146 research outputs found
A note on Neuberger's double pass algorithm
We analyze Neuberger's double pass algorithm for the matrix-vector
multiplication R(H).Y (where R(H) is (n-1,n)-th degree rational polynomial of
positive definite operator H), and show that the number of floating point
operations is independent of the degree n, provided that the number of sites is
much larger than the number of iterations in the conjugate gradient. This
implies that the matrix-vector product can be approximated to very high precision with sufficiently large n,
without noticeably extra costs. Further, we show that there exists a threshold
such that the double pass is faster than the single pass for , where for most platforms.Comment: 18 pages, v3: CPU time formulas are obtained, to appear in Physical
Review
Quenched chiral logarithms in lattice QCD with exact chiral symmetry
We examine quenched chiral logarithms in lattice QCD with overlap Dirac
quark. For 100 gauge configurations generated with the Wilson gauge action at on the lattice, we compute quenched quark
propagators for 12 bare quark masses. The pion decay constant is extracted from
the pion propagator, and from which the lattice spacing is determined to be
0.147 fm. The presence of quenched chiral logarithm in the pion mass is
confirmed, and its coefficient is determined to be , in agreement with the theoretical estimate in quenched chiral perturbation
theory. Further, we obtain the topological susceptibility of these 100 gauge
configurations by measuring the index of the overlap Dirac operator. Using a
formula due to exact chiral symmetry, we obtain the mass in quenched
chiral perturbation theory, Mev, and an estimate
of , which is in good agreement with that
determined from the pion mass.Comment: 24 pages, 6 EPS figures; v2: some clarifications added, to appear in
Physical Review
Perturbation Calculation of the Axial Anomaly of a Ginsparg-Wilson lattice Dirac operator
A recent proposal suggests that even if a Ginsparg-Wilson lattice Dirac
operator does not possess any topological zero modes in
topologically-nontrivial gauge backgrounds, it can reproduce correct axial
anomaly for sufficiently smooth gauge configurations, provided that it is
exponentially-local, doublers-free, and has correct continuum behavior. In this
paper, we calculate the axial anomaly of this lattice Dirac operator in weak
coupling perturbation theory, and show that it recovers the topological charge
density in the continuum limit.Comment: 25 pages, v2: calculation up to O(g^4) for nonabelian gauge
backgroun
Generalized Ginsparg-Wilson algebra and index theorem on the lattice
Recent studies of the topological properties of a general class of lattice
Dirac operators are reported. This is based on a specific algebraic realization
of the Ginsparg-Wilson relation in the form
where stands for a non-negative integer.
The choice corresponds to the commonly discussed Ginsparg-Wilson relation
and thus to the overlap operator. It is shown that local chiral anomaly and the
instanton-related index of all these operators are identical. The locality of
all these Dirac operators for vanishing gauge fields is proved on the basis of
explicit construction, but the locality with dynamical gauge fields has not
been established yet. We suggest that the Wilsonian effective action is
essential to avoid infrared singularities encountered in general perturbative
analyses.Comment: 11 pages. Talk given at APCTP-Nankai Joint Symposium on Lattice
Statistics and Mathematical Physics, Tianjin, China, 8-11 October, 2001. To
be published in the Proceedings and in Int. Jour. Mod. Phys.
Domain wall fermion and CP symmetry breaking
We examine the CP properties of chiral gauge theory defined by a formulation
of the domain wall fermion, where the light field variables and
together with Pauli-Villars fields and are utilized. It is shown
that this domain wall representation in the infinite flavor limit is
valid only in the topologically trivial sector, and that the conflict among
lattice chiral symmetry, strict locality and CP symmetry still persists for
finite lattice spacing . The CP transformation generally sends one
representation of lattice chiral gauge theory into another representation of
lattice chiral gauge theory, resulting in the inevitable change of propagators.
A modified form of lattice CP transformation motivated by the domain wall
fermion, which keeps the chiral action in terms of the Ginsparg-Wilson fermion
invariant, is analyzed in detail; this provides an alternative way to
understand the breaking of CP symmetry at least in the topologically trivial
sector. We note that the conflict with CP symmetry could be regarded as a
topological obstruction. We also discuss the issues related to the definition
of Majorana fermions in connection with the supersymmetric Wess-Zumino model on
the lattice.Comment: 33 pages. Note added and a new reference were added. Phys. Rev.D (in
press
Mass dependence of the hairpin vertex in quenched QCD
The pseudoscalar ``hairpin'' vertex (i.e. quark-disconnected vertex) plays a
key role in quenched chiral perturbation theory. Direct calculations using
lattice simulations find that it has a significant dependence on quark mass. I
show that this mass dependence can be used to determine the quenched
Gasser-Leutwyler constant L5. This complements the calculation of L5 using the
mass dependence of the axial decay constant of the pion. In an appendix, I
discuss power counting for quenched chiral perturbation theory and describe the
particular scheme used in this paper.Comment: 12 pages, 4 figures. Version to appear in Phys. Rev. D. Central
result unchanged, but explanation of calculation improved and minor errors
corrected. New appendix discusses power counting schemes in quenched chiral
perturbation theor
Light-Front Approach for Pentaquark Strong Decays
Assuming the two diquark structure for the pentaquark state as advocated in
the Jaffe-Wilczek model, we study the strong decays of light and heavy
parity-even pentaquark states using the light-front quark model in conjunction
with the spectator approximation. The narrowness of the Theta width is ascribed
to the p-wave configuration of the diquark pair. Taking the Theta width as a
benchmark, we estimate the rates of the strong decays Xi_{3/2}-- to Xi- pi-,
Sigma- K-, Sigma_{5c}0 to D_s- p, D_{s0}*- p and Xi_{5c}0 to D_s- Sigma+,
D_{s0}^{*-} Sigma+ with Sigma_{5c} Xi_{5c} being antisextet charmed pentaquarks
and D_{s0}* a scalar strange charmed meson. The ratio of Gamma(P_c to Baryon
D_{s0}*)/Gamma(P_c to Baryon D_s) is very useful for verifying the parity of
the antisextet charmed pentaquark P_c. It is expected to be of order unity for
an even parity P_c and much less than one for an odd parity pentaquark.Comment: 24 pages, 2 figure
Chiral Logs in Quenched QCD
The quenched chiral logs are examined on a lattice with
Iwasaki gauge action and overlap fermions. The pion decay constant is
used to set the lattice spacing, . With pion mass as low
as , we see the quenched chiral logs clearly in
and , the pseudoscalar decay constant. We analyze the data
to determine how low the pion mass needs to be in order for the quenched
one-loop chiral perturbation theory (PT) to apply. With the constrained
curve-fitting method, we are able to extract the quenched chiral log parameter
together with other low-energy parameters. Only for do we obtain a consistent and stable fit with a constant
which we determine to be 0.24(3)(4) (at the chiral scale ). By comparing to the lattice, we estimate the
finite volume effect to be about 2.7% for the smallest pion mass. We also
fitted the pion mass to the form for the re-summed cactus diagrams and found
that its applicable region is extended farther than the range for the one-loop
formula, perhaps up to MeV. The scale independent
is determined to be 0.20(3) in this case. We study the quenched
non-analytic terms in the nucleon mass and find that the coefficient
in the nucleon mass is consistent with the prediction of one-loop PT\@.
We also obtain the low energy constant from . We conclude from
this study that it is imperative to cover only the range of data with the pion
mass less than in order to examine the chiral behavior of
the hadron masses and decay constants in quenched QCD and match them with
quenched one-loop PT\@.Comment: 37 pages and 24 figures, pion masses are fitted to the form for the
re-summed cactus diagrams, figures added, to appear in PR
Study of Bc --> J/psi pi, etac pi decays with perturbative QCD approach
The Bc --> J/psi pi, etac pi decays are studied with the perturbative QCD
approach. It is found that form factors and branching ratios are sensitive to
the parameters w, v, f_J/psi and f_etac, where w and v are the parameters of
the charmonium wave functions for Coulomb potential and harmonic oscillator
potential, respectively, f_J/psi and f_etac are the decay constants of the
J/psi and etac mesons, respectively. The large branching ratios and the clear
signals of the final states make the Bc --> J/psi pi, etac pi decays to be the
prospective channels for measurements at the hadron collidersComment: 21 pages, revtex
Studying Paths of Participation in Viral Diffusion Process
Authors propose a conceptual model of participation in viral diffusion
process composed of four stages: awareness, infection, engagement and action.
To verify the model it has been applied and studied in the virtual social chat
environment settings. The study investigates the behavioral paths of actions
that reflect the stages of participation in the diffusion and presents
shortcuts, that lead to the final action, i.e. the attendance in a virtual
event. The results show that the participation in each stage of the process
increases the probability of reaching the final action. Nevertheless, the
majority of users involved in the virtual event did not go through each stage
of the process but followed the shortcuts. That suggests that the viral
diffusion process is not necessarily a linear sequence of human actions but
rather a dynamic system.Comment: In proceedings of the 4th International Conference on Social
Informatics, SocInfo 201
- âŠ