Finite Energy Chiral Sum Rules and Τ Spectral Functions

A combination of finite energy sum rule techniques and Chiral Perturbation Theory (χPT) is used in order to exploit recent ALEPH data on the non-strange τ vector (V ) and axial-vector (A) spectral functions with respect to an experimental determination of the χPT quantity L10. A constrained fit of R (k,l) τ,V−A inverse moments (l < 0) and positive spectral moments (l ≥ 0) adjusts simultaneously L10 and the nonperturbative power terms of the Operator Product Expansion. We give explicit formulae for the first k = 0, 1 and l = −1,−2 strange and non-strange inverse moment chiral sum rules to one-loop order generalized χPT. Our final result reads L10(Mρ) = −(5.13 ± 0.19) × 10−3, where the error includes experimental and theoretical uncertainties. (Submitted to Physics Letters B) E-mail: [email protected] E-mail: [email protected] E-mail: [email protected] E-mail: [email protected]