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The near threshold expansion of generalized sunset-type (water melon) diagrams with arbitrary masses is constructed by using a configuration space technique. We present analytical expressions for the expansion of the spectral density near threshold and compare it with the exact expression obtained earlier using the method of the Hankel transform. We formulate a generalized threshold expansion with partial resummation of the small mass corrections for the strongly asymmetric case where one particle in the intermediate state is much lighter than the others.

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“…Ref. [44]) against the latter which one can find in the literature is that the Bessel functions are complicated (see e.g. Ref.…”

Section: Equal Mass Sunset Diagrammentioning

confidence: 95%

Threshold expansion of Feynman diagrams within a configuration space technique

Groote

Пивоваров

2000

Nuclear Physics B

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“…The OPE for current correlators in QED 2 was analyzed in Ref. [47]. In this model the scale of power corrections is given by the dimensional charge e (the model is super-renormalizable).…”

Section: A Note On Theoretical Models For Power Correctionsmentioning

confidence: 99%

“…The interesting channels are that of the scalar and pseudoscalar currents, the correlators for which are known exactly and give an example of a really nontrivial spectrum [47].…”

Section: A Note On Theoretical Models For Power Correctionsmentioning

confidence: 99%

Spectral moments of two-point correlators in perturbation theory and beyond

2002

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We discuss the choice of weight functions for the moments of the spectral density for two-point correlators of hadronic currents over a finite energy interval. Of phenomenological relevance is an analysis of the spectra of lepton decay on the energy interval ͓0,M ͔ and the low-energy hadron production in e ϩ e Ϫ annihilation. General arguments are given for the calculability of such moments in perturbation theory using both a finiteorder analysis and infinite resummation on the contour. Nonperturbative contributions emerging from the operator product expansion for two-point correlators are discussed within explicit models for the physical spectra. The quantitative analysis strongly disfavors weight functions that suppress the high-energy contribution to theoretical moments. This is in agreement with expectations from qualitative considerations in perturbative QCD with asymptotic freedom. We discuss the implication of our results for the ultimate accuracy that can be reached in decays and low-energy e ϩ e Ϫ annihilation into hadrons with present experimental data.

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