Operator product expansion and analyticity

Details Operator product expansion and analyticity Operator product expansion and analyticity

1999-08-27

arxiv.org/abs/hep-ph/9908484v1

Int.J.Mod.Phys. A14 (1999) 4819-4840

Physics

High Energy Physics

High Energy Physics - Phenomenology

Preprint PRA-HEP 99/04, 20 pages

Scientific paper

10.1142/S0217751X9900227X

We discuss the current use of the operator product expansion in QCD calculations. Treating the OPE as an expansion in inverse powers of an energy-squared variable (with possible exponential terms added), approximating the vacuum expectation value of the operator product by several terms and assuming a bound on the remainder along the euclidean region, we observe how the bound varies with increasing deflection from the euclidean ray down to the cut (Minkowski region). We argue that the assumption that the remainder is constant for all angles in the cut complex plane is not justified. Making specific assumptions on the properties of the expanded function, we obtain bounds on the remainder in explicit form and show that they are very sensitive both to the deflection angle and to the class of functions chosen. The results obtained are discussed in connetcion with calculations of the coupling constant \alpha_{s} from the \tau decay.

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