Applications of QCD Sum Rules to Heavy Quark Physics

Abstract

• Correlation function of local quark currents is defined. The simplest, two-point correlation function is formed by two quark-antiquark current operators sandwiched between the QCD vacuum states. This is a function of the 4-momentum transfer between the currents. In the region of large spacelike momentum transfers, the correlation function represents a short-distance fluctuation of quark-antiquark fields. The propagation of quarks and antiquarks at short distances is asymptotically free, the gluon exchanges being suppressed by a small QCD coupling. In addition, the interactions with “soft” (low momentum) quark-antiquark and gluon fields populating the QCD vacuum have to be taken into account. • Operator-product expansion (OPE) of the correlation function is worked out. This expansion provides an analytical expression for the correlation function at spacelike momentum transfers, with a systematic separation of short- and long-distance eects. The former are described by Feynman diagrams with quark and gluon propagators and vertices, whereas the latter are encoded by universal parameters related to the nonperturbative QCD dynamics. In the case of two-point sum rules, these parameters are the averaged local densities of the QCD vacuum fields, the condensates. The contributions of vacuum eects in OPE are suppressed by inverse powers of the large momentum and/or heavy-quark mass scale, allowing one to truncate the expansion at some maximal power.