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On the use of the Operator Product Expansion in finite-energy sum rules for light-quark correlators
by Diogo Boito, Maarten Golterman, Kim Maltman, Santiago Peris
Submission summary
| Authors (as registered SciPost users): | Maarten Golterman |
| Submission information | |
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| Preprint Link: | scipost_202112_00035v1 (pdf) |
| Date accepted: | 2024-12-09 |
| Date submitted: | 2021-12-14 21:33 |
| Submitted by: | Golterman, Maarten |
| Submitted to: | SciPost Physics Proceedings |
| Proceedings issue: | 16th International Workshop on Tau Lepton Physics (TAU2021) |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
Tau-based finite-energy sum-rule (FESR) analyses often assume that scales $s_0\sim m_\tau^2$ are large enough that (i) integrated duality violations (DVs) can be neglected, and (ii) contributions from non-perturbative OPE condensates of dimension $D$ scale as $(\Lambda_{\rm QCD}/m_\tau )^D$, allowing the OPE series to be truncated at low dimension. The latter assumption is not necessarily valid since the OPE series is not convergent, while the former is open to question given experimental results for the electromagnetic, $I=1$ vector ($V$), $I=1$ axial vector ($A$) and $I=1$ $V+A$ current spectral functions, which show DV oscillations with amplitudes comparable in size to the corresponding $\alpha_s$-dependent perturbative contributions at $s\sim2-3$~GeV$^2$. Here, we discuss recently introduced new tools for assessing the numerical relevance of omitted higher-$D$ OPE contributions. Applying these to the ``truncated OPE'' strategy used in Refs.~{\cite{Davier:2013sfa,Pich:2016bdg}} and earlier work by the same authors, we find that this strategy fails to yield reliable results for the strong coupling from hadronic $\tau$ decays.
Current status:
Editorial decision:
For Journal SciPost Physics Proceedings: Publish
(status: Editorial decision fixed and (if required) accepted by authors)
Reports on this Submission
Report #1 by Swagato Banerjee (Referee 1) on 2024-11-30 (Invited Report)
Report
The role of the Operator Product Expansion (OPE) in Finite-Energy Sum Rules used in the determination of the strong coupling constant from hadronic τ-decay data are discussed using new tools designed to study the numerical relevance of omitted higher dimensional contributions. The “truncated OPE” strategy, which assumes negligible contributions from higher-order OPE terms and duality violations, leads to unreliable results due to unquantifiable systematic errors particularly at scales near the τ-mass. For precise determinations of the strong coupling constant, alternative methods such as duality-violation models could yield a more reliable analyses.
Recommendation
Publish (surpasses expectations and criteria for this Journal; among top 10%)