Abstract
We introduce and solve an infinite class of loop integrals which generalises the well-known ladder series. The integrals are described in terms of single-valued poly-logarithmic functions which satisfy certain differential equations. The combination of the differential equations and single-valued behaviour allow us to explicitly construct the poly-logarithms recursively. For this class of integrals the symbol may be read off from the integrand in a particularly simple way. We give an explicit formula for the simplest generalisation of the ladder series. We also relate the generalised ladder integrals to a class of vacuum diagrams which includes both the wheels and the zigzags.
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ArXiv ePrint: 1207.3284
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Drummond, J.M. Generalised ladders and single-valued polylogs. J. High Energ. Phys. 2013, 92 (2013). https://doi.org/10.1007/JHEP02(2013)092
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DOI: https://doi.org/10.1007/JHEP02(2013)092