arXiv subjects
Publications and source records attributed to Ivo Vrkoc.
The commonly used West and Yennie integral formula for the relative phase between the Coulomb and elastic hadronic amplitudes might be consistently applied to only if the hadronic amplitude had the constant ratio of the real to the imaginary parts al all kinematically allowed values of four momentum transfer squared.
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 α_{s} from the τdecay.
The role of the operator-product expansion in QCD calculations is discussed. Approximating the two-point correlation function by several terms and assuming an upper bound on the truncation error along the euclidean ray, we consider two model situations to examine how the bound develops with increasing deflection from the euclidean ray towards the cut. We obtain explicit bounds on the truncation error and show how they worsen with the increasing deflection. The result does not support the believe that the remainder is constant for all angles in the complex energy plane. Further refinements of the formalism are dicussed.