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⁡β\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 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

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

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