A new method for QCD sum rules: The L∞ norm approach

Abstract

QCD is considered to be a good candidate for a theory of strong interactions. However, it is believed that non perturbative contributions are important at low energies, although their calculation from the QCD Lagrangian is a very difficult task. For a phenomenological approach, they have been parametrized in term of “condensates” [4]. Several methods to deal with these non perturbative contributions, the so-called QCD sum rules, have been used. Most of them do not take fully into account the errors in a quantitative and explicit way, and/or need assumptions on the derivatives of the amplitude. We argue that one should give oneself an a priori model of the errors on the amplitude itself, both in the time-like range and in the space-like range. A set of parameters (values of condensates or mass and width of a resonance) is then acceptable if there exists at least one analytic function going through the “error corridors”. We develop approximate methods to solve this L∞ norm problem.