an additive ambiguity in the
definition of the quark mass. This calls into question the acceptability of
attempts to solve the strong CP problem via a vanishing mass for the lightest
quark.Comment: 9 pages, 1 figure. Revision as will appear in Physical Review
Letters. Simplified renormalization group discussion and title change
requested by PR
Improving lattice perturbation theory
Lepage and Mackenzie have shown that tadpole renormalization and systematic
improvement of lattice perturbation theory can lead to much improved numerical
results in lattice gauge theory. It is shown that lattice perturbation theory
using the Cayley parametrization of unitary matrices gives a simple analytical
approach to tadpole renormalization, and that the Cayley parametrization gives
lattice gauge potentials gauge transformations close to the continuum form. For
example, at the lowest order in perturbation theory, for SU(3) lattice gauge
theory, at the `tadpole renormalized' coupling to be compared to the non-perturbative numerical value Comment: Plain TeX, 8 page
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