order of the polarization operator in Coulomb field at low energy

Kirilin, G. G.; Lee, Roman N.

doi:10.1016/j.nuclphysb.2008.08.010

Cited by 5 publications

(7 citation statements)

References 27 publications

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“…It is of interest, that three other, quite different and in a sense more general approaches would also be impossible without intensive use of the reduction of Feynman integrals to masters. We mean (i) the method of differential equations 24 , (ii) the use of difference equations [5,98] and, at last, very new method [99][100][101] based on recurrence equations with respect to the space-time dimension D [102].…”

Section: Discussionmentioning

confidence: 99%

Four loop massless propagators: An algebraic evaluation of all master integrals

2010

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The old "glue-and-cut" symmetry of massless propagators, first established in Ref. [1], leads -after reduction to master integrals is performed -to a host of non-trivial relations between the latter. The relations constrain the master integrals so tightly that they all can be analytically expressed in terms of only few, essentially trivial, watermelon-like integrals. As a consequence we arrive at explicit analytical results for all master integrals appearing in the process of reduction of massless propagators at three and four loops. The transcendental structure of the results suggests a clean explanation of the well-known mystery of the absence of even zetas (ζ 2n ) in the Adler function and other similar functions essentially reducible to massless propagators. Once a reduction of massless propagators at five loops is available, our approach should be also applicable for explicitly performing the corresponding five-loop master integrals.1 The so-called Laporta approach [4-6] seems to be most often utilized but a few other promising methods are being now actively developed [7][8][9][10][11][12].2 At least well-established in practice. See below for an instructive particular example of a class of massless propagators and also [13,14] for an attempt to formalize the concept of the masters integrals and to prove the universality property in general. A related discussion could be found in [15][16][17][18].

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Section: Discussionmentioning

confidence: 99%

Four loop massless propagators: An algebraic evaluation of all master integrals

2010

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“…In Ref. [6] this integral has been considered using the dimensional recurrence relation. However, in that paper in order to fix the periodic function parametrizing the homogeneous solution we had to resort to the Laporta's difference equation.…”

Section: Examplementioning

confidence: 99%

Calculating multiloop integrals using dimensional recurrence relation and D-analyticity

Lee

2010

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“…Recently, in Ref. [11] the method of the dimensional recurrence relation was successfully applied to the calculation of certain four-loop tadpole. In that paper, an arbitrary periodic function parametrizing the solution of the homogeneous equation was numerically shown to be equal to zero by using the Laporta-like difference equation with respect to the power of massive denominator.…”

Section: Introductionmentioning

confidence: 99%