Pure & Applied Mathematics (Scholarly Publications)
http://hdl.handle.net/2262/172
Pure & Applied Mathematics (Scholarly Publications)2017-02-25T11:59:36ZSymanzik Iimprovement of the gradient flow in lattice gauge theories
http://hdl.handle.net/2262/78727
Symanzik Iimprovement of the gradient flow in lattice gauge theories
SINT, STEFAN
We apply the Symanzik improvement progra-
mme to the 4
+
1-dimensional local re-formulation of the
gradient flow in pure
SU
(
N
)
lattice gauge theories. We show
that the classical nature of the flow equation allows one to
eliminate all cutoff effects at
O
(
a
2
)
, which originate either
from the discretised gradient flow equation or from the gradi-
ent flow observable. All the remaining
O
(
a
2
)
effects can be
understood in terms of local counterterms at the zero flow-
time boundary. We classify these counterterms and provide
a complete set as required for on-shell improvement. Com-
pared to the 4-dimensional pure gauge theory only a single
additional counterterm is required, which corresponds to a
modified initial condition for the flow equation. A consis-
tency test in perturbation theory is passed and allows one to
determine all counterterm coefficients to lowest non-trivial
order in the coupling.
PUBLISHED
2015-01-01T00:00:00ZFlavour symmetry restoration and kaon weak matrix elements in quenched twisted mass QCD
http://hdl.handle.net/2262/78726
Flavour symmetry restoration and kaon weak matrix elements in quenched twisted mass QCD
SINT, STEFAN
We simulate two variants of quenched twisted mass QCD (tmQCD), with degenerate Wilson quarks of masses equal to or heavier than half the strange quark mass. We use Ward identities in order to measure the twist angles of the theory and thus check the quality of the tuning of mass parameters to a physics condition which stays constant as the lattice spacing is varied. Flavour symmetry breaking in tmQCD is studied in a framework of two fully twisted and two standard Wilson quark flavours, tuned to be degenerate in the continuum. Comparing pseudoscalar masses, obtained from connected quark diagrams made of tmQCD and/or standard Wilson quark propagators, we confirm that flavour symmetry breaking effects, which are at most 5%, decrease as we approach the continuum limit. We also compute the pseudoscalar decay constant in the continuum limit, with reduced systematics. As a consequence of improved tuning of the mass parameters at β=6.1β=6.1, we reanalyze our previous BKBK results. Our main phenomenological findings are r0fK=0.421(7)r0fK=0.421(7) and View the MathML sourceBˆK=0.735(71).
PUBLISHED; authors appear in alphabetical order
2007-01-01T00:00:00ZA precise determination of B_K in quenched QCD
http://hdl.handle.net/2262/78725
A precise determination of B_K in quenched QCD
SINT, STEFAN
The
B
K
parameter is computed in quenched lattice QCD with Wilson twisted mass fermions. Two
variants of tmQCD are used; in both of them the relevant
S
=
2 four-fermion operator is renormalised
multiplicatively. The renormalisation adopted is non-perturbative, with a Schrödinger functional renormal-
isation condition. Renormalisation group running is also non-perturbative, up to very high energy scales.
In one of the two tmQCD frameworks the computations have been performed at the physical
K
-meson
mass, thus eliminating the need of mass extrapolations. Simulations have been performed at several lattice
spacings and the continuum limit was reached by combining results from both tmQCD regularisations. Fi-
nite volume effects have been partially checked and turned out to be small. Exploratory studies have also
been performed with non-degenerate valence flavours. The final result for the RGI bag parameter, with all
sources of uncertainty (except quenching) under control, is
ˆ
B
K
=
0
.
789
±
0
.
046.
2006-01-01T00:00:00ZDetermination of the QCD Î Parameter and the Accuracy of Perturbation Theory at High Energies
http://hdl.handle.net/2262/78718
Determination of the QCD Î Parameter and the Accuracy of Perturbation Theory at High Energies
SINT, STEFAN
We discuss the determination of the strong coupling
α
MS
ð
m
Z
Þ
or, equivalently, the QCD
Λ
parameter. Its
determination requires the use of perturbation theory in
α
s
ð
μ
Þ
in some scheme
s
and at some energy scale
μ
.
The higher the scale
μ
, the more accurate perturbation theory becomes, owing to asymptotic freedom. As
one step in our computation of the
Λ
parameter in three-flavor QCD, we perform lattice computations in a
scheme that allows us to nonperturbatively reach very high energies, corresponding to
α
s
¼
0
.
1
and below.
We find that (continuum) perturbation theory is very accurate there, yielding a 3% error in the
Λ
parameter,
while data around
α
s
≈
0
.
2
are clearly insufficient to quote such a precision. It is important to realize that
these findings are expected to be generic, as our scheme has advantageous properties regarding the
applicability of perturbation theory.
2016-01-01T00:00:00Z