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Title: Evidence against naive truncations of the OPE from e + e − → hadrons below charm

Abstract

The operator product expansion (OPE), truncated in dimension, is employed in many contexts. An example is the extraction of the strong coupling, $$\alpha_s$$, from hadronic $$\tau$$-decay data, using a variety of analysis methods based on finite-energy sum rules. Here, we reconsider a long-used method, which parametrizes non-perturbative contributions to the $I=1$ vector and axial vacuum polarizations with the OPE, setting several higher-dimension coefficients to zero in order to implement the method in practice. The assumption that doing this has a negligible effect on the value of $$\alpha_s$$ is tantamount to the assumption that the low-dimension part of the OPE converges rapidly with increasing dimension near the $$\tau$$ mass. Were this assumption valid, it would certainly have to be valid at energies above the $$\tau$$ mass as well. It follows that the method can be tested using data obtained from $$e^+e^-\to\mbox{hadrons}$$, as they are not limited by the kinematic constraints of $$\tau$$ decays. We carry out such an investigation using a recent high-precision compilation for the $$R$$ ratio, arguing that it provides insights into the validity of the strategy, even if it probes a different, though related channel. We find that $e^+e^-$-based tests call into question the implied assumption of rapid convergence of the low-dimension part of the OPE around the $$\tau$$ mass, and thus underscore the need to restrict finite-energy sum-rule analyses to observables which receive only contributions from lower-order terms in the OPE.

Authors:
; ORCiD logo; ORCiD logo; ORCiD logo
Publication Date:
Research Org.:
San Francisco State Univ., San Francisco, CA (United States); San Francisco State Univ., CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP); São Paulo Research Foundation (FAPESP)
OSTI Identifier:
1570035
Alternate Identifier(s):
OSTI ID: 1569841; OSTI ID: 1594604; OSTI ID: 1901683
Grant/Contract Number:  
FG03-92ER40711; SC0013682; 2015/20689-9; 309847/2018-4; CICYTFEDER-FPA2017-86989-P
Resource Type:
Published Article
Journal Name:
Physical Review. D.
Additional Journal Information:
Journal Name: Physical Review. D. Journal Volume: 100 Journal Issue: 7; Journal ID: ISSN 2470-0010
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Quantum chromodynamics; Strong interaction

Citation Formats

Boito, Diogo, Golterman, Maarten, Maltman, Kim, and Peris, Santiago. Evidence against naive truncations of the OPE from e + e − → hadrons below charm. United States: N. p., 2019. Web. doi:10.1103/PhysRevD.100.074009.
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Boito, Diogo, Golterman, Maarten, Maltman, Kim, & Peris, Santiago. Evidence against naive truncations of the OPE from e + e − → hadrons below charm. United States. https://doi.org/10.1103/PhysRevD.100.074009
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Boito, Diogo, Golterman, Maarten, Maltman, Kim, and Peris, Santiago. Thu . "Evidence against naive truncations of the OPE from e + e − → hadrons below charm". United States. https://doi.org/10.1103/PhysRevD.100.074009.
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@article{osti_1570035,
title = {Evidence against naive truncations of the OPE from e + e − → hadrons below charm},
author = {Boito, Diogo and Golterman, Maarten and Maltman, Kim and Peris, Santiago},
abstractNote = {The operator product expansion (OPE), truncated in dimension, is employed in many contexts. An example is the extraction of the strong coupling, $\alpha_s$, from hadronic $\tau$-decay data, using a variety of analysis methods based on finite-energy sum rules. Here, we reconsider a long-used method, which parametrizes non-perturbative contributions to the $I=1$ vector and axial vacuum polarizations with the OPE, setting several higher-dimension coefficients to zero in order to implement the method in practice. The assumption that doing this has a negligible effect on the value of $\alpha_s$ is tantamount to the assumption that the low-dimension part of the OPE converges rapidly with increasing dimension near the $\tau$ mass. Were this assumption valid, it would certainly have to be valid at energies above the $\tau$ mass as well. It follows that the method can be tested using data obtained from $e^+e^-\to\mbox{hadrons}$, as they are not limited by the kinematic constraints of $\tau$ decays. We carry out such an investigation using a recent high-precision compilation for the $R$ ratio, arguing that it provides insights into the validity of the strategy, even if it probes a different, though related channel. We find that $e^+e^-$-based tests call into question the implied assumption of rapid convergence of the low-dimension part of the OPE around the $\tau$ mass, and thus underscore the need to restrict finite-energy sum-rule analyses to observables which receive only contributions from lower-order terms in the OPE.},
doi = {10.1103/PhysRevD.100.074009},
journal = {Physical Review. D.},
number = 7,
volume = 100,
place = {United States},
year = {Thu Oct 10 00:00:00 EDT 2019},
month = {Thu Oct 10 00:00:00 EDT 2019}
}
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Journal Article:
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Publisher's Version of Record
https://doi.org/10.1103/PhysRevD.100.074009
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Cited by: 11 works
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Figures / Tables:

FIG. 1 FIG. 1: A blowup of R ratio in the region 2 ≤ s ≤ 6 GeV2. The red solid and red dashed lines show the results obtained from perturbation theory with αs(more » $m$$^{2}_{τ}$) = 0.28 and αs($m$$^{2}_{τ}$) = 0.32, respectively. The vertical dashed line is s = $m$$^{2}_{τ}$.« less
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    FIG. 1 (p. 4)figure
    FIG. 2 (p. 4)figure
    TABLE I (p. 4)table
    TABLE II (p. 4)table
    FIG. 3 (p. 5)figure
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    FIG. 9 (p. 11)figure
    FIG. 10 (p. 12)figure
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