Symbolic Summation for Particle Physics

Carsten Schneider, Johannes Bluemlein, Alexander Hasselhuhn
2013 Proceedings of 10th International Symposium on Radiative Corrections (Applications of Quantum Field Theory to Phenomenology) — PoS(RADCOR2011)   unpublished
A big class of Feynman integrals, in particular, the coefficients of their Laurent series expansion w.r.t. the dimension parameter ε can be transformed to multi-sums over hypergeometric terms and harmonic sums. In this article, we present a general summation method based on difference fields that simplifies these multi-sums by transforming them from inside to outside to representations in terms of indefinite nested sums and products. In particular, we present techniques that assist in the task
more » ... o simplify huge expressions of such multi-sums in a completely automatic fashion. The ideas are illustrated on new calculations coming from 3-loop topologies of gluonic massive operator matrix elements containing two fermion lines, which contribute to the transition matrix elements in the variable flavor scheme.
doi:10.22323/1.145.0032 fatcat:4u7ecesz4zb5df6e3d6kmmivfm