Elliptic polylogarithms and iterated integrals on elliptic curves II: an application to the sunrise integral

摘要

We introduce a class of iterated integrals that generalize multiplepolylogarithms to elliptic curves. These elliptic multiple polylogarithms areclosely related to similar functions defined in pure math- ematics and stringtheory. We then focus on the equal-mass and non-equal-mass sunrise integrals,and we develop a formalism that enables us to compute these Feynman integralsin terms of our iterated integrals on elliptic curves. The key idea is to useintegration-by-parts identities to identify a set of integral kernels, whoseprecise form is determined by the branch points of the integral in question.These kernels allow us to express all iterated integrals on an elliptic curvein terms of them. The flexibility of our approach leads us to expect that itwill be applicable to a large variety of integrals in high-energy physics.