912 research outputs found
Preliminary lattice study of scattering
We deliver the realistic ab initio lattice investigations of
scattering. In the Asqtad-improved staggered dynamical fermion formulation, we
carefully measure four-point function in the channel by
moving wall sources without gauge fixing, and clearly find an attractive
interaction in this channel, which is in agreement with the theoretical
predictions. An essential ingredient in our lattice calculation is to properly
treat the disconnected diagram. Moreover, we explain the difficulties of these
lattice calculations, and discuss the way to improve the statistics. Our
lattice investigations are carried out with the MILC gauge configuration
at lattice spacing ~fm.Comment: Accepted for publication in Commun. Theor. Phy
Lattice calculation of meson
We study the meson in 2+1 flavor QCD with sufficiently light
quarks. Using numerical simulation we measure the point-to-point
correlators in the "Asqtad" improved staggered fermion formulation. We analyze
those correlators using the rooted staggered chiral perturbation theory
(rSPT), particular attention is paid to the bubble contribution. After
chiral extrapolation, we obtain the physical mass with MeV,
which is within the recent experimental value MeV. These numerical
simulations are carried out with MILC 2+1 flavor gauge configurations at
lattice spacing fm.Comment: Accepted in Chinese Physics
Preliminary lattice study of meson decay width
We report an exploratory lattice investigation of meson decay width
using s-wave scattering phase for isospin I=0 pion-pion () system.
Rummukainen-Gottlieb formula is used to estimate the scattering phase, which
demonstrate the presence of a resonance around meson. Using the
effective range formula we extract the effective coupling
constant as GeV, which is consistent with
theoretical predictions. The estimated decay width is about MeV.
These simulations are carried out on a MILC gauge configuration
with the flavor of the "Asqtad" improved staggered dynamical sea
quarks at and the lattice spacing fm.Comment: Remove some typos and make it concise and easily understan
Studying meson with a MILC fine lattice
Using the lattice simulations in the Asqtad-improved staggered fermion
formulation we compute the point-to-point correlators, which are
analyzed by the rooted staggered chiral perturbation theory (rSPT). After
chiral extrapolation, we secure the physical mass with MeV,
which is in agreement with the BES experimental results. The computations are
performed using a MILC 2+1 flavor fine gauge configuration at a lattice spacing
of fm.Comment: Remove some typo
Higher Codimensional Alpha Invariants and Characterization of Projective Spaces
We generalize the definition of alpha invariant to arbitrary codimension. We
also give a lower bound of these alpha invariants for K-semistable Q-Fano
varieties and show that we can characterize projective spaces among all
K-semistable Fano manifolds in terms of higher codimensional alpha invariants.
Our results demonstrate the relation between alpha invariants of any
codimension and volumes of Fano manifolds in the characterization of projective
spaces.Comment: 14 pages. Second version: deleted Proposition 3.7 due to a gap in the
proof and modified corresponding statements throughout the article. To appear
in Internat. J. Mat
Lattice QCD study on meson decay width
We deliver an exploratory lattice QCD examination of the meson
decay width with the help of the p-wave scattering phase of
pion-kaon () system in the isospin channel, which are extracted
by the modified Rummukainen-Gottlieb formula for two-particle system with
arbitrary mass, and it clearly reveals the entity of a resonance at a mass
around meson mass. The effective range formula is applied to
describe the energy dependence of the scattering phase and we obtain the
effective coupling constant as , and subsequently achieve the decay width to be MeV,
which is in reasonable accordance with the current experiment. Our lattice
investigations are conducted on a MILC full QCD gauge
configuration at and the lattice
spacing fm.Comment: Correct some typos and replace some figures with high quality one
Forbidden pairs for equality of edge-connectivity and minimum degree
Let be a class of given graphs. A graph is said to be
-free if contains no induced copies of for any . In this article, we characterize all pairs of graphs
such that every connected -free graph has the same edge-connectivity
and minimum degree
A relaxation of the strong Bordeaux Conjecture
Let be non-negative integers. A graph is
-colorable if the vertex set can be partitioned into
sets , such that the subgraph , induced by
, has maximum degree at most for . Let
denote the family of plane graphs with neither adjacent 3-cycles
nor -cycle. Borodin and Raspaud (2003) conjectured that each graph in
is -colorable. In this paper, we prove that each graph
in is -colorable, which improves the results by Xu
(2009) and Liu-Li-Yu (2014+).Comment: 14 page
Hadronic coupling constants of in lattice QCD
We investigate the coupling constant for the hadronic
decay only using the relevant three-point function, which is
evaluated by the moving-wall source technique with a pretty good
noise-to-signal ratio. This simulation is carried out on a MILC
gauge configuration with flavor of the "Asqtad" improved staggered
dynamical sea quarks at the lattice spacing fm. Our estimated
value for this given MILC fine lattice gauge ensemble
GeV.Comment: Submitted to Chinese Physics
Robust Bayesian Synthetic Likelihood via a Semi-Parametric Approach
Bayesian synthetic likelihood (BSL) is now a well established method for
performing approximate Bayesian parameter estimation for simulation-based
models that do not possess a tractable likelihood function. BSL approximates an
intractable likelihood function of a carefully chosen summary statistic at a
parameter value with a multivariate normal distribution. The mean and
covariance matrix of this normal distribution are estimated from independent
simulations of the model. Due to the parametric assumption implicit in BSL, it
can be preferred to its non-parametric competitor, approximate Bayesian
computation, in certain applications where a high-dimensional summary statistic
is of interest. However, despite several successful applications of BSL, its
widespread use in scientific fields may be hindered by the strong normality
assumption. In this paper, we develop a semi-parametric approach to relax this
assumption to an extent and maintain the computational advantages of BSL
without any additional tuning. We test our new method, semiBSL, on several
challenging examples involving simulated and real data and demonstrate that
semiBSL can be significantly more robust than BSL and another approach in the
literature.Comment: 37 pages Latex; the paper has been re-organised, moved section 4 and
5 to appendices, moved less important example figures to appendices, added
"sensitivity to n" section to appendices, added a shrinkage example to
appendices, typos and references correcte
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