Using improved operator product expansion in Borel–Laplace sum rules with ALEPH decay data, and determination of pQCD coupling

César Ayala; Gorazd Cvetič; Diego Teca

doi:10.1140/epjc/s10052-022-10298-w

2023 Impact factor 4.2

Particles and Fields

Open Access

Eur. Phys. J. C (2022) 82: 362
https://doi.org/10.1140/epjc/s10052-022-10298-w

Regular Article - Theoretical Physics

Using improved operator product expansion in Borel–Laplace sum rules with ALEPH $τ$ $\tau$ decay data, and determination of pQCD coupling

César Ayala¹, Gorazd Cvetič² and Diego Teca²^c

¹ Instituto de Alta Investigación, Sede Esmeralda, Universidad de Tarapacá, Av. Luis Emilio Recabarren 2477, Iquique, Chile
² Department of Physics, Universidad Técnica Federico Santa María (UTFSM), Casilla 110-V, Valparaíso, Chile

^c diegotecawellmann@gmail.com

Received: 10 December 2021
Accepted: 6 April 2022
Published online: 25 April 2022

Abstract

We use improved truncated operator product expansion (OPE) for the Adler function, involving two types of terms with dimension $D = 6$ $$D=6$$ , in the double-pinched Borel–Laplace sum rules and finite energy sum rules for the V + A channel strangeless semihadronic $τ$ $\tau$ decays. The generation of the higher order perturbative QCD terms of the $D = 0$ $$D=0$$ part of the Adler function is carried out using a renormalon-motivated ansatz incorporating the leading UV renormalon and the first two leading IR renormalons. The trunacted $D = 0$ $$D=0$$ part of the sum rules is evaluated by two variants of the fixed-order perturbation theory (FO), by principal value of the Borel resummation (PV), and by contour-improved perturbation theory (CI). For the experimental V + A channel spectral function we use the ALEPH $τ$ $\tau$ -decay data. We point out that the truncated FO and PV evaluation methods account correctly for the renormalon structure of the sum rules, while this is not the case for the truncated CI evaluation. We extract the value of the $\bar{MS}$ ${\overline{\mathrm{MS}}}$ coupling $α_{s} (m_{τ}^{2}) = 0 . 3235_{- 0.0126}^{+ 0.0138}$ $\alpha _s(m_{\tau }^2) = 0.3235^{+0.0138}_{-0.0126}$ [ $α_{s} (M_{Z}^{2}) = 0.1191 \pm 0.0016$ $\alpha _s(M_Z^2)=0.1191 \pm 0.0016$ ] for the average of the two FO methods and the PV method, which we consider as our main result. If we included in the average also CI extraction, the value would be $α_{s} (m_{τ}^{2}) = 0 . 3299_{- 0.0225}^{+ 0.0232}$ $\alpha _s(m_{\tau }^2) = 0.3299^{+0.0232}_{-0.0225}$ [ $α_{s} (M_{Z}^{2}) = 0 . 1199_{- 0.0028}^{+ 0.0026}$ $\alpha _s(M_Z^2)=0.1199^{+0.0026}_{-0.0028}$ ]. This work is an extension and improvement of our previous work (Ayala et al. in Eur Phys J. C 81(10): 930, 2021, arXiv:2105.00356 [hep-ph]) where we used for the truncated OPE a more naive (and widely used) form and where the extracted values for $α_{s} (M_{Z}^{2})$ $\alpha _s(M_Z^2)$ were somewhat lower.

© The Author(s) 2022

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Funded by SCOAP³

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Using improved operator product expansion in Borel–Laplace sum rules with ALEPH τ decay data, and determination of pQCD coupling

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Using improved operator product expansion in Borel–Laplace sum rules with ALEPH $τ$ $\tau$ decay data, and determination of pQCD coupling