Calculation of Feynman diagrams with low thresholds from their small momentum expansion.
Abstract
The calculation of Feynman diagrams in terms of a Taylor expansion w.r.t. small momenta squared is a very promising method and may become particularly important for the higher loop diagrams. If the lowest thresholds are very low, however, then the Taylor series expansion is either difficult to apply or extremely many Taylor coefficients might be needed to achieve convergence. In the case of one variable, q^{2}, the relevant normalization is r = {q ^{2}}/{q ^{2}_{staggered th}} ( q^{2}_{staggeredth} = threshold value of q^{2}) and we demonstrate that with 30 Taylor coefficients up to r = 100 a precision of 3 to 4 decimals can be achieved. For the case of a low threshold we compare our results with the zero threshold case obtained by first applying a large mass expansion. As expected the deviation is small which serves as an excellent test for both the methods.
 Publication:

Nuclear Physics B Proceedings Supplements, Vol. 51
 Pub Date:
 December 1996
 DOI:
 10.1016/S09205632(96)900390
 Bibcode:
 1996NuPhS..51..295F