The analytic value of the sunrise self-mass with two equal masses and the external invariant equal to the third squared mass Original Research Article

We consider the two-loop self-mass sunrise amplitude with two equal masses M and the external invariant equal to the square of the third mass m in the usual d-continuous dimensional regularization. We write a second order differential equation for the amplitude in x=m/M and show as solve it in close analytic form. As a result, all the coefficients of the Laurent expansion in d−4 of the amplitude are expressed in terms of harmonic polylogarithms of argument x and increasing weight. As a by product, we give the explicit analytic expressions of the value of the amplitude at x=1, corresponding to the on-mass-shell sunrise amplitude in the equal mass case, up to the (d−4)5 term included.