A method of gauge-invariant regularization

Ashmore, Jonathan

doi:10.1007/bf02824407

Cited by 483 publications

(206 citation statements)

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“…(2.11) a regularization procedure and a renormalization scheme need to be selected. We choose dimensional regularization [46][47][48][49] and the modified [50] minimal subtraction [51] scheme, MS, the standard choice for modern higher-order calculations in QCD. For this choice the running coupling in D = 4 − 2ε dimensions evolves according to where β n denote the usual four-dimensional expansion coefficients of the beta function in QCD [52][53][54][55][56][57], β 0 = 11 − 2/3 n f etc, with n f representing the number of active quark flavours.…”

Section: General Formalismmentioning

confidence: 99%

“…For brevity suppressing the function arguments for the rest of this section, the expansion of the 'master formula' (2.19) to the third order in the strong coupling α s can by written as The factor S ε = exp(ε{ln(4π) − γ e }), where γ e denotes the Euler-Mascheroni constant, is an artefact of dimensional regularization [46][47][48][49] kept out of the coefficient functions and anomalous dimensions in the MS scheme [50]. δ k collects the quark charge factors,…”

Section: General Formalismmentioning

confidence: 99%

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The third-order QCD corrections to deep-inelastic scattering by photon exchange

2005

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We compute the full three-loop coefficient functions for the structure functions F 2 and F L in massless perturbative QCD. The results for F L complete the next-to-next-to-leading order description of unpolarized electromagnetic deep-inelastic scattering. The third-order coefficient functions for F 2 form, at not too small values of the Bjorken variable x, the dominant part of the next-to-next-tonext-to-leading order corrections, thus facilitating improved determinations of the strong coupling α s from scaling violations. The three-loop corrections to F L are larger than those for F 2 . Especially for the latter quantity the expansion in powers of α s is very stable, for photon virtualities Q 2 ≫ 1 GeV 2 , over the full x-range accessible to fixed-target and collider measurements.

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Section: General Formalismmentioning

confidence: 99%

Section: General Formalismmentioning

confidence: 99%

The third-order QCD corrections to deep-inelastic scattering by photon exchange

2005

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“…In [24][25][26][27] in D = 4 − 2ε dimensions and the modified minimal subtraction [28,29] scheme, MS. The running coupling evolves according to…”

Section: Renormalizationmentioning

confidence: 99%

Charged current deep-inelastic scattering at three loops

Moch

Rogal

2007

Nuclear Physics B

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We derive for deep-inelastic neutrino(ν)-proton(P) scattering in the combination νP −νP the perturbative QCD corrections to three loops for the charged current structure functions F 2 , F L and F 3 . In leading twist approximation we calculate the first five odd-integer Mellin moments in the case of F 2 and F L and the first five even-integer moments in the case of F 3 . As a new result we obtain the coefficient functions to O(α 3 s ) while the corresponding anomalous dimensions agree with known results in the literature.

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“…Kenneth G. Wilson and Michael E. Fischer [35] were writing a paper proposing to calculate critical phenomena in statistical physics in 4 − ε dimensions as an expansion in ε. And independently of us C. Bollini and J. Giambiagi [36], and J. Ashmore [37], also suggested to use analyticity in space-time dimensions as a regulator.…”

Section: The Higgs-kibble Mechanism and Dimensional Renormalizationmentioning

confidence: 99%