====== TTP03-36 The analytic value of a 4-loop sunrise graph in a particular kinematical configuration ======
 
 
   <hidden TTP03-36  The analytic value of a 4-loop sunrise graph in a particular kinematical configuration > The 4-loop sunrise graph with two massless lines, two lines of equal 
 mass M and a line of mass m, for external invariant timelike and 
 equal to m^2 is considered. We write differential equations 
 in x=m/M for the Master Integrals of the problem, which we Laurent-expand 
 in the regularizing continuous dimension $d$ around $d=4$, and then 
 solve exactly in x up to order (d-4)^3 included; 
 the result is expressed in terms of Harmonic PolyLogarithms of 
 argument x and maximum weight 7. As a by product, 
 we obtain the x=1 value, expected to be relevant in QED 4-loop 
 static quantities like the electron (g-2). The analytic results 
 were checked by an independent precise numerical calculation
 </hidden>
|**S. Laporta, P. Mastrolia and E. Remiddi**  | 
|**  Nucl. Phys. B  688 165-188 2004  **  |
| {{preprints:2003:ttp03-36.pdf|PDF}} {{preprints:2003:ttp03-36.ps|PostScript}} [[http://arxiv.org/abs/hep-ph/0311255|arXiv]]   |
| |