arXiv subjects

Diego Teca

Publications and source records attributed to Diego Teca.

4 recordsLinked to original sources

arXiv2023

Borel-Laplace Sum Rules with $τ$ decay data, using OPE with improved anomalous dimensions

We perform numerical analysis of double-pinched Borel-Laplace QCD sum rules for the strangeless semihadronic $τ$-decay data. The $D=0$ contribution to the theoretical contour integral in the sum rules is evaluated by the (truncated) Fixed Order perturbation theory method (FO) and by the Principal Value (PV) of the Borel integration. We use for the full Adler function the Operator Product Expansion (OPE) with the terms $\sim \langle O_D \rangle$ of dimension $D=2 n$ where $2 \leq n \leq 5$ for the (V+A)-channel, and $2 \leq n \leq 7$ for the V-channel data. In our previous works [1,2], only the (V+A)-channel data was analysed. In this work, the analysis of a new set of V-channel data is performed as well. Further, a renormalon-motivated construction of the $D=0$ part of the Adler function is improved in the $u=3$ infrared renormalon sector, by involving the recently known information on the two principal noninteger values $k^{(j)}=γ^{(1)}(O_6^{(j)})/β_0$ of the effective leading-order anomalous dimensions. Additionally, the OPE of the Adler function has now the D=6 contribution with the principal anomalous dimension ($\sim α_s^{k^{(1)}}$), and terms of higher dimension (with zero anomalous dimension). Cross-checks of the obtained extracted values of $α_s$ and of the condensates were performed by reproduction of the (central) experimental values of several double-pinched momenta $a^{(2,n)}$. The averaged final extracted values of the (MSbar) coupling are: $α_s(m_τ^2) = 0.3169^{+0.0070}_{-0.0096}$, corresponding to $α_s(M_Z^2)=0.1183^{+0.0009}_{-0.0012}$.

hep-ph↗

arXiv2022

Using improved Operator Product Expansion in Borel-Laplace Sum Rules with ALEPH $τ$ decay data, and determination of pQCD coupling

We use improved truncated Operator Product Expansion (OPE) for the Adler function, involving two types of terms with dimension $D=6$, in the double-pinched Borel-Laplace Sum Rules and Finite Energy Sum Rules for the V+A channel strangeless semihadronic $τ$ decays. The generation of the higher order perturbative QCD terms of the $D=0$ 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 $D=0$ 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 $τ$-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 ${\overline {\rm MS}}$ coupling $α_s(m_τ^2) = 0.3235^{+0.0138}_{-0.0126}$ [$α_s(M_Z^2)=0.1191 \pm 0.0016$] 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 $α_s(m_τ^2) = 0.3299^{+0.0232}_{-0.0225}$ [$α_s(M_Z^2)=0.1199^{+0.0026}_{-0.0028}$]. This work is an extension and improvement of our previous work [Eur.Phys.J.C81 (2021) 10, 930] where we used for the truncated OPE a more naive (and widely used) form and where the extracted values for $α_s(M_Z^2)$ were somewhat lower.

hep-ph↗

arXiv2022

Extraction of $α_s$ using Borel-Laplace sum rules for tau decay data

Double-pinched Borel-Laplace sum rules are applied to ALEPH $τ$-decay data. For the leading-twist ($D=0$) Adler function a renormalon-motivated extension is used, and the 5-loop coefficient is taken to be $d_4=275 \pm 63$. Two $D=6$ terms appear in the truncated OPE ($D \leq 6$) to enable cancellation of the corresponding renormalon ambiguities. Two variants of the fixed order perturbation theory, and the inverse Borel transform, are applied to the evaluation of the $D=0$ contribution. Truncation index $N_t$ is fixed by the requirement of local insensitivity of the momenta $a^{(2,0)}$ and $a^{(2,1)}$ under variation of $N_t$. The averaged value of the coupling obtained is $α_s(m_τ^2)=0.3235^{+0.0138}_{-0.0126}$ [$α_s(M_Z^2)=0.1191 \pm 0.0016$]. The theoretical uncertainties are significantly larger than the experimental ones.

hep-ph↗

arXiv2021

Determination of perturbative QCD coupling from ALEPH $τ$ decay data using pinched Borel-Laplace and Finite Energy Sum Rules

We present a determination of the perturbative QCD (pQCD) coupling using the V+A channel ALEPH $τ$-decay data. The determination involves the double-pinched Borel-Laplace Sum Rules and Finite Energy Sum Rules. The theoretical basis is the Operator Product Expansion (OPE) of the V+A channel Adler function in which the higher order terms of the leading-twist part originate from a model based on the known structure of the leading renormalons of this quantity. The applied evaluation methods are contour-improved perturbation theory (CIPT), fixed-order perturbation theory (FOPT), and Principal Value of the Borel resummation (PV). All the methods involve truncations in the order of the coupling. In contrast to the truncated CIPT method, the truncated FOPT and PV methods account correctly for the suppression of various renormalon contributions of the Adler function in the mentioned sum rules. The extracted value of the ${\overline {\rm MS}}$ coupling is $α_s(m_τ^2) = 0.3116 \pm 0.0073$ [$α_s(M_Z^2)=0.1176 \pm 0.0010$] for the average of the FOPT and PV methods, which we regard as our main result. On the other hand, if we include in the average also the CIPT method, the resulting values are significantly higher, $α_s(m_τ^2) = 0.3194 \pm 0.0167$ [$α_s(M_Z^2)=0.1186 \pm 0.0021$].

hep-ph↗