Laurent series expansion of a class of massive scalar one-loop integrals to<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="script">O</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:msup><mml:mi>ε</mml:mi><mml:mn>2</mml:mn></mml:msup><mml:mo stretchy="false">)</mml:mo></mml:math>

Körner, Jürgen; Merebashvili, Z.; Rogal, M.

doi:10.1103/physrevd.71.054028

Cited by 29 publications

(80 citation statements)

References 36 publications

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“…In Sec. II we recapitulate material on the definition of the single and triple index L functions as they arise in the approach of [1]. Simple symmetry relations allow one to restrict the discussion to the triple index L functions L −++ and L +++ , and to the single index L function L + .…”

Section: Introductionmentioning

confidence: 99%

“…In fact, recently a computer code has been written for the numerical evaluation of the multiple polylogarithms [9]. It is therefore timely that we express the results of [1] also in terms of multiple polylogarithms.…”

Section: Introductionmentioning

confidence: 99%

“…It is a purpose of this paper to show that the single and triple index L functions introduced in [1] can all be related to multiple polylogarithms. This is done in explicit form.…”

Section: Introductionmentioning

confidence: 99%

“…In the notation of [1] these are the three-point coefficient functions Re C (2) 1 , Re C (2) 2 and Re C (2) 5 , and the four-point coefficient functions Re D (2) 1 , Re D (2) 2 and Re D (2) 3 . For the sake of brevity we have decided to present multiple polylogarithm results in this paper only for the four-point coefficient function Re D (2) 1 .…”

Section: Introductionmentioning

confidence: 99%

“…Recently, we have calculated the complete set of massive one-loop master integrals [1] needed in the calculation of the next-to-next-to-leading order (NNLO) parton model corrections to the hadroproduction of heavy flavors [2]. We used Feynman parametrization to evaluate the one-loop master integrals in n = 4 − 2ε dimensions.…”

Section: Introductionmentioning

confidence: 99%

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Laurent series expansion of a class of massive scalar one-loop integrals up to O(ε2) in terms of multiple polylogarithms

Körner

Merebashvili

Rogal

2006

Journal of Mathematical Physics

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In a recent paper we have presented results for a set of massive scalar one-loop master integrals needed in the NNLO parton model description of the hadroproduction of heavy flavors. The one-loop integrals were evaluated in n = 4 − 2ε dimension and the results were presented in terms of a Laurent series expansion up to O(ε 2 ). We found that some of the ε 2 coefficients contain a new class of functions which we termed the L functions. The L functions are defined in terms of one-dimensional integrals involving products of logarithm and dilogarithm functions. In this paper we derive a complete set of algebraic relations that allow one to convert the L functions of our previous approach to a sum of classical and multiple polylogarithms. Using these results we are now able to present the ε 2 coefficients of the one-loop master integrals in terms of classical and multiple polylogarithms.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…It is a purpose of this paper to show that the single and triple index L functions introduced in [1] can all be related to multiple polylogarithms. This is done in explicit form.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Laurent series expansion of a class of massive scalar one-loop integrals up to O(ε2) in terms of multiple polylogarithms

Körner

Merebashvili

Rogal

2006

Journal of Mathematical Physics

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Functional reduction of Feynman integrals

Tarasov

2019

J. High Energ. Phys.

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A method for reducing Feynman integrals, depending on several kinematic variables and masses, to a combination of integrals with fewer variables is proposed. The method is based on iterative application of functional equations proposed by the author. The reduction of the one-loop scalar triangle and box integrals with massless internal propagators to simpler integrals is described in detail. The triangle integral depending on three variables is represented as a sum over three integrals depending on two variables. By solving the dimensional recurrence relations for these integrals, an analytic expression in terms of the 2 F 1 Gauss hypergeometric function and the logarithmic function was derived.By using the functional equations, the one-loop box integral with massless internal propagators, which depends on six kinematic variables, was expressed as a sum of 12 terms. These terms are proportional to the same integral depending only on three variables different for each term. For this integral with three variables, an analytic result in terms of the F 1 Appell and 2 F 1 Gauss hypergeometric functions was derived by solving the recurrence relation with respect to the spacetime dimension d. The reduction equations for the box integral with some kinematic variables equal to zero are considered.

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Heavy-quark production in gluon fusion at two loops in QCD

2008

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We present the two-loop virtual QCD corrections to the production of heavy quarks in gluon fusion. The results are exact in the limit when all kinematical invariants are large compared to the mass of the heavy quark up to terms suppressed by powers of the heavy-quark mass. Our derivation uses a simple relation between massless and massive QCD scattering amplitudes as well as a direct calculation of the massive amplitude at two loops. The results presented here together with those obtained previously for quark-quark scattering form important parts of the next-to-next-to-leading order QCD corrections to heavy-quark production in hadron-hadron collisions.Comment: 31 pages latex, 4 figure

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Laurent series expansion of a class of massive scalar one-loop integrals toO(ε2)

Cited by 29 publications

References 36 publications

Laurent series expansion of a class of massive scalar one-loop integrals up to O(ε2) in terms of multiple polylogarithms

Laurent series expansion of a class of massive scalar one-loop integrals up to O(ε2) in terms of multiple polylogarithms

Functional reduction of Feynman integrals

Heavy-quark production in gluon fusion at two loops in QCD

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