Threshold Expansion. One Heavy Mass in the Threshold

Abstract

In this and the next chapter, we investigate asymptotic expansions of Feynman integrals near threshold, i.e. when an external momentum squared tends to a threshold value, and their operator analogues. This chapter deals with the case where only one particle with a heavy mass contributes to the threshold. As is well known, thresholds are located at q ² = (Σ m _i )², where q is the sum of the external momenta flowing through a cut in a diagram, and the m _i are the masses of the lines in the cut. We shall consider two kinds of such threshold limits:

• (A) The external momentum is on the mass shell corresponding to the heavy mass M, and there is another mass m (or several masses) which is (are) small. The limit is m/M → 0.

• (B) The masses in the diagram are either heavy or zero. The threshold is composed of one heavy mass and some zero masses. The external momentum squared tends to its threshold value.