160 research outputs found
Heavy quark action on the anisotropic lattice
We investigate the improved quark action on anisotropic lattice as a
potential framework for the heavy quark, which may enable precision computation
of hadronic matrix elements of heavy-light mesons. The relativity relations of
heavy-light mesons as well as of heavy quarkonium are examined on a quenched
lattice with spatial lattice cutoff 1.6 GeV and the
anisotropy . We find that the bare anisotropy parameter tuned for the
massless quark describes both the heavy-heavy and heavy-light mesons within 2%
accuracy for the quark mass , which covers the charm quark
mass. This bare anisotropy parameter also successfully describes the
heavy-light mesons in the quark mass region within the
same accuracy. Beyond this region, the discretization effects seem to grow
gradually. The anisotropic lattice is expected to extend by a factor the
quark mass region in which the parameters in the action tuned for the massless
limit are applicable for heavy-light systems with well controlled systematic
errors.Comment: 11 pages, REVTeX4, 11 eps figure
Heavy Quarks on Anisotropic Lattices: The Charmonium Spectrum
We present results for the mass spectrum of mesons simulated on
anisotropic lattices where the temporal spacing is only half of the
spatial spacing . The lattice QCD action is the Wilson gauge action plus
the clover-improved Wilson fermion action. The two clover coefficients on an
anisotropic lattice are estimated using mean links in Landau gauge. The bare
velocity of light has been tuned to keep the anisotropic, heavy-quark
Wilson action relativistic. Local meson operators and three box sources are
used in obtaining clear statistics for the lowest lying and first excited
charmonium states of , , , and . The
continuum limit is discussed by extrapolating from quenched simulations at four
lattice spacings in the range 0.1 - 0.3 fm. Results are compared with the
observed values in nature and other lattice approaches. Finite volume effects
and dispersion relations are checked.Comment: 36 pages, 6 figur
Numerical study of O(a) improved Wilson quark action on anisotropic lattice
The improved Wilson quark action on the anisotropic lattice is
investigated. We carry out numerical simulations in the quenched approximation
at three values of lattice spacing (--2 GeV) with the
anisotropy , where and are
the spatial and the temporal lattice spacings, respectively. The bare
anisotropy in the quark field action is numerically tuned by the
dispersion relation of mesons so that the renormalized fermionic anisotropy
coincides with that of gauge field. This calibration of bare anisotropy is
performed to the level of 1 % statistical accuracy in the quark mass region
below the charm quark mass. The systematic uncertainty in the calibration is
estimated by comparing the results from different types of dispersion
relations, which results in 3 % on our coarsest lattice and tends to vanish in
the continuum limit. In the chiral limit, there is an additional systematic
uncertainty of 1 % from the chiral extrapolation.
Taking the central value from the result of the
calibration, we compute the light hadron spectrum. Our hadron spectrum is
consistent with the result by UKQCD Collaboration on the isotropic lattice. We
also study the response of the hadron spectrum to the change of anisotropic
parameter, . We find that the change
of by 2 % induces a change of 1 % in the spectrum for physical quark
masses. Thus the systematic uncertainty on the anisotropic lattice, as well as
the statistical one, is under control.Comment: 27 pages, 25 eps figures, LaTe
Accurate Scale Determinations for the Wilson Gauge Action
Accurate determinations of the physical scale of a lattice action are
required to check scaling and take the continuum limit. We present a high
statistics study of the static potential for the SU(3) Wilson gauge action on
coarse lattices (). Using an improved analysis
procedure we determine the string tension and the Sommer scale (and
related quantities) to 1% accuracy, including all systematic errors. Combining
our results with earlier ones on finer lattices, we present parameterizations
of these quantities that should be accurate to about 1% for . We estimate the \La-parameter of quenched QCD to be \La_\MSb =
247(16) MeV.Comment: 18 pages, LaTeX, 5 ps files (corrected typo in table 5, updated
references
Proofs of Two Conjectures Related to the Thermodynamic Bethe Ansatz
We prove that the solution to a pair of nonlinear integral equations arising
in the thermodynamic Bethe Ansatz can be expressed in terms of the resolvent
kernel of the linear integral operator with kernel
exp(-u(theta)-u(theta'))/cosh[(1/2)(theta-theta')]Comment: 16 pages, LaTeX file, no figures. Revision has minor change
Improving Lattice Quark Actions
We explore the first stage of the Symanzik improvement program for lattice
Dirac fermions, namely the construction of doubler-free, highly improved
classical actions on isotropic as well as anisotropic lattices (where the
temporal lattice spacing, a_t, is smaller than the spatial one). Using field
transformations to eliminate doublers, we derive the previously presented
isotropic D234 action with O(a^3) errors, as well as anisotropic D234 actions
with O(a^4) or O(a_t^3, a^4) errors. Besides allowing the simulation of heavy
quarks within a relativistic framework, anisotropic lattices alleviate
potential problems due to unphysical branches of the quark dispersion relation
(which are generic to improved actions), facilitate studies of lattice
thermodynamics, and allow accurate mass determinations for particles with bad
signal/noise properties, like glueballs and P-state mesons. We also show how
field transformations can be used to completely eliminate unphysical branches
of the dispersion relation. Finally, we briefly discuss future steps in the
improvement program.Comment: Tiny changes to agree with version to appear in Nucl. Phys. B (33
pages, LaTeX, 13 eps files
Entropic C-theorems in free and interacting two-dimensional field theories
The relative entropy in two-dimensional field theory is studied on a cylinder
geometry, interpreted as finite-temperature field theory. The width of the
cylinder provides an infrared scale that allows us to define a dimensionless
relative entropy analogous to Zamolodchikov's function. The one-dimensional
quantum thermodynamic entropy gives rise to another monotonic dimensionless
quantity. I illustrate these monotonicity theorems with examples ranging from
free field theories to interacting models soluble with the thermodynamic Bethe
ansatz. Both dimensionless entropies are explicitly shown to be monotonic in
the examples that we analyze.Comment: 34 pages, 3 figures (8 EPS files), Latex2e file, continuation of
hep-th/9710241; rigorous analysis of sufficient conditions for universality
of the dimensionless relative entropy, more detailed discussion of the
relation with Zamolodchikov's theorem, references added; to appear in Phys.
Rev.
Scaling Laws and Effective Dimension in Lattice SU(2) Yang-Mills Theory with a Compactified Extra Dimension
Monte Carlo simulations are performed in a five-dimensional lattice SU(2)
Yang-Mills theory with a compactified extra dimension, and scaling laws are
studied. Our simulations indicate that as the compactification radius
decreases, the confining phase spreads more and more to the weak coupling
regime, and the effective dimension of the theory changes gradually from five
to four. Our simulations also indicate that the limit with
kept fixed exists both in the confining and deconfining phases if is
small enough, where is the lattice spacing in the four-dimensional
direction. We argue that the color degrees of freedom in QCD are confined only
for , where a rough estimate shows that lies
in the TeV range. Comments on deconstructing extra dimensions are given.Comment: 15 pages, TeX, 5 figure
Charmonium Spectrum from Quenched Anisotropic Lattice QCD
We present a detailed study of the charmonium spectrum using anisotropic
lattice QCD. We first derive a tree-level improved clover quark action on the
anisotropic lattice for arbitrary quark mass. The heavy quark mass dependences
of the improvement coefficients, i.e. the ratio of the hopping parameters
and the clover coefficients , are examined at the tree
level. We then compute the charmonium spectrum in the quenched approximation
employing anisotropic lattices. Simulations are made with
the standard anisotropic gauge action and the anisotropic clover quark action
at four lattice spacings in the range =0.07-0.2 fm. The clover
coefficients are estimated from tree-level tadpole improvement. On
the other hand, for the ratio of the hopping parameters , we adopt both
the tree-level tadpole-improved value and a non-perturbative one. We calculate
the spectrum of S- and P-states and their excitations. The results largely
depend on the scale input even in the continuum limit, showing a quenching
effect. When the lattice spacing is determined from the splitting, the
deviation from the experimental value is estimated to be 30% for the
S-state hyperfine splitting and 20% for the P-state fine structure. Our
results are consistent with previous results at obtained by Chen when
the lattice spacing is determined from the Sommer scale . We also address
the problem with the hyperfine splitting that different choices of the clover
coefficients lead to disagreeing results in the continuum limit.Comment: 43 pages, 49 eps figures, revtex; minor changes, version to appear in
Physical Review
Renormalization group improved action on anisotropic lattices
We study a block spin transformation in the SU(3) lattice gauge theory on
anisotropic lattices to obtain Iwasaki's renormalization group improved action
for anisotropic cases. For the class of actions with plaquette and
rectangular terms, we determine the improvement parameters as functions of the
anisotropy . We find that the program of improvement works well
also on anisotropic lattices. From a study of an indicator which estimates the
distance to the renormalized trajectory, we show that, for the range of the
anisotropy --4, the coupling parameters previously determined
for isotropic lattices improve the theory considerably.Comment: 15 pages, 10 figure
- âŠ