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preprints:2002:ttp02-01 [2016/03/15 20:39] (current)
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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}} ​  | 
 +| |