14,374 research outputs found
The PHMC algorithm for simulations of dynamical fermions: II - Performance analysis
We compare the performance of the PHMC algorithm with the one of the HMC
algorithm in practical simulations of lattice QCD. We show that the PHMC
algorithm can lead to an acceleration of numerical simulations. It is
demonstrated that the PHMC algorithm generates configurations carrying small
isolated eigenvalues of the lattice Dirac operator and hence leads to a
sampling of configuration space that is different from that of the HMC
algorithm.Comment: Latex2e file, 6 figures, 31 page
Non-perturbative running of the average momentum of non-singlet parton densities
We determine non-perturbatively the anomalous dimensions of the second moment
of non-singlet parton densities from a continuum extrapolation of results
computed in quenched lattice simulations at different lattice spacings. We use
a Schr\"odinger functional scheme for the definition of the renormalization
constant of the relevant twist-2 operator. In the region of renormalized
couplings explored, we obtain a good description of our data in terms of a
three-loop expression for the anomalous dimensions. The calculation can be used
for exploring values of the coupling where a perturbative expansion of the
anomalous dimensions is not valid a priori. Moreover, our results provide the
non-perturbative renormalization constant that connects hadron matrix elements
on the lattice, renormalized at a low scale, with the experimental results,
renormalized at much higher energy scales.Comment: Latex2e file, 6 figures, 25 pages, Corrected errors on linear fit in
table 2 and discussion on anomalous dimension of f_
How the PHMC algorithm samples configuration space
We show that in practical simulations of lattice QCD with two dynamical light
fermion species the PHMC algorithm samples configuration space differently from
the commonly used HMC algorithm.Comment: 3 pages, 2 figures, LATTICE98 (Algorithms
Constraint on the Low Energy Constants of Wilson Chiral Perturbation Theory
Wilson chiral perturbation theory (WChPT) is the effective field theory
describing the long- distance properties of lattice QCD with Wilson or
twisted-mass fermions. We consider here WChPT for the theory with two light
flavors of Wilson fermions or a single light twisted-mass fermion.
Discretization errors introduce three low energy constants (LECs) into
partially quenched WChPT at O(a^2), conventionally called W'_6, W'_7 and W'_8 .
The phase structure of the theory at non-zero a depends on the sign of the
combination 2W'_6 + W'_8, while the spectrum of the lattice Hermitian
Wilson-Dirac operator depends on all three constants. It has been argued, based
on the positivity of partition functions of fixed topological charge, and on
the convergence of graded group integrals that arise in the epsilon-regime of
ChPT, that there is a constraint on the LECs arising from the underlying
lattice theory. In particular, for W'_6 = W'_7 = 0, the constraint found is
W'_8 \le 0. Here we provide an alternative line of argument, based on mass
inequalities for the underlying partially quenched theory. We find that W'_8
\le 0, irrespective of the values of W'_6 and W'_7. Our constraint implies that
2W'_6 > |W'_8| if the phase diagram is to be described by the first-order
scenario, as recent simulations suggest is the case for some choices of action.Comment: 10 pages, no figure
Non-perturbative renormalization of moments of parton distribution functions
We compute non-perturbatively the evolution of the twist-2 operators
corresponding to the average momentum of non-singlet quark densities. The
calculation is based on a finite-size technique, using the Schr\"odinger
Functional, in quenched QCD. We find that a careful choice of the boundary
conditions, is essential, for such operators, to render possible the
computation. As a by-product we apply the non-perturbatively computed
renormalization constants to available data of bare matrix elements between
nucleon states.Comment: Lattice2003(Matrix); 3 pages, 3 figures. Talk by A.
The eta' meson from lattice QCD
We study the flavour singlet pseudoscalar mesons from first principles using
lattice QCD. With N_f=2 flavours of light quark, this is the so-called eta_2
meson and we discuss the phenomenological status of this. Using maximally
twisted-mass lattice QCD, we extract the mass of the eta_2 meson at two values
of the lattice spacing for lighter quarks than previously discussed in the
literature. We are able to estimate the mass value in the limit of light quarks
with their physical masses.Comment: 16 pages: version accepted for publicatio
Ordering monomial factors of polynomials in the product representation
The numerical construction of polynomials in the product representation (as
used for instance in variants of the multiboson technique) can become
problematic if rounding errors induce an imprecise or even unstable evaluation
of the polynomial. We give criteria to quantify the effects of these rounding
errors on the computation of polynomials approximating the function . We
consider polynomials both in a real variable and in a Hermitian matrix. By
investigating several ordering schemes for the monomials of these polynomials,
we finally demonstrate that there exist orderings of the monomials that keep
rounding errors at a tolerable level.Comment: Latex2e file, 7 figures, 32 page
Complexity and Inapproximability Results for Parallel Task Scheduling and Strip Packing
We study the Parallel Task Scheduling problem with a
constant number of machines. This problem is known to be strongly NP-complete
for each , while it is solvable in pseudo-polynomial time for each . We give a positive answer to the long-standing open question whether
this problem is strongly -complete for . As a second result, we
improve the lower bound of for approximating pseudo-polynomial
Strip Packing to . Since the best known approximation algorithm
for this problem has a ratio of , this result
narrows the gap between approximation ratio and inapproximability result by a
significant step. Both results are proven by a reduction from the strongly
-complete problem 3-Partition
{\eta} and {\eta}' mesons from Nf=2+1+1 twisted mass lattice QCD
We determine mass and mixing angles of eta and eta' states using Nf=2+1+1
Wilson twisted mass lattice QCD. We describe how those flavour singlet states
need to be treated in this lattice formulation. Results are presented for three
values of the lattice spacing, a=0.061 fm, a=0.078 fm and a=0.086 fm, with
light quark masses corresponding to values of the charged pion mass in a range
of 230 to 500 MeV and fixed bare strange and charm quark mass values. We obtain
557(15)(45) MeV for the eta mass (first error statistical, second systematic)
and 44(5) degrees for the mixing angle in the quark flavour basis,
corresponding to -10(5) degrees in the octet-singlet basis.Comment: 28 pages, 9 figures, version to appear in JHEP, extended discussion
of autocorrelation times and comparison to results available in the
literature, added a comment for FS-effects and clarified the description of
our blocking procedur
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