The correct renormalization of the gluon operator in a covariant gauge

Hamberg, Roelof; Neerven, W.L. van

doi:10.1016/0550-3213(92)90593-z

Cited by 114 publications

(131 citation statements)

References 25 publications

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“…[36]. The results by the two groups agreed with each other except in the part of γ (1),n GG proportional to C 2 G , but this discrepancy was solved later [37]. They are given by…”

Section: Anomalous Dimensionssupporting

confidence: 74%

Virtual photon structure functions to the next-to-next-to-leading order in QCD

2007

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We investigate the unpolarized virtual photon structure functions F γ 2 (x, Q 2 , P 2 ) and F γ L (x, Q 2 , P 2 ) in perturbative QCD for the kinematical region Λ 2 ≪ P 2 ≪ Q 2 , where −Q 2 (−P 2 ) is the mass squared of the probe (target) photon and Λ is the QCD scale parameter. Using the framework of the operator product expansion supplemented by the renormalization group method, we derive the definite predictions for the moments of F γ 2 (x, Q 2 , P 2 ) up to the next-to-next-to-leading order (NNLO) (the order αα s ) and for the moments of F γ L (x, Q 2 , P 2 ) up to the next-to-leading order (NLO) (the order αα s ). The NNLO corrections to the sum rule of F γ 2 (x, Q 2 , P 2 ) are negative and found to be 7% ∼ 10% of the sum of the LO and NLO contributions, when P 2 = 1GeV 2 and Q 2 = 30 ∼ 100GeV 2 or P 2 = 3GeV 2 and Q 2 = 100GeV 2 , and the number of active quark flavors n f is three or four. The NLO corrections to F γ L are also negative. The moments are inverted numerically to obtain the predictions for F γ 2 (x, Q 2 , P 2 ) and F γ L (x, Q 2 , P 2 ) as functions of x.

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“…[36]. The results by the two groups agreed with each other except in the part of γ (1),n GG proportional to C 2 G , but this discrepancy was solved later [37]. They are given by…”

Section: Anomalous Dimensionssupporting

confidence: 74%

Virtual photon structure functions to the next-to-next-to-leading order in QCD

2007

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“…Indeed if one considers the simple example of the renormalization of (G a µν ) 2 as discussed in [7], an incorrect value for the β-function would be obtained if one took the naive values for the renormalization which emerged. More detailed discussion of this issue has been given in [14,15,16]. Therefore, we will insert each operator with a non-zero momentum which means that whilst each Green's function has n gluon legs external, it is in fact an (n + 1)-point function due to the extra external momentum.…”

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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“…It is known that the gauge invariant operators O q and O g mix under renormalization with unphysical operators [7,31]. These are BRST variations of some operators or else vanish by the equations of motion.…”

Section: Renormalizationmentioning

confidence: 99%

“…The qualitative quest for understanding scaling violations of the structure functions in terms of asymptotic freedom in QCD [1] soon changed to the quantitative task of reducing theoretical uncertainties due to higher order QCD corrections and the necessary calculations to obtain next-to-leading order (NLO) perturbative QCD predictions were performed in refs. [2,3,4,5,6,7,8,9,10,11,12].…”

Section: Introductionmentioning

confidence: 99%

Deep-inelastic structure functions at two loops

2000

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We present the analytic calculation of the Mellin moments of the structure functions F 2 , F 3 and F L in perturbative QCD up to second order corrections and in leading twist approximation. We calculate the 2-loop contributions to the anomalous dimensions of the singlet and non-singlet operator matrix elements and the 2-loop coefficient functions of F 2 , F 3 and F L . We perform the inverse Mellin transformation analytically and find our results in agreement with earlier calculations in the literature by Zijlstra and van Neerven.

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The correct renormalization of the gluon operator in a covariant gauge

Cited by 114 publications

References 25 publications

Virtual photon structure functions to the next-to-next-to-leading order in QCD

Virtual photon structure functions to the next-to-next-to-leading order in QCD

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

Deep-inelastic structure functions at two loops

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