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Special Functions and Abbreviations in Package-X

Package-X attempts to provide compact analytic expressions in terms of elementary functions for one loop integrals. To accomodate cases involving general kinematics, Package-X defines a limited set of special functions (output by LoopRefine) that serve as abbreviations for commonly occuring expressions. They can be numerically evaluated at any real-valued kinematic point with arbitrary precision, expanded in Taylor series to arbitrary order, or be expressed in terms of known mathematical functions.

ReferenceReference

Special Functions

DiscB (DiscExpand) logarithmic part of the two-point function

ScalarC0 (C0Expand) three-point scalar function

ScalarC0IR6

ScalarD0 (D0Expand) four-point scalar function

ScalarD0IR12  ▪  ScalarD0IR13  ▪  ScalarD0IR16

Logarithms

Ln  ▪  DiLog  ▪  ContinuedDiLog

Gramian Determinants

Kallenλ (KallenExpand) kinematic triangle function

Kibbleϕ (KibbleExpand) kinematic cubic function