# Differences

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+ | ====== TTP02-01 The analytic value of the sunrise self-mass with two equal masses and the external invariant equal to the third squared mass ====== | ||

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+ | <hidden 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. | ||

+ | </hidden> | ||

+ | |**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}} | | ||

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