CALCULATION OF FEYNMAN DIAGRAMS WITH LOW THRESHOLDS FROM THEIR SMALL MOMENTUM EXPANSION

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 pa rticularly important for the higher loop diagrams. If the lowest thres holds are very low, however, then the Taylor series expansion is eithe r difficult to apply or extremely many Taylor coefficients might be ne eded to achieve convergence. In the case of one variable, q(2), the re levant normalization is r = q(2)/q(th)(2) (q(th)(2) = 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 obt ained by first applying a large mass expansion. bs expected the deviat ion is small which serves as an excellent test for both the methods.