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Abstract
We explore the correspondence between oneloop Feynman integrals and (hyperbolic) simplicial geometry to describe the allmass case: integrals with generic external and internal masses. Specifically, we focus on nparticle integrals in exactly n spacetime dimensions, as these integrals have particularly nice geometric properties and respect a dual conformal symmetry. In four dimensions, we leverage this geometric connection to give a concise dilogarithmic expression for the allmass box in terms of the MurakamiYano formula. In five dimensions, we use a generalized GaussBonnet theorem to derive a similar dilogarithmic expression for the allmass pentagon. We also use the Schläfli formula to write down the symbol of these integrals for all n. Finally, we discuss how the geometry behind these formulas depends on spacetime signature, and we gather together many results related to these integrals from the mathematics and physics literature.
Original language  English 

Article number  29 
Journal  Journal of High Energy Physics 
DOIs  
Publication status  Published  6 Aug 2020 
Keywords
 hepth
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Projects
 1 Active

Particle Theory at the Higgs Centre
Ball, R., Boyle, P., Del Debbio, L., Gardi, E., Horsley, R., Kennedy, A., O'Connell, D., Smillie, J. & Zwicky, R.
1/10/17 → 30/09/21
Project: Research