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

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 In 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. (C) 2002 Elsevier Science B.V. All rights reserved.