19 research outputs found
Dispersion relation and unphysical poles of M\"obius domain-wall fermions in free field theory at finite
We investigate the dispersion relation of M\"obius domain-wall fermions in
free field theory at finite . We find that there are extra poles
of M\"obius domain-wall fermions in addition to the pole which realizes the
physical mode in the continuum limit. The unphysical contribution of these
extra poles could be significant when we introduce heavy quarks. We show in
this report the fundamental properties of these unphysical poles and discuss
the optimal choice of M\"obius parameters to minimize their contribution to
four-dimensional physics.Comment: 8 pages, Proceedings of the 35th International Symposium on Lattice
Field Theory (Lattice 2017
All-mode Renormalization for Tensor Network with Stochastic Noise
In usual (non-stochastic) tensor network calculations, the truncated singular
value decomposition (SVD) is often used for approximating a tensor, and it
causes systematic errors. By introducing stochastic noise in the approximation,
however, one can avoid such systematic errors at the expense of statistical
errors which can be straightforwardly controlled. Therefore in principle, exact
results can be obtained even at finite bond dimension up to the statistical
errors. A previous study of the unbiased method implemented in tensor
renormalization group (TRG) algorithm, however, showed that the statistical
errors for physical quantity are not negligible, and furthermore the
computational cost is linearly proportional to a system volume. In this paper,
we introduce a new way of stochastic noise such that the statistical error is
suppressed, and moreover, in order to reduce the computational cost we propose
common noise method whose cost is proportional to the logarithm of volume. We
find that the method provides better accuracy for the free energy compared with
the truncated SVD when applying to TRG for Ising model on square lattice.
Although the common noise method introduces systematic error originated from a
correlation of noises, we show that the error can be described by a simple
functional form in terms of the number of noises, thus the error can be
straightforwardly controlled in an actual analysis. We also apply the method to
the graph independent local truncation algorithm and show that the accuracy is
further improved.Comment: 34 pages, 19 figures, 2 tables, version published in Phys.Rev.
and channels of decay at the physical point with periodic boundary conditions
We present a lattice calculation of the matrix elements and
amplitudes with both the and 1/2 channels and ,
the measure of direct violation. We use periodic boundary conditions
(PBC), where the correct kinematics of can be achieved via an
excited two-pion final state. To overcome the difficulty associated with the
extraction of excited states, our previous work \cite{Bai:2015nea,RBC:2020kdj}
successfully employed G-parity boundary conditions, where pions are forced to
have non-zero momentum enabling the two-pion ground state to express the
on-shell kinematics of the decay. Here instead we overcome the
problem using the variational method which allows us to resolve the two-pion
spectrum and matrix elements up to the relevant energy where the decay
amplitude is on-shell.
In this paper we report an exploratory calculation of decay
amplitudes and using PBC on a coarser lattice size of
with inverse lattice spacing GeV and the physical
pion and kaon masses. The results are promising enough to motivate us to
continue our measurements on finer lattice ensembles in order to improve the
precision in the near future
Isospin 0 and 2 two-pion scattering at physical pion mass using all-to-all propagators with periodic boundary conditions in lattice QCD
A study of two-pion scattering for the isospin channels, and ,
using lattice QCD is presented. M\"obius domain wall fermions on top of the
Iwasaki-DSDR gauge action for gluons with periodic boundary conditions are used
for the lattice computations which are carried out on two ensembles of gauge
field configurations generated by the RBC and UKQCD collaborations with
physical masses, inverse lattice spacings of 1.023 and 1.378 GeV, and spatial
extents of and 4.58 fm, respectively. The all-to-all propagator method
is employed to compute a matrix of correlation functions of two-pion operators.
The generalized eigenvalue problem (GEVP) is solved for a matrix of correlation
functions to extract phase shifts with multiple states, two pions with a
non-zero relative momentum as well as two pions at rest. Our results for phase
shifts for both and channels are consistent with and the Roy
Equation and chiral perturbation theory, though at this preliminary stage our
errors for are large. An important finding of this work is that GEVP is
useful to obtain signals and matrix elements from multiple states
Lattice QCD and Particle Physics
Contribution from the USQCD Collaboration to the Proceedings of the US Community Study on the Future of Particle Physics (Snowmass 2021)