QCD Sum-Rule Invisibility of the sigma Meson

Abstract

QCD Laplace sum-rules for light-quark I=0,1 scalar currents are used to investigate candidates for the lightest $q\bar{q}$ scalar mesons. The theoretical predictions for the sum-rules include instanton contributions which split the degeneracy between the I=0 and I=1 channels. The self-consistency of the theoretical predictions is verified through a Hölder inequality analysis, confirming the existence of an effective instanton contribution to the continuum. The sum-rule analysis indicates that the f_0(980) and a_0(1450) should be interpreted as the lightest $q\bar{q}$ scalar mesons. This apparent decoupling of the f_0(400-1200) (or $\sigma$) and a_0(980) from the quark scalar currents suggests a non-$q\bar{q}$ interpretation of these resonances.

Comments: 6 pages, latex. Talk at the Workshop on Hadron Spectroscopy, WHS'99, Frascati, March 1999