Space-time dimensionality D as complex variable: Calculating loop integrals using dimensional recurrence relation and analytical properties with respect to D

By Roman N. Lee. 2009

210 citations recorded by the source corpus.

Abstract We show that dimensional recurrence relation and analytical properties of the loop integrals as functions of complex variable D (space–time dimensionality) provide a regular way to derive analytical representations of loop integrals. The representations derived have a form of exponentially converging sums. Several examples of the developed technique are given.

Subfields: Applied Mathematics, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/b077439af37b6a0ffebec0a66b987b92deedd2fe

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In Applied Mathematics

In Atomic and Molecular Physics, and Optics

Citations in the corpus

Analytic results for massless three-loop form factors (2010, methodology): “[ 7 ] is the analysis of the analytic properties of a given integral in a basic stripe of the complex plane d. The proper choice of the master integral, the basic stripe, and the summation factor can essentially simplify the analysis reducing the number of (or totally fixing) the constants parametri”
A quasi-finite basis for multi-loop Feynman integrals (2014, background): “11) or the one introduced by Tarasov [36–38],9 we can express the basis Bd in terms of integrals in d + 2 dimensions.”
Feynman integrals and hyperlogarithms (2015, result): “They have been used to derive difference equations that allow for rapid numerical evaluation to very high precision [116, 117], but we could not find a statement similar to our result in the literature.”
Presenting LiteRed: a tool for the Loop InTEgrals REDuction (2012, methodology): “rators and dots. We will call Eqs. (2.8) and (2.9) the raising dimensional recurrence relations. { 6 { For completeness, we present also the lowering dimensional recurrence relation, obtained in Ref. [22] J (d+2) (n) = (2)L[V(p 1;:::;p E)] 1 (d E L+ 1) L P(B 1;:::;B N)J ) (n); (2.10) where L = (+ 1)”
Decomposition of Feynman integrals on the maximal cut by intersection numbers (2019, background): “, [12, 88] or Appendix A of [1].”
Collider physics at the precision frontier (2020, unknown): “[478, 479] to achieve convenient dimension shifts.”
Soft triple-real radiation for Higgs production at N3LO (2013, background): “After reduction to master integrals, the dimensional shift identities reduce to recurrence relations in the space-time dimension D for the master integrals themselves [71–75].”
Feynman integrals and intersection theory (2018, methodology): “In this appendix we review the derivation of the Baikov representation [13, 32, 58] for a scalar Feynman integral with L loops, E+1 external momenta, and N propagators:”