158 research outputs found

### Perturbative improvement of staggered fermions using fat links

We study possibility of improving staggered fermions using various fat links
in order to reduce perturbative corrections to the gauge-invariant staggered
fermion operators. We prove five theorems on SU(3) projection, triviality in
renormalization, multiple SU(3) projections, uniqueness and equivalence. As a
result of these theorems, we show that, at one loop level, the renormalization
of staggered fermion operators is identical between SU(3) projected Fat7 links
and hypercubic links, as long as the action and operators are constructed by
imposing the same perturbative improvement condition. In addition, we propose a
new view of SU(3) projection as a tool of tadpole improvement for the staggered
fermion doublers. As a conclusion, we present alternative choices of
constructing fat links to improve the staggered fermion action and operators,
which deserve further investigation.Comment: 11 page, no figure (typo corrected, references added, conclusion
clarified

### $Re(A_0)$, $Re(A_2)$ and RG evolution for $N_f=3$

We present results of $Re (A_0)$ and $Re (A_2)$ calculated using HYP
staggered fermions on the lattice of $16^3 \times 64$ at $\beta=6.0$. These
results are obtained using leading order chiral perturbation in quenched QCD.
Buras's original RG evolution matrix develops a removable singularity for
$N_f=3$. This subtlety is resolved by finding a finite solution to RG equation
and the results are presented.Comment: 3 pages, 4 figures, contribution to Lattice 2004 International
Symposiu

### The eigSUMR inverter for overlap fermion

We discuss the usage and applicability of deflation methods for the overlap
lattice Dirac operator, focussing on calculating the eigenvalues using a method
similar to the eigCG algorithm used for other Dirac operators. The overlap
operator, which contains several theoretical advantages over other formulations
of lattice Quantum Chromodynamics, is more computationally expensive because it
requires the computation of the matrix sign function. The principle change made
compared to deflation methods for other formulations of lattice QCD is that it
is necessary for best performance to tune or relax the accuracy of the matrix
sign function as the computation proceeds.
We adapt the eigCG algorithm for two inversion algorithms for overlap
fermions, GMRESR(relCG) and GMRESR(relSUMR). Before deflation, the rate of
convergence of these routines in terms of iterations is similar, but, since the
Shifted Unitary Minimal Residual (SUMR) algorithm only requires one call to the
matrix sign function compared to the two calls required for Conjugate Gradient
(CG), SUMR is usually preferred for single inversions of the Dirac operator. We
construct bounds for the required accuracy of the matrix sign function during
the eigenvalue calculation. For the SUMR algorithm, we use a Galerkin
projection to perform the deflation; while for the CG algorithm, we are able to
use a considerably superior spectral pre-conditioner. The superior performance
of the spectral preconditioner, and its need for less accurate eigenvalues,
almost erodes SUMR's advantage over CG as an inversion algorithm.
We see factor of three gains for the inversion algorithm from the deflation
on our small test lattices. There is, however, a significant cost in the
eigenvalue calculation because we cannot relax the accuracy of the matrix sign
function as aggressively when calculating the eigenvalues as we do while
performing the inversions

### Numerical Study of $K^0$--$\bar{K}^0$ Mixing and $B_K$

We have computed $B_K$ with staggered fermions, using two different
methods: both in the one spin trace form and two spin trace form. Renormalized
results in both forms are in good agreement. The numerical simulations were
performed on a $16^3 \times 40$ lattice in full QCD with $\beta = 5.7$. We
also tried an improved wall source method in order to select only the
pseudo-Goldstone bosons and compare the numerical results obtained with those
from the conventional wall source method. We have studied $B_K$ with a series
of non-degenerate quark anti-quark pairs and saw no effect on $B_K$, although
dramatic effects in the chiral limit were seen on the individual terms making
up $B_K$.Comment: 51 pages, latex, 21 figures, uses epsf.sty, submitted to Phys. Rev.

### Overlap fermions on GPUs

We report on our efforts to implement overlap fermions on NVIDIA GPUs using
CUDA, commenting on the algorithms used, implemetation details, and the
performance of our code.Comment: 7 Pages, 2 figures, Lattice 2015(Algorithms and Machines); v2 minor
updates to plot

### Gell-Mann-Oakes-Renner relation for multiple chiral symmetries

As a first step towards considering a chiral perturbation theory for overlap
fermions, we investigate whether there are any ambiguities in the expression
for the pion mass resulting from multiple chiral symmetries. The concern is
that, calculating the conserved current for Ginsparg Wilson chiral symmetries
in the usual way, different expressions of the chiral symmetries lead to
different currents. This implies an ambiguity in the definition of the pion and
pion decay constant for all Ginsparg-Wilson expressions of the Dirac operator,
including the overlap operator. We use a renormalisation group mapping
procedure to consider local chiral symmetry transformations for a continuum
Ginsparg-Wilson "Dirac-operator." We find that this naturally leads to an
expression for the conserved current that differs from the standard expression
by cut-off artefacts, but is independent of which of the Ginsparg-Wilson
symmetries is chosen. We recover the standard expressions for the massive Dirac
operator, propagator, and chiral condensate. With this in place, we proceed to
calculate the pion mass in the mapped theory as a function of the quark mass,
and discover a unique expression for $F_\pi$ and $m_\pi$, recovering the usual
Gell-Mann-Oakes-Renner relation, baring the substitution of the chiral
condensate with its modified value. We hypothesise that the argument can be
carried directly over to the lattice theory.Comment: Lattice 2011 (Chiral symmetry), 7 page

### Current Status of Indirect CP Violation in Neutral Kaon System

In the standard model (SM), the CP violation is introduced through a single
phase in the CKM matrix. The neutral kaon system is one of the most precise
channels to test how the SM theory describes the experiment data such as
$\epsilon_K$ accurately. The indirect CP violation is parametrized into
$\epsilon_{K}$, which can be calculated directly using lattice QCD. In this
calculation, the largest uncertainty comes from two sources: one is $\hat{B}_K$
and the other is $V_{cb}$. We use the lattice results of $\hat{B}_K$ and
exclusive $V_{cb}$ to calculate the theoretical estimate of $\epsilon_K$, which
turns out to be $3.1\sigma$ away from its experimental value. Here, the error
is evaluated using the standard error propagation method.Comment: 7 pages, 2 figures, Lattice 2012 conference proceedin

### Eradication of singularities in the next-to-leading order RG evolution for the \Delta S = 1 effective Hamiltonian with 3 quark flavours

We consider the renormalization group evolution for the operators in the
$\Delta S=1$ effective Hamiltonian with 3 active quark flavors, which is needed
in the numerical analysis of data sets for $\epsilon'/\epsilon$ calculated in
lattice QCD. Singularities are present in the original solution of Buras et al.
at next-to-leading order. We show how these can be eradicated through a method
of analytic continuation to obtain the correct finite solution in this case.
Furthermore, we trace the origin of the singularities to a breakdown of the
approach of Buras et al. in the 3 flavour case, and show how it can be
rectified so that singularitites are absent from the beginning.Comment: 7 pages, presented at the XXV International Symposium on Lattice
Field Theory, July 30 - August 4 2007, Regensbur

### The conserved axial current in the presence of multiple chiral symmetries

In response to a recent work by Mandula, we investigate whether there are any
ambiguities in the expression for the pion mass resulting from multiple chiral
symmetries. If the conserved current for Ginsparg Wilson chiral symmetries is
calculated in the usual way, different expressions of the chiral symmetry lead
to different currents. This implies an ambiguity in the definition of the pion
and pion decay constant for all Ginsparg-Wilson expressions of the Dirac
operator, including the overlap operator on the lattice (although all these
currents would have the same continuum limit). We use a renormalisation group
mapping procedure to consider local chiral symmetry transformations for a
continuum Ginsparg-Wilson "Dirac-operator." We find that this naturally leads
to an expression for the conserved current which is independent of which of the
Ginsparg-Wilson symmetries is chosen. We recover the standard expressions for
the massive Dirac operator, propagator, and chiral condensate. Our main
conclusion is that, when the currents are properly constructed and consistently
applied, no observable depends on which Mandula symmetry is used; at least in
these continuum Ginsparg-Wilson theories. We will consider whether the same
argument applies to lattice theories in a subsequent paper.Comment: 8 page

### $B_7$, $B_8$ and chiral Ward identities

We present recent progress in understanding weak matrix elements on the
lattice. We use HYP staggered fermions in quenched QCD to study numerically
various properties of the $K^+\to\pi^+$ amplitudes of the electroweak penguin
operators $Q_7$ and $Q_8$. We check chiral Ward identities to probe the
validity of using improved staggered fermions in the calculation of weak matrix
elements. We address the issue of mixing with unphysical lower dimension
operators, which causes a divergent term in the case of the $\Delta I = 1/2$
amplitudes. We propose a particular subtraction method as the best choice. We
also measure the gold-plated ratio $R$ originally suggested by Becirevic and
Villadoro.Comment: 6 pages, 5 figures, lattice 2005 proceedin

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