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 — preprints:2002:ttp02-01 [2016/03/15 20:39] (current) Line 1: Line 1: + ====== TTP02-01 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 $m$ 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. + ​ + |**M. Argeri, P. Mastrolia, E. Remiddi** ​ | + |**  Nucl.Phys.B ​ 631 388-400 2002  **  | + | {{preprints:​2002:​ttp02-01.pdf|PDF}} {{preprints:​2002:​ttp02-01.ps|PostScript}} ​  | + | |