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|As Contributors:||Kim Maltman · Santiago Peris|
|Submitted by:||Peris, Santiago|
|Submitted to:||SciPost Physics Proceedings|
|Subject area:||High-Energy Physics - Phenomenology|
We discuss sum-rule determinations of $\alpha_s$ from non-strange hadronic $\tau$-decay data. We investigate, in particular, the reliability of the assumptions underlying the "truncated OPE strategy," which specifies a certain treatment of non-perturbative contributions, and which was employed in Refs. [1-3]. Here, we test this strategy by applying the strategy to the $R$-ratio obtained from $e^+e^-$ data, which extend beyond the $\tau$ mass, and, based on the outcome of these tests, we demonstrate the failure of this strategy.We then present a brief overview of new results on the form of duality-violating non-perturbative contributions, which are conspicuously present in the experimentally determined spectral functions. As we show, with the current precision claimed for the extraction of $\alpha_s$, including a representation of duality violations is unavoidable if one wishes to avoid uncontrolled theoretical errors.
This contribution aims at showing that duality violations cannot be neglected in the determination of the QCD coupling from hadronic $\tau$ decays. While the analysis of duality violations is certainly an important topic that needs to be addressed case by case, I have some doubts about the adopted strategy and I miss some crucial information in the text. Therefore, I would like to ask the authors to consider the points described under "Requested changes", and modify the paper accordingly.
1. I believe that the authors do not show compelling evidence that the analysis in section 2 of $e^+e^-$ data (V channel) should imply the failure of OPE-based analyses applied to $\tau$-decay in the V+A channel. As I said, these issues must be addressed in detail case by case. The authors instead do not go beyond general claims, and these general claims are repeated many times in the paper. As the authors themselves observe, the V case is different from the V+A case. I would like the authors to limit their comments to those based on quantifiable and clearly formulated evidence.
2. The title is misleading, because it is an analysis of $e^+e^-$ data, see point 1. Maybe the authors can find a title that better captures the full content of the contribution.
3. I cannot find a clear error analysis of the theoretical predictions, e.g. the uncertainties associated to the curves shown in Figure 3, and how they could actually impact the $\tau$-decay determinations of $\alpha_s$. I would like the authors to address more precisely the theoretical uncertainties in their analysis, also by means of references to the appropriate published works.
4. The authors define a truncated-OPE strategy in section 2, where they assume that certain higher dimensional condensates can be neglected. They also seem to imply that this is what is done in other analyses which they criticise. I disagree. My understanding of the latter analyses is that the sensitivity of the result, e.g., $\alpha_s$, to higher dimensional condensates has been estimated through fits to data with varying weights. The same should be done for the example in Figure 3. I would like the authors to better formulate the related text.
5. In section 3 the authors discuss a model for duality violations. The parameters of this model are determined in specific ranges of $q^2$ and for specific processes. The authors then observe that the agreement of (20) with the results from the fit involving $\tau$ data is rather satisfactory. However, I could not find a complete analysis by the authors showing how their fitted parameterisation (20) behaves outside the fitted regions and for $\tau$-data versus $e^+e^-$ data. The authors should be more clear about this aspect and provide the relevant information.