Trace and dilatation anomalies in gauge theories

Collins, John C.; Duncan, Anthony; Joglekar, Satish D.

doi:10.1103/physrevd.16.438

Cited by 469 publications

(432 citation statements)

References 23 publications

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“…Including the respective contributions from the β-function allows one to compare the final expressions for the anomalous dimension of each operator. The anomalous dimension for O 62 is new and is the same as the one loop Yang-Mills β-function, [24,25].…”

Section: One Loop Renormalizationmentioning

confidence: 99%

Classification and one loop renormalization of dimension six and eight operators in quantum gluodynamics

Gracey

2002

Nuclear Physics B

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Section: One Loop Renormalizationmentioning

confidence: 99%

Classification and one loop renormalization of dimension six and eight operators in quantum gluodynamics

Gracey

2002

Nuclear Physics B

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“…The current J(x) is the lowest-order version of the operator β(α)G 2 (x), which is renormalization-group invariant for chiral quarks [3,4]. As first noted in [5,6], the one-loop gluon condensate contribution to (1)…”

mentioning

confidence: 99%

“…(3). Modification of these one-loop results for a change of operator basis to β(α)G 2 from αG 2 (in the operator J and/or in the OPE) can be achieved by algebraic rearrangements.…”

mentioning

confidence: 99%

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

Harnett

Steele

2004

J. High Energy Phys.

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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 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).The QCD correlation function of scalar gluonic currentsis used to study the properties of scalar gluonium via QCD sum-rule techniques [1,2]. The current J(x) is the lowest-order version of the operator β(α)G 2 (x), which is renormalization-group invariant for chiral quarks [3,4]. As first noted in [5,6], the one-loop gluon condensate contribution to (1)where {a 0 , b 0 , b 1 } are numerical coefficients (see (26)- (28) below), represents the leading condensate contribution to those sum-rules independent of the low-energy theorem [7], and so provide important nonperturbative effects within sum-rule analyses of scalar glueballs. The one-loop coefficients b 0 and b 1 were evaluated in [5] in the absence of quark effects (i.e. the n f = 0 limit). As these n f = 0 gluon condensate effects have been used in a number of sum-rule analyses where the effects of three quark flavours have been included in the perturbative part [2], it is necessary to extend the results of [5] to enable self-consistent sum-rule analyses in the presence of n f chiral quarks. *

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“…We emphasize, however, that there is abuse of notation in (29) since the field strength early eighties from lattice gauge theories [32,33,34]. The most recent value for the non-natural case of the pure SU(2) gauge theory is given by [36] O 4 ≈ 0.15 GeV 4 (30) and was calculated from field strength correlation functions (for a recent review of the method see e.g. [37]).…”

Section: Numerical Results For the Z(2) Vortex Induced Gluon Condensatementioning

confidence: 99%

“…Therefore the function C ψ 0 (q 2 ) in (19) does depend on the state (see below and [29] for an illustration). This fact is just a reflection of the scale anomaly [30]. The other Wilson coefficient functions are defined in (18) without reference to a particular state.…”

Section: The Operator Product Expansionmentioning

confidence: 99%

Gauge invariant Z(2) vortex vacuum textures and the SU(2) gluon condensate

2001

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For SU (2) lattice gauge theory, a new SO(3) cooling procedure is proposed which removes the SU (2)/Z(2) coset fields from the lattice configurations and reveals a Z(2) vortex vacuum texture different from the P -vortex content obtained in the maximal center gauge. Cooling can be restricted in a renormalization group invariant way by a parameter controlling the remaining SO(3) action density. A gauge invariant Z(2) vortex vacuum emerges asymptotically if cooling is not restricted. This "vortex texture" does not support the string tension σ or a finite part of it. The SU (2) action density associated with the new Z(2) vortex texture has a smooth extrapolation to the continuum limit. We propose an interpretation as a mass dimension four condensate related to the gluon condensate featuring in the operator product expansion.

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Trace and dilatation anomalies in gauge theories

Cited by 469 publications

References 23 publications

Classification and one loop renormalization of dimension six and eight operators in quantum gluodynamics

Classification and one loop renormalization of dimension six and eight operators in quantum gluodynamics

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

Gauge invariant Z(2) vortex vacuum textures and the SU(2) gluon condensate

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