Introducing SummerTime: a package for high-precision computation of sums appearing in DRA method
Roman N. Lee, Kirill T. Mingulov
TL;DR
This work presents SummerTime, a Mathematica package enabling arbitrary-precision computation of expansion coefficients for results obtained from the DRA method applied to one-scale multiloop integrals. It formalizes the dimensional-recurrence solution and introduces tree sums, along with convergence-acceleration techniques and an approach that preserves the order of Laurent expansions in the dimensional parameter $d$ via uniform convergence in $\epsilon$. The package extends beyond DRA by providing high-precision evaluation of conventional transcendental numbers and functions, including multiple zeta values and harmonic polylogarithms, and demonstrates practical usage with an application example to four-loop propagator-type integrals. These capabilities give researchers direct access to DRA results and support high-precision analyses in quantum-field-theory calculations, with future plans to extend to matrix sums. Overall, SummerTime broadens the toolkit for precise multiloop computations and transcendental-number evaluations in high-energy physics.
Abstract
We introduce the Mathematica package SummerTime for arbitrary-precision computation of sums appearing in the results of DRA method. So far these results include the following families of the integrals: 3-loop onshell massless vertices, 3-loop onshell mass operator type integrals, 4-loop QED-type tadpoles, 4-loop massless propagators. The package can be used for high-precision numerical computation of the expansion coefficients of the integrals from the above families around arbitrary space-time dimension. In addition, this package can also be used for calculation of multiple zeta values, harmonic polylogarithms and other transcendental numbers expressed in terms of nested sums with factorized summand.