On the use of the operator product expansion in finite-energy sum rules for light-quark correlators
Bibliographic record
Abstract
Tau-based finite-energy sum-rule (FESR) analyses often assume that scales s_0\sim m_\tau^2 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:msub> <mml:mi>s</mml:mi> <mml:mn>0</mml:mn> </mml:msub> <mml:mo>∼</mml:mo> <mml:msubsup> <mml:mi>m</mml:mi> <mml:mi>τ</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> </mml:mrow> </mml:math> are large enough that (i) integrated duality violations (DVs) can be neglected, and (ii) contributions from non-perturbative OPE condensates of dimension D <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>D</mml:mi> </mml:math> scale as (\Lambda_{QCD}/m_\tau )^D <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mo stretchy="false" form="prefix">(</mml:mo> <mml:msub> <mml:mi>Λ</mml:mi> <mml:mrow> <mml:mi>Q</mml:mi> <mml:mi>C</mml:mi> <mml:mi>D</mml:mi> </mml:mrow> </mml:msub> <mml:mi>/</mml:mi> <mml:msub> <mml:mi>m</mml:mi> <mml:mi>τ</mml:mi> </mml:msub> <mml:msup> <mml:mo stretchy="false" form="postfix">)</mml:mo> <mml:mi>D</mml:mi> </mml:msup> </mml:mrow> </mml:math> , 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>I</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> vector ( V <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>V</mml:mi> </mml:math> ), I=1 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>I</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> axial vector ( A <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>A</mml:mi> </mml:math> ) and I=1 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>I</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> V+A <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>V</mml:mi> <mml:mo>+</mml:mo> <mml:mi>A</mml:mi> </mml:mrow> </mml:math> current spectral functions, which show DV oscillations with amplitudes comparable in size to the corresponding \alpha_s <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mi>α</mml:mi> <mml:mi>s</mml:mi> </mml:msub> </mml:math> -dependent perturbative contributions at s\sim2-3 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>s</mml:mi> <mml:mo>∼</mml:mo> <mml:mn>2</mml:mn> <mml:mo>−</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> </mml:math> GeV ^2 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msup> <mml:mi/> <mml:mn>2</mml:mn> </mml:msup> </mml:math> . Here, we discuss recently introduced new tools for assessing the numerical relevance of omitted higher- D <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>D</mml:mi> </mml:math> OPE contributions. Applying these to the “truncated OPE” strategy used in Refs.[M. Davier et al., Eur. Phys. J. C 74, 2803 (2014); A. Pich and A. Rodríguez-Sánchez, Phys. Rev. D 94, 034027 (2016)] and earlier work by the same authors, we find that this strategy fails to yield reliable results for the strong coupling from hadronic \tau <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>τ</mml:mi> </mml:math> decays.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".