A form of QCD sum rules, tested and found to be very reliable in the isovector vector channel, is used to determine the scalar current decay constants of the a0 resonances. Comparison to the corresponding decay constant of the K~( 1430) is used to shed light on the nature of the a0(980). It is shown that the results of this analysis strongly favor the "unitarized quark model" scenario for the a0(980).
The scalar meson resonances display a spectral pattern which differs significantly from that of other channels. This anomalous pattern, together with the proximity of the f0(980) and a0(980) to K/( threshold, has led to extensive debate about the nature of these resonances, and a number of distinct proposals for their structure. Among those still discussed in the literature are (1) the KK "molecule" picture, in which the f0(980) and a0(980) are viewed as weakly bound two-meson states[l]; (2) the cryptoexotic "fourquark" picture, in which the states contain both a light quark and (hidden) strange quark pair[2]; (3) the "unitarized quark model" (UQM) picture, in which the coupling of "normal" quark model meson to the nearby K/-( channel creates strong distortions and significant K/f admixture in the meson wavefunction [3]; and (4) the "minion" picture, in which the f0(980) and a0(980) are viewed as very small scale (~ 0.1 -0.2 fm) excitations of the light quark vacuum condensate[@ A major feature distinguishing the various scenarios is the spatial extent of the corresponding states. Thus, a weakly bound KK molecule should be rather large and diffuse, a cryptoexotic somewhat larger than an ordinary q~ meson, a minion much smaller than an ordinary meson, while, in the UQM scenario, the states should contain a "n0rmal" quark model core, somewhat diluted by the admixture of the longer range two meson component. Quantities proposed to test the validity of the various scenarios, Ff0,~0.~n7 and F~_~on ' f0n [5,6], focus precisely on this expected difference in spatial distributions. Unfortunately, the necessity of modeling the non-triviM dynamics of these processes produces systematic theoretical uncertainties, as one can readily verify from a perusal of the existing literature.
An alternate choice of short-distance-dominated observable, much less obscured by intervening dynamics, is the class of scalar meson decay constants, fs, describing the coupling of scalar meson states, S, to that member of the octet of scalar currents, J = (ms -rrz~,)-~q, having the same flavor as the meson, S.