Neural network parametrization of spectral functions from hadronic tau decays and determination of QCD vacuum condensates

TL;DR

The paper presents a neural-network framework to parametrize the spectral function difference $\rho_{V-A}(s)$ from hadronic tau-decay data, preserving full experimental uncertainties and enforcing chiral sum rules to minimize theoretical bias. By fitting to ALEPH and OPAL data via Monte Carlo replicas and incorporating sum-rule constraints through genetic-algorithm training, the authors extract nonperturbative QCD vacuum condensates, finding negative central values for $⟨\mathcal{O}_6⟩$ and $⟨\mathcal{O}_8⟩$ with quantified uncertainties. This approach reduces dependence on specific finite-energy sum rules and provides a robust, bias-controlled determination of higher-dimension condensates, with implications for precision QCD phenomenology and related electroweak penguin analyses.

Abstract

The spectral function $ρ_{V-A}(s)$ is determined from ALEPH and OPAL data on hadronic tau decays using a neural network parametrization trained to retain the full experimental information on errors, their correlations and chiral sum rules: the DMO sum rule, the first and second Weinberg sum rules and the electromagnetic mass splitting of the pion sum rule. Nonperturbative QCD vacuum condensates can then be determined from finite energy sum rules. Our method minimizes all sources of theoretical uncertainty and bias producing an estimate of the condensates which is independent of the specific finite energy sum rule used. The results for the central values of the condensates $O_6$ and $O_8$ are both negative.

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