375 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
Nucleon mass, sigma term and lattice QCD
We investigate the quark mass dependence of the nucleon mass M_N. An
interpolation of this observable, between a selected set of fully dynamical
two-flavor lattice QCD data and its physical value, is studied using
relativistic baryon chiral perturbation theory up to order p^4. In order to
minimize uncertainties due to lattice discretization and finite volume effects
our numerical analysis takes into account only simulations performed with
lattice spacings a5. We have also restricted ourselves to
data with m_pi<600 MeV and m_sea=m_val. A good interpolation function is found
already at one-loop level and chiral order p^3. We show that the
next-to-leading one-loop corrections are small. From the p^4 numerical analysis
we deduce the nucleon mass in the chiral limit, M_0 approx 0.88 GeV, and the
pion-nucleon sigma term sigma_N= (49 +/- 3) MeV at the physical value of the
pion mass.Comment: 12 pages, 4 figures, revised journal versio
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
Measuring the aspect ratio renormalization of anisotropic-lattice gluons
Using tadpole inproved actions we investigate the consistency between
different methods of measuring the aspect ratio renormalization of
anisotropic-lattice gluons for bare aspect ratios \chi_0=4,6,10 and inverse
lattice spacing in the range a_s^{-1}=660-840 MeV. The tadpole corrections to
the action, which are established self-consistently, are defined for two cases,
mean link tadpoles in Landau gauge and gauge invariant mean plaquette tadpoles.
Parameters in the latter case exhibited no dependence on the spatial lattice
size, L, while in the former, parameters showed only a weak dependence on L
easily extrapolated to L=\infty.
The renormalized anisotropy \chi_R was measured using both the torelon
dispersion relation and the sideways potential method. We found good agreement
between these different approaches. Any discrepancy was at worst 3-4% which is
consistent with the effect of lattice artifacts that for the torelon we
estimate as O(\a_Sa_s^2/R^2) where R is the flux-tube radius.
We also present some new data that suggests that rotational invariance is
established more accurately for the mean-link action than the plaquette action.Comment: LaTeX 18 pages including 7 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
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 much more accurately than previously possible. For pure SU(3) we
find that the coupling scales on the percent level for .Comment: 47 pages, incl. 4 figures in LaTeX [Added remarks on correlated vs.
uncorrelated fits in sect. 4; corrected misprints; updated references.
Two flavors of dynamical quarks on anisotropic lattices
We report on our study of two-flavor full QCD on anisotropic lattices using
-improved Wilson quarks coupled with an RG-improved glue. The bare gauge
and quark anisotropies corresponding to the renormalized anisotropy
are determined as functions of and , which
covers the region of spatial lattice spacings --0.16 fm and
--0.9. The calibrations of the bare anisotropies are
performed with the Wilson loop and the meson dispersion relation at 4 lattice
cutoffs and 5--6 quark masses. Using the calibration results we calculate the
meson mass spectrum and the Sommer scale . We confirm that the values of
calculated for the calibration using pseudo scalar and vector meson
energy momentum dispersion relation coincide in the continuum limit within
errors. This work serves to lay ground toward studies of heavy quark systems
and thermodynamics of QCD including the extraction of the equation of state in
the continuum limit using Wilson-type quark actions.Comment: 16 pages, 23 figures, Version accepted for publication in Physical
Review
Quenched charmonium spectrum
We study charmonium using the standard relativistic formalism in the quenched
approximation, on a set of lattices with isotropic lattice spacings ranging
from 0.1 to 0.04 fm. We concentrate on the calculation of the hyperfine
splitting between eta_c and J/psi, aiming for a controlled continuum
extrapolation of this quantity. The splitting extracted from the
non-perturbatively improved clover Dirac operator shows very little dependence
on the lattice spacing for fm. The dependence is much stronger for
Wilson and tree-level improved clover operators, but they still yield
consistent extrapolations if sufficiently fine lattices, fm (), are used. Our result for the hyperfine splitting is
77(2)(6) MeV (where Sommer's parameter, r_0, is used to fix the scale). This
value remains about 30% below experiment. Dynamical fermions and OZI-forbidden
diagrams both contribute to the remainder. Results for the eta_c and J/psi wave
functions are also presented.Comment: 22 pages, 7 figure
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