The unequal mass sunrise integral expressed through iterated integrals on \(\overline{\mathcal{M}}_{1,3}\)

DOI10.1016/J.NUCLPHYSB.2020.114991zbMATH Open1503.81031arXiv1907.01251OpenAlexW2954229826MaRDI QIDQ2230275

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Publication date: 17 September 2021

Published in: (Search for Journal in Brave)

Abstract: We solve the two-loop sunrise integral with unequal masses systematically to all orders in the dimensional regularisation parameter $varepsilon$. In order to do so, we transform the system of differential equations for the master integrals to an $varepsilon$-form. The sunrise integral with unequal masses depends on three kinematical variables. We perform a change of variables to standard coordinates on the moduli space ${mathcalM}_{1,3}$ of a genus one Riemann surface with three marked points. This gives us the solution as iterated integrals on $overline{mathcalM}_{1,3}$. On the hypersurface $au=mboxconst$ our result reduces to elliptic polylogarithms. In the equal mass case our result reduces to iterated integrals of modular forms.

Full work available at URL: https://arxiv.org/abs/1907.01251

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