Hopf algebra structure of the two loop three mass nonplanar Feynman diagram

The method of using Hopf algebras for calculating Feynman integrals developed by Abreu et al. is applied to the two-loop nonplanar on-shell diagram with massless propagators and three external mass scales. We show that existence cut diagrams comprising coproduct, first entry condition integrability was found be true planar case also holds case; furthermore, symbol alphabet same as case. This one main results this work which have been obtained a systematic analysis relevant cuts, symbolic manipulation codes hypexp polylogtools. result cross-checked an known original integral result. In addition, we reconstruct full from symbol. second paper.