121 research outputs found

### Quark Effects in the Gluon Condensate Contribution to the Scalar Glueball Correlation Function

One-loop quark contributions to the dimension-four gluon condensate term in
the operator product expansion (OPE) of the scalar glueball correlation
function are calculated in the MS-bar scheme in the chiral limit of $n_f$ quark
flavours. The presence of quark effects is shown not to alter the cancellation
of infrared (IR) singularities in the gluon condensate OPE coefficients. The
dimension-four gluonic condensate term represents the leading power corrections
to the scalar glueball correlator and, therein, the one-loop logarithmic
contributions provide the most important condensate contribution to those QCD
sum-rules independent of the low-energy theorem (the subtracted sum-rules).Comment: latex2e, 6 pages, 7 figures embedded in latex fil

### Staggered Fermion, its Symmetry and Ichimatsu-Patterned Lattice

We investigate exact symmetries of a staggered fermion in D dimensions. The
Dirac operator is reformulated by SO(2D) Clifford algebra. The chiral symmetry,
rotational invariance and parity symmetries are clarified in any dimension.
Local scalar and pseudo-scalar modes are definitely determined, in which we
find non-standard modes. The relation to Ichimatsu-patterned lattice approach
is discussed.Comment: 3 pages, 1 figure, "Talk at Lattice2004(theory), Fermilab, June
21-26, 2004

### Gauge dependence and renormalization of $\tan\beta$ in the MSSM

Well-known and newly developed renormalization schemes for $\tan\beta$ are
analyzed in view of three desirable properties: gauge independence, process
independence, and numerical stability in perturbation theory. Arguments are
provided that no scheme can meet all three requirements, and as an
illustration, a ``No-Go-Theorem'' for the renormalization of $\tan\beta$ is
established. Nevertheless, two particularly attractive schemes emerge. A
discussion about which scheme might be the best compromise in practice is
given.Comment: 20 pages, improved version that was published in PRD D66 (2002

### Gauge dependence of effective action and renormalization group functions in effective gauge theories

The Caswell-Wilczek analysis on the gauge dependence of the effective action
and the renormalization group functions in Yang-Mills theories is generalized
to generic, possibly power counting non renormalizable gauge theories. It is
shown that the physical coupling constants of the classical theory can be
redefined by gauge parameter dependent contributions of higher orders in
$\hbar$ in such a way that the effective action depends trivially on the gauge
parameters, while suitably defined physical beta functions do not depend on
those parameters.Comment: 13 pages Latex file, additional comments in section

### On the notion of potential in quantum gravity

The problem of consistent definition of the quantum corrected gravitational
field is considered in the framework of the $S$-matrix method. Gauge dependence
of the one-particle-reducible part of the two-scalar-particle scattering
amplitude, with the help of which the potential is usually defined, is
investigated at the one-loop approximation. The $1/r^2$-terms in the potential,
which are of zero order in the Planck constant $\hbar,$ are shown to be
independent of the gauge parameter weighting the gauge condition in the action.
However, the $1/r^3$-terms, proportional to $\hbar,$ describing the first
proper quantum correction, are proved to be gauge-dependent. With the help of
the Slavnov identities, their dependence on the weighting parameter is
calculated explicitly. The reason the gauge dependence originates from is
briefly discussed.Comment: LaTex 2.09, 16 pages, 5 ps figure

### Gauge Consistent Wilson Renormalization Group I: Abelian Case

A version of the Wilson Renormalization Group Equation consistent with gauge
symmetry is presented. A perturbative renormalizability proof is established. A
wilsonian derivation of the Callan-Symanzik equation is given.Comment: Latex2e, 39 pages, 3 eps figures. Revised version to appear in Int.
J. Mod. Phy

### Gauge Dependence in Chern-Simons Theory

We compute the contribution to the modulus of the one-loop effective action
in pure non-Abelian Chern-Simons theory in an arbitrary covariant gauge. We
find that the results are dependent on both the gauge parameter ($\alpha$) and
the metric required in the gauge fixing. A contribution arises that has not
been previously encountered; it is of the form $(\alpha / \sqrt{p^2}) \epsilon
_{\mu \lambda \nu} p^\lambda$. This is possible as in three dimensions $\alpha$
is dimensionful. A variant of proper time regularization is used to render
these integrals well behaved (although no divergences occur when the
regularization is turned off at the end of the calculation). Since the original
Lagrangian is unaltered in this approach, no symmetries of the classical theory
are explicitly broken and $\epsilon_{\mu \lambda \nu}$ is handled unambiguously
since the system is three dimensional at all stages of the calculation. The
results are shown to be consistent with the so-called Nielsen identities which
predict the explicit gauge parameter dependence using an extension of BRS
symmetry. We demonstrate that this $\alpha$ dependence may potentially
contribute to the vacuum expectation values of products of Wilson loops.Comment: 17 pp (including 3 figures). Uses REVTeX 3.0 and epsfig.sty
(available from LANL). Latex thric

### Testing universality and the fractional power prescription for the staggered fermion determinant

In [Phys.Rev.Lett.92:162002 (2004), hep-lat/0312025] expressions for the
continuous Euclidean time limits of various lattice fermion determinants were
derived and compared in order to test universality expectations in Lattice QCD.
Here we review that work with emphasis on its relevance for assessing the
fractional power prescription for the determinant in dynamical staggered
fermion simulations. Some new supplementary material is presented; in
particular the status of the "universality anomaly" is clarified: it is shown
to be gauge field-independent and therefore physically inconsequential.Comment: 7 pages, contributed to Lattice2004(plenary

### The three-loop beta-fuction of QCD with the clover action

We calculate, to 3 loops in perturbation theory, the bare $\beta$-function of
QCD, formulated on the lattice with the clover fermionic action. The dependence
of our result on the number of colors $N$, the number of fermionic flavors
$N_f$, as well as the clover parameter $c_{SW}$, is shown explicitly.
A direct outcome of our calculation is the two-loop relation between the bare
coupling constant $g_0$ and the one renormalized in the MS-bar scheme.
Further, we can immediately derive the three-loop correction to the relation
between the lattice $\Lambda$-parameter and $g_0$, which is important in checks
of asymptotic scaling. For typical values of $c_{SW}$, this correction is found
to be very pronounced.Comment: 14 pages, 2 eps figure

### Gauge and parametrization dependence in higher derivative quantum gravity

The structure of counterterms in higher derivative quantum gravity is
reexamined. Nontrivial dependence of charges on the gauge and parametrization
is established. Explicit calculations of two-loop contributions are carried out
with the help of the generalized renormgroup method demonstrating consistency
of the results obtained.Comment: 22 pages, Latex, no figure

- âŠ