# Constraints on Hadronic Spectral Functions From Continuous Families of Finite Energy Sum Rules Source: [Constraints on Hadronic Spectral Functions From Continuous Families of Finite Energy Sum Rules]() Collection index: [llms.txt]() Data updated: 2025-10-24T13:14:00.166Z Authors: K. Maltman Published: 1999-01-07T04:16:13.000Z ## Abstract Hadronic tau decay data is used to study the reliability of various finite energy sum rules (FESR's). For intermediate scales (of order 2-3 GeV^2), those FESR's with weights s^k are found to have significant 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 rather strong constraints to be placed on the hadronic spectral function without sacrificing the excellent agreement between OPE and hadronic representations. The method then is applied to the strangeness -1 and pseudoscalar isovector channels, where it is shown to provide novel 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 ans\\"atz in the latter channel, in particular, is shown to produce a rather poor match to the corresponding OPE representation, hence re-opening the question of the value of the light quark mass combination m\_u+m\_d. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. ## Original sources and implementation [Original paper]() [PDF]()