Worldline approach to Sudakov-type form factors in non-Abelian gauge theories

Gellas, G. C.; Karanikas, A. I.; Ktorides, C.N.; Stefanis, N. G.

doi:10.1016/s0370-2693(97)01055-1

Cited by 16 publications

(34 citation statements)

References 53 publications

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“…6 Still another possibility is to use the analytic coupling [56], as done in [28,29] (see next section). In order to protect the BLM scale from intruding into the forbidden nonperturbative soft region, where perturbation theory becomes invalid, one can make use of a minimum scale, µ min , based on the grounds of QCD factorization theorems and the OPE, as applied for instance in [104,105,106,107] and also in [32]:…”

Section: A Ms Schemementioning

confidence: 99%

Publisher's Note: Pion form factor in QCD: From nonlocal condensates to next-to-leading-order analytic perturbation theory [Phys. Rev. D 70, 033014 (2004)]

Bakulev¹,

Passek‐Kumerički²,

Schroers³

et al. 2004

Phys. Rev. D

118

252

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We present an investigation of the pion's electromagnetic form factor F π (Q 2 ) in the spacelike region utilizing two new ingredients: (i) a double-humped, endpoint-suppressed pion distribution amplitude derived before via QCD sum rules with nonlocal condensates-found to comply at the 1σ level with the CLEO data on the πγ transition-and (ii) analytic perturbation theory at the level of parton amplitudes for hadronic reactions. The computation of F π (Q 2 ) within this approach is performed at NLO of QCD perturbation theory (standard and analytic), including the evolution of the pion distribution amplitude at the same order. We consider the NLO corrections to the form factor in the MS scheme with various renormalization scale settings and also in the α Vscheme. We find that using standard perturbation theory, the size of the NLO corrections is quite sensitive to the adopted renormalization scheme and scale setting. The main results of our analysis are the following: (i) Replacing the QCD coupling and its powers by their analytic images, both dependencies are diminished and the predictions for the pion form factor are quasi scheme and scale-setting independent. (ii) The magnitude of the factorized pion form factor, calculated with the aforementioned pion distribution amplitude, is only slightly larger than the result obtained with the asymptotic one in all considered schemes. (iii) Including the soft pion form factor via local duality and ensuring the Ward identity at Q 2 = 0, we present predictions that are in remarkably good agreement with the existing experimental data both in trend and magnitude.

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Section: A Ms Schemementioning

confidence: 99%

Publisher's Note: Pion form factor in QCD: From nonlocal condensates to next-to-leading-order analytic perturbation theory [Phys. Rev. D 70, 033014 (2004)]

Bakulev¹,

Passek‐Kumerički²,

Schroers³

et al. 2004

Phys. Rev. D

118

252

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“…Fig. 2), where only gluons with virtualities between C 1 /b and C 2 ξQ are active degrees of freedom, quark propagation and gluon emission can be described by eikonal techniques, using either Feynman diagrams [41,31] or by employing a world-line casting of QCD which reverts the fermion functional integral into a first-quantized, i.e., particle-based path integral [39]. Then the Sudakov functions, entering Eq.…”

Section: Input Parametersmentioning

confidence: 99%

“…(29) are calculable using the non-Abelian extension to QCD [41] of the Grammer-Yennie method [52] for QED. Alternatively, one can calculate the cusp anomalous dimension employing Wilson (world) lines [37][38][39]50]. 7 In this latter approach (see, e.g., [39]), the IR behavior of the cusped Wilson (world) line is expressed in terms of an effective fermion vertex function whose variance with the momentum scale is governed by the anomalous dimension of the cusp within the isolated effective sub-sector (see Fig.…”

Section: Input Parametersmentioning

confidence: 99%

Analytic coupling and Sudakov effects in exclusive processes: pion and $\gamma ^*\gamma \to \pi ^0$ form factors

2000

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We develop and discuss in technical detail an infrared-finite factorization and optimized renormalization scheme for calculating exclusive processes, which enables the inclusion of transverse degrees of freedom without entailing suppression of calculated observables, like form factors. This is achieved by employing an analytic, i.e., infrared stable, running strong coupling α s (Q 2 ) which removes the Landau singularity at Q 2 = Λ 2 QCD by a minimum power-behaved correction. The ensuing contributions to the cusp anomalous dimensionrelated to the Sudakov form factor -and to the quark anomalous dimension -which controls evolution -lead to an enhancement at high Q 2 of the hard part of exclusive amplitudes, calculated in perturbative QCD, while simultaneously improving its scaling behavior. The phenomenological implications of this framework are analyzed by applying it to the pion's electromagnetic form factor, including the NLO contribution to the hard-scattering amplitude, and also to the pion-photon transition at LO. For the pion wave function, an improved ansatz of the Brodsky-Huang-Lepage type is employed, which includes an effective (constituent-like) quark mass, m q = 0.33 GeV. Predictions for both form factors are presented and compared to the experimental data, applying Brodsky-Lepage-Mackenzie commensurate scale setting. We find that the perturbative hart part prevails at momentum transfers above about 20 GeV 2 , while at lower Q 2 -values the pion form factor is dominated by Feynman-type contributions. The theoretical prediction for the γ * γ → π 0 form factor indicates that the true pion distribution amplitude may be somewhat broader than the asymptotic one.

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“…To be sure, the situation presently considered refers to the hypothetical situation where the scattering process involves quarks and associated gluon radiation without reference to hadrons. It does, nevertheless, fall within the spirit that marks our approach to IR issues in QCD [16,17]: Once off-mass shell IR protection is employed -by an amount that exceeds Λ QCD -one actually tests how far one can go by remaining strictly within the confines of QCD before attempting to make contact with real hadrons. Granted the opposite route, from hadrons to quarks and gluons, via the use of quantities like structure/fragmentation functions, the employment of tools such as the operator product expansion, etc., constitutes a more realistic procedure for investigating the same physical problems.…”

Section: Introductionmentioning

confidence: 99%

World-line techniques for resumming gluon radiative corrections at the cross-section level

2003

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Worldline approach to Sudakov-type form factors in non-Abelian gauge theories

Cited by 16 publications

References 53 publications

Publisher's Note: Pion form factor in QCD: From nonlocal condensates to next-to-leading-order analytic perturbation theory [Phys. Rev. D 70, 033014 (2004)]

Publisher's Note: Pion form factor in QCD: From nonlocal condensates to next-to-leading-order analytic perturbation theory [Phys. Rev. D 70, 033014 (2004)]

Analytic coupling and Sudakov effects in exclusive processes: pion and $\gamma ^*\gamma \to \pi ^0$ form factors

World-line techniques for resumming gluon radiative corrections at the cross-section level

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