CONSTRAINTS ON HADRONIC SPECTRAL FUNCTIONS FROM CONTINUOUS FAMILIES OF FINITE-ENERGY SUM-RULES

Hadronic tau decay data is used to study the reliability of various fi nite energy sum rules (FESR's). For intermediate scales (s(0) similar to 2-3 GeV2), those FESR's with weights s(k) are found to have signifi cant errors, whereas those with weights having a zero at the juncture (s = s(0)) of the cut and circular part of the contour work very well. It is also shown that a combination of two such sum rules allows rath er strong constraints to be placed on the hadronic spectral function w ithout sacrificing the excellent agreement between OPE and hadronic re presentations. The method then is applied to the strangeness S = -1 an d pseudoscalar isovector channels, where it is shown to provide navel constraints on those ansatze for the unmeasured continuum parts of the spectral functions employed in existing extractions of m(u) + m(d), m (s). The continuum ansatz in the latter channel, in particular, is sho wn to produce a rather poor match to the corresponding OPE representat ion, hence re-opening the question of the value of the light quark mas s combination m(u) + m(d). (C) 1998 Elsevier Science B.V. All rights r eserved.