Institute for Theoretical Particle Physics (TTP)

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preprints:2002:ttp02-39 [2016/03/17 11:03] (current)
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 +====== TTP02-39 The analytic value of a 3-loop sunrise graph in a particular kinematical configuration ====== 
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 +   <hidden TTP02-39  The analytic value of a 3-loop sunrise graph in a particular kinematical configuration > We consider the scalar integral associated to the 3-loop sunrise graph 
 + with a massless line, two massive lines of equal mass $M$, a fourth line of 
 + mass equal to $Mx$, and the external invariant timelike and equal to the 
 + square of the fourth mass. We write the differential equation in $x$ 
 + satisfied by the integral, expand it in the continuous dimension $d$ 
 + around $d=4$ and solve the system of the resulting chained differential 
 + equations in closed analytic form, expressing the solutions in terms of 
 + Harmonic Polylogarithms. As a byproduct, we give the limiting values of 
 + the coefficients of the $(d-4)$ expansion at $x=1$ and $x=0$. 
 + </hidden> 
 +|**P. Mastrolia, E. Remiddi**  |  
 +|**  Nucl.Phys.B  657 397-406 2003  **  | 
 +| {{preprints:2002:ttp02-39.pdf|PDF}} {{preprints:2002:ttp02-39.ps|PostScript}} [[http://arxiv.org/abs/hep-ph/0211451|arXiv]]   | 
 +| |