One-loop amplitudes for four-point functions with two external massive quarks and two external massless partons up toO(ε2)

Abstract

We present complete analytical O" 2 results on the one-loop amplitudes relevant for the next-to-nextto-leading order (NNLO) quark-parton model description of the hadroproduction of heavy quarks as given by the so-called loop-by-loop contributions. All results of the perturbative calculation are given in the dimensional regularization scheme. These one-loop amplitudes can also be used as input in the determination of the corresponding NNLO cross sections for heavy flavor photoproduction, and in photon-photon reactions.

Two-loop leading color corrections to heavy-quark pair production in the gluon fusion channel

“…(2.3) arises from the interference of one-loop diagrams with the tree-level amplitude [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24]. The O(α 2 S ) term A 2 consists of two parts, the interference of two-loop diagrams with the Born amplitude and the interference of one-loop diagrams among themselves: The term A (1×1) 2 was derived in [87][88][89][90]. A (2×0) 2 , originating from the two-loop diagrams, can be decomposed according to color and flavor structures as follows: 6) where N l and N h are the number of light-and heavy-quark flavors, respectively.…”

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

“…(1) and (2)] that occur in our O(ε 2 ) results [1] for the Laurent series expansion of massive scalar one-loop integrals to multiple polylogarithms. We have used these relations to transform our results on massive one-loop integrals involving L functions to corresponding results involving multiple polylogarithms.…”

“…In this Appendix we consider as an example the real part of the O(ε 2 ) coefficient Re D (2) 1 of the Laurent series expansion of the massive box D 1 with three massive propagators. Using the rules written down in the main text of this paper we have expressed the corresponding results of [1] involving L functions in terms of multiple 1 in [1] is sufficiently rich to provide an illustration of the corresponding complexity in terms of multiple polylogarithms when transforming to the latter representation.…”

“…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 . This result is listed in the Appendix.…”

“…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.…”