A comprehensive study is performed of two-loop Feynman diagrams with three external legs which, due to the exchange of massless gauge-bosons, give raise to infrared and collinear divergencies. Their relevance in assembling realistic computations of next-to-next-to-leading corrections to physical observables is emphasised. A classification of infrared singular configurations, based on solutions ...

We give numerical integration results for Feynman loop diagrams through 3-loop such as those covered by Laporta [1]. The methods are based on automatic adaptive integration, using iterated integration and extrapolation with programs from the QUADPACK package, or multivariate techniques from the ParInt package. The Dqags algorithm from QUADPACK accommodates boundary singularities of fairly gener...

Founded in the mid1950s, the field of system dynamics has intellectual roots reaching much further into the past. The Archives section of the Review seeks to publish material from that past which can contribute to current theory and practice. The section welcomes previously unpublished but deserving system dynamics work, classics from past system dynamics literature that should receive renewed ...

Two-loop HQET propagator diagrams were reduced [1] to two master integrals, using integration by parts [2] identities. There are 10 generic topologies of three-loop HQET propagator diagrams (Fig. 1). They can be reduced [3], using integration by parts relations, to 8 master integrals (Fig. 2). The algorithm has been constructed by hand, and implemented as a REDUCE package Grinder [3]. It is ana...

Cultivating a deeper understanding of the response mechanism cultural ecosystem services to urbanization is increasingly recognized as critical component sustainable governance and land-use decision making. However, except for range studies exploring changes in during that address merely one service type, few investigations reveal changing rapid urbanization. To fill this knowledge gap, study s...

We elucidate the one-loop twistor-space structure corresponding to momentum-space MHV diagrams. We also discuss the infrared divergences, and argue that only a limited set of MHV diagrams contain them. We show how to introduce a twistor-space regulator corresponding to dimensional regularization for the infrared-divergent diagrams. We also evaluate explicitly the ‘holomorphic anomaly’ pointed o...

The operator approach to analytical evaluation of multi-loop Feynman diagrams is proposed. We show that the known analytical methods of evaluation of massless Feynman integrals, such as the integration by parts method and the method of ”uniqueness” (which is based on the star-triangle relation), can be drastically simplified by using this operator approach. To demonstrate the advantages of the ...