Speaker
Dr
Roman Lee
(Budker Institute of Nuclear Physics, Novosibirsk)
Description
We derive reduction formulae, differential equations and dimensional recurrence relations for $L$-loop two-point massive tadpoles and sunrises with arbitrary masses and regularized both dimensionally and analytically. The differential system obtained has a Pfaff form and can be turned into $(\epsilon+\tfrac{1}{2})$-form when the analytic regularization is removed. For odd $d$ this form allows us to present coefficients of $\epsilon$-expansion explicitly in terms of Goncharov's polylogarithms. Using the symmetry properties of the matrix in the right-hand side of the differential system, we obtain quadratic constraints for the solutions of the obtained differential system near any integer $d$.
Primary author
Dr
Roman Lee
(Budker Institute of Nuclear Physics, Novosibirsk)
