Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
1996-05-24
Z.Phys. C74 (1997) 379-386
Physics
High Energy Physics
High Energy Physics - Phenomenology
17 pages with figures and tables, PostScript file gzip'ed and uuencoded
Scientific paper
A method of calculating Feynman diagrams from their small momentum expansion [1] is extended to diagrams with zero mass thresholds. We start from the asymptotic expansion in large masses [2] (applied to the case when all $M_i^2$ are large compared to all momenta squared). Using dimensional regularization, a finite result is obtained in terms of powers of logarithms (describing the zero-threshold singularity) times power series in the momentum squared. Surprisingly, these latter ones represent functions, which not only have the expected physical `second threshold' but have a branchcut singularity as well below threshold at a mirror position. These can be understood as pseudothresholds corresponding to solutions of the Landau equations. In the spacelike region the imaginary parts from the various contributions cancel. For the two-loop examples with one mass $M$, in the timelike region for $q^2 \approx M^2$ we obtain approximations of high precision. This will be of relevance in particular for the calculation of the decay $Z \to b\bar{b}$ in the $m_b=0$ approximation.
Fleischer Jochem
Smirnov Vladimir A.
Tarasov Oleg V.
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