2,594 research outputs found

### Further one-loop results in O(a) improved lattice QCD

Using the Schr\"odinger functional we have computed a variety of renormalized
on-shell correlation functions to one-loop order of perturbation theory. By
studying their approach to the continuum limit we have determined the O($a$)
counterterms needed to improve the quark mass and a number of isovector quark
bilinear operators.Comment: 3 pages Latex using espcrc2.sty, to appear in the conference
proceedings of Lattice '97, Edinburg

### The Schr\"odinger functional running coupling with staggered fermions and its application to many flavor QCD

We discuss the Schr\"odinger functional in lattice QCD with staggered
fermions and relate it, in the classical continuum limit, to the Schr\"odinger
functional regularized with Wilson fermions. We compute the strong coupling
constant defined via the Schr\"odinger functional with staggered fermions at
one loop and show that it agrees with the continuum running coupling constant
in the Schr\"odinger functional formalism. We compute this running coupling in
the ``weak coupling phase'' of many flavor QCD numerically at several values of
the bare coupling and for several system sizes from $L/a=4$ to 12. The results
indicate that the $\beta$-function for 16 flavors has the opposite sign than
for few flavor QCD, in agreement with a recent claim, and with the perturbative
prediction.Comment: 3 pages with 2 ps figures; to appear in the proceedings of Lattice
'97, Edinburgh, Scotland, July 22--26, 199

### The running quark mass in the SF scheme and its two-loop anomalous dimension

The non-perturbatively defined running quark mass introduced by the ALPHA
collaboration is based on the PCAC relation between correlation functions
derived from the Schr\"odinger functional (SF). In order to complete its
definition it remains to specify a number of parameters, including the ratio of
time to spatial extent, $T/L$, and the angle $\theta$ which appears in the
spatial boundary conditions for the quark fields. We investigate the running
mass in perturbation theory and propose a choice of parameters which attains
two desired properties: firstly the two-loop anomalous dimension \d1SF is
reasonably small. This is needed in order to ease matching with the
non-perturbative computations and to achieve a precise determination of the
renormalization group invariant quark mass. Secondly, to one-loop order of
perturbation theory, cut-off effects in the step-scaling function are small in
O($a$) improved lattice QCD.Comment: 17 pages, gzipped tar-fil

### The Schr\"odinger functional in QCD

The Schr\"odinger functional in Wilson's lattice QCD leads to a sensible
classical continuum theory which can be taken as starting point for a
perturbative analysis. In dimensional regularization, the saddle point
expansion of the Schr\"odinger functional is performed to one-loop order of
perturbation theory. The divergences are partly cancelled by the usual coupling
constant and quark mass renormalization. An additional divergence can be
absorbed in a multiplicative renormalization of the quark boundary fields. The
corresponding boundary counterterm being a local polynomial in the fields we
confirm the general expectation expressed by Symanzik~\cite{Symanzik}.Comment: 3 pages in postscript (no figures), talk presented at Lattice '94 in
Bielefeld 9/27--10/1/9

### The chirally rotated Schr\"odinger functional with Wilson fermions and automatic O(a) improvement

A modified formulation of the Schr\"odinger functional (SF) is proposed. In
the continuum it is related to the standard SF by a non-singlet chiral field
rotation and therefore referred to as the chirally rotated SF ($\chi$SF). On
the lattice with Wilson fermions the relation is not exact, suggesting some
interesting tests of universality. The main advantage of the $\chi$SF consists
in its compatibility with the mechanism of automatic O($a$) improvement. In
this paper the basic set-up is introduced and discussed. Chirally rotated SF
boundary conditions are implemented on the lattice using an orbifold
construction. The lattice symmetries imply a list of counterterms, which
determine how the action and the basic fermionic two-point functions are
renormalised and O($a$) improved. As with the standard SF, a logarithmically
divergent boundary counterterm leads to a multiplicative renormalisation of the
fermionic boundary fields. In addition, a finite dimension 3 boundary
counterterm must be tuned in order to preserve the chirally rotated boundary
conditions in the interacting theory. Once this is achieved, O($a$) effects
originating from the bulk action or from insertions of composite operators in
the bulk can be avoided by the mechanism of automatic O($a$) improvement. The
remaining O($a$) effects arise from the boundaries and can be cancelled by
tuning a couple of O($a$) boundary counterterms. The general results are
illustrated in the free theory where the Sheikholeslami-Wohlert term is shown
to affect correlation functions only at O($a^2$), irrespective of its
coefficient.Comment: 51 pages, 2 figures, revised version: improved and extended
discussion of Ward identities in section 3 and of the inclusion of
counterterms in section 5; eliminated some typos, introduced new ones,
results unchange

### Some remarks on O(a) improved twisted mass QCD

Twisted mass QCD (tmQCD) has been introduced as a solution to the problem of
unphysical fermion zero modes in lattice QCD with quarks of the Wilson type. We
here argue that O(a) improvement of the tmQCD action and simple quark bilinear
operators can be more economical than in the standard framework. In particular,
an improved and renormalized estimator of the pion decay constant in
two-flavour QCD is available, given only the Sheikholeslami-Wohlert coefficient
c_sw and an estimate of the critical mass m_c.Comment: Lattice2001(improvement), 3 page

### Non-perturbative results for the coefficients b_m and b_a-b_p in O(a) improved lattice QCD

We determine the improvement coefficients b_m and b_a-bp in quenched lattice
QCD for a range of beta-values, which is relevant for current large scale
simulations. At fixed beta, the results are rather sensitive to the precise
choices of parameters. We therefore impose improvement conditions at constant
renormalized parameters, and the coefficients are then obtained as smooth
functions of g_0^2. Other improvement conditions yield a different functional
dependence, but the difference between the coefficients vanishes with a rate
proportional to the lattice spacing. We verify this theoretical expectation in
a few examples and are therefore confident that O(a) improvement is achieved
for physical quantities. As a byproduct of our analysis we also obtain the
finite renormalization constant which relates the subtracted bare quark mass to
the bare PCAC mass.Comment: 25 pages, 8 figures, minor change at figure

- …