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Probing the Energy-Smeared R Ratio Using Lattice QCD

Physical Review Letters 2023年第24期130卷 241901-241901页

作者： Constantia Alexandrou Simone Bacchio Alessandro De Santis Petros Dimopoulos Jacob Finkenrath Roberto Frezzotti Giuseppe Gagliardi Marco Garofalo Kyriakos Hadjiyiannakou Bartosz Kostrzewa Karl Jansen Vittorio Lubicz Marcus Petschlies Francesco Sanfilippo Silvano Simula Nazario Tantalo Carsten Urbach Urs Wenger Department of Physics University of Cyprus 20537 Nicosia Cyprus Computation-based Science and Technology Research Center The Cyprus Institute 20 Konstantinou Kavafi Street 2121 Nicosia Cyprus Dipartimento di Fisica and INFN Università di Roma Tor Vergata Via della Ricerca Scientifica 1 I-00133 Roma Italy Dipartimento di Scienze Matematiche Fisiche e Informatiche Università di Parma and INFN Gruppo Collegato di Parma Parco Area delle Scienze 7/a (Campus) 43124 Parma Italy Istituto Nazionale di Fisica Nucleare Sezione di Roma Tre Via della Vasca Navale 84 I-00146 Rome Italy HISKP (Theory) Rheinische Friedrich-Wilhelms-Universität Bonn Nussallee 14-16 53115 Bonn Germany High Performance Computing and Analytics Lab Rheinische Friedrich-Wilhelms-Universität Bonn Friedrich-Hirzebruch-Allee 8 53115 Bonn Germany NIC DESY Platanenallee 6 D-15738 Zeuthen Germany Dipartimento di Matematica e Fisica Università Roma Tre and INFN Sezione di Roma Tre Via della Vasca Navale 84 I-00146 Rome Italy Institute for Theoretical Physics Albert Einstein Center for Fundamental Physics University of Bern Sidlerstrasse 5 CH-3012 Bern Switzerland

We present a first-principles lattice QCD investigation of the R ratio between the e+e− cross section into hadrons and into muons. By using the method of Ref. [1], that allows one to extract smeared spectral densities from Euclidean correlators, we compute the R ratio convoluted with Gaussian smearing kernels of widths of about 600 MeV and central energies from 220 MeV up to 2.5 GeV. Our theoretical results are compared with the corresponding quantities obtained by smearing the KNT19 compilation [2] of R-ratio experimental measurements with the same kernels and, by centering the Gaussians in the region around the ρ-resonance peak, a tension of about 3 standard deviations is observed. From the phenomenological perspective, we have not included yet in our calculation QED and strong isospin-breaking corrections, and this might affect the observed tension. From the methodological perspective, our calculation demonstrates that it is possible to study the R ratio in Gaussian energy bins on the lattice at the level of accuracy required in order to perform precision tests of the standard model.

关键词： Hadron-hadron interactions Lattice QCD

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Determination of the light, strange and charm quark masses using twisted mass fermions 38

Determination of the light, strange and charm quark masses u...

引用

38th International Symposium on Lattice Field Theory, LATTICE 2021

作者： Alexandrou, C. Bacchio, S. Bergner, G. Constantinou, M. Di Carlo, M. Dimopoulos, P. Finkenrath, J. Fiorenza, E. Frezzotti, R. Garofalo, M. Hadjiyiannakou, K. Kostrzewa, B. Koutsou, G. Jansen, K. Lubicz, V. Mangin-Brinet, M. Manigrasso, F. Martinelli, G. Pittler, F. Rossi, G.C. Sanfilippo, F. Simula, S. Tarantino, C. Todaro, A. Urbach, C. Wenger, U. Department of Physics University of Cyprus Nicosia20537 Cyprus Computation-Based Science and Technology Research Center The Cyprus Institute Cyprus University of Jena Institute for Theoretical Physics Max-Wien-Platz 1 JenaD-07743 Germany Department of Physics Temple University PhiladelphiaPA19122-1801 United States School of Physics and Astronomy The University of Edinburgh EdinburghEH9 3FD United Kingdom Istituto Nazionale di Fisica Nucleare Sezione di Roma La Sapienza Italy Dipartimento di Scienze Matematiche Fisiche e Informatiche Università di Parma INFN Italy CP3-Origins University of Southern Denmark Campusvej 55 Odense5230 Denmark Dipartimento di Fisica INFN Università di Roma "Tor Vergata" RomeI-00133 Italy Rheinische Friedrich-Wilhelms-Universität Bonn Germany High Performance Computing and Analytics Lab Rheinische Friedrich-Wilhelms-Universität Bonn Germany NIC DESY Platanenallee 6 ZeuthenD-15738 Germany Dipartimento di Matematica e Fisica Università Roma Tre INFN Sezione di Roma Tre Italy Theory Group Laboratoire de Physique Subatomique et de Cosmologie Grenoble France Institut für Physik Humboldt-Universität zu Berlin Newtonstrasse 15 Berlin12489 Germany Dipartimento di Fisica INFN Università di Roma "La Sapienza" RomeI-00185 Italy Centro Fermi Museo Storico della Fisica e Centro Studi e Ricerche "Enrico Fermi" Italy Istituto Nazionale di Fisica Nucleare Sezione di Roma Tre Italy Institute for Theoretical Physics Albert Einstein Center for Fundamental Physics Switzerland

We present results for the light, strange and charm quark masses using Nf = 2 + 1 + 1 twisted mass fermion ensembles at three values of the lattice spacing, including two ensembles simulated with the physical value of the pion mass. The analysis is done both in the meson and baryon sectors. The difference in the mean values found in the two sectors is included as part of the systematic error. The presentation is based on the work of Ref. [1], where more details can be found. © Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0)

关键词： Lattice theory

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Pseudoscalar-pole contributions to the muon g-2 at the physical point

arXiv

引用

arXiv 2022年

作者： Burri, S. Kanwar, G. Alexandrou, C. Bacchio, S. Bergner, G. Finkenrath, J. Gasbarro, A. Hadjiyiannakou, K. Jansen, K. Kostrzewa, B. Koutsou, G. Ottnad, K. Petschlies, M. Pittler, F. Steffens, F. Urbach, C. Wenger, U. Albert Einstein Center for Fundamental Physics Institute for Theoretical Physics University of Bern Sidlerstrasse 5 BernCH–3012 Switzerland Department of Physics University of Cyprus Nicosia20537 Cyprus Computation-based Science and Technology Research Center The Cyprus Institute 20 Konstantinou Kavafi Street Nicosia2121 Cyprus University of Jena Institute for Theoretical Physics Max-Wien-Platz 1 JenaD-07743 Germany Deutsches Elektronen-Synchrotron DESY Platanenallee 6 Zeuthen15738 Germany High Performance Computing and Analytics Lab Rheinische Friedrich-Wilhelms-Universität Bonn Friedrich-Hirzebruch-Allee 8 BonnD-53115 Germany PRISMA+ Cluster of Excellence Institut für Kernphysik Johannes Gutenberg-Universität Mainz Johann-Joachim-Becher-Weg 45 MainzD-55128 Germany Rheinische Friedrich-Wilhelms-Universität Bonn Nussallee 14-16 BonnD-53115 Germany Bethe Center for Theoretical Physics Rheinische Friedrich-Wilhelms-Universität Bonn Wegelerstraße 10 BonnD-53115 Germany

Pseudoscalar-pole diagrams are an important component of estimates of the hadronic light-by-light (HLbL) contribution to the muon g − 2. We report on our computation of the transition form factors Fp→γ∗γ∗ for the neutral pseudoscalar mesons P = π0 and η. The calculation is performed using twisted-mass lattice QCD with physical quark masses. On the lattice, we have access to a broad range of (space-like) photon four-momenta and therefore produce form factor data complementary to the experimentally accessible single-virtual direction, which directly leads to an estimate of the pion- and η-pole components of the muon g − 2. For the pion, our result for the g − 2 contribution in the continuum is comparable with previous lattice and data-driven determinations, with combined relative uncertainties below 10%. For the η meson, we report on a preliminary determination from a single lattice spacing. Copyright © 2022, The Authors. All rights reserved.

关键词： Poles

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Pion-pole contribution to HLbL from twisted mass lattice QCD at the physical point

arXiv

引用

arXiv 2021年

作者： Burri, S. Alexandrou, C. Bacchio, S. Bergner, G. Finkenrath, J. Gasbarro, A. Hadjiyiannakou, K. Jansen, K. Kostrzewa, B. Koutsou, G. Ottnad, K. Petschlies, M. Pittler, F. Steffens, F. Urbach, C. Wenger, U. Albert Einstein Center for Fundamental Physics Institute for Theoretical Physics University of Bern Sidlerstrasse 5 BernCH–3012 Switzerland Department of Physics University of Cyprus Nicosia20537 Cyprus Computation-based Science and Technology Research Center The Cyprus Institute 20 Konstantinou Kavafi Street Nicosia2121 Cyprus University of Jena Institute for Theoretical Physics Max-Wien-Platz 1 JenaD-07743 Germany Deutsches Elektronen-Synchrotron DESY Platanenallee 6 Zeuthen15738 Germany High Performance Computing and Analytics Lab Rheinische Friedrich-Wilhelms-Universität Bonn Friedrich-Hirzebruch-Allee 8 BonnD-53115 Germany PRISMA+ Cluster of Excellence and Institut für Kernphysik Johannes Gutenberg-Universität Mainz Johann-Joachim-Becher-Weg 45 MainzD-55128 Germany Rheinische Friedrich-Wilhelms-Universität Bonn Nussallee 14-16 BonnD-53115 Germany Bethe Center for Theoretical Physics Rheinische Friedrich-Wilhelms-Universität Bonn Wegelerstraße 10 BonnD-53115 Germany

We report on our computation of the pion transition form factor Fπ→γ∗γ∗ from twisted mass lattice QCD in order to determine the numerically dominant light pseudoscalar pole contribution in the hadronic light-by-light scattering contribution to the anomalous magnetic moment of the muon aμ = (g − 2)μ. The pion transition form factor is computed directly at the physical point. We present first results for our estimate of the pion-pole contribution with kinematic setup for the pion at rest. Copyright © 2021, The Authors. All rights reserved.

关键词： Quantum theory

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Pion transition form factor from twisted-mass lattice QCD and the hadronic light-by-light π0-pole contribution to the muon g−2

引用

Physical Review D 2023年第9期108卷 094514-094514页

作者： C. Alexandrou S. Bacchio G. Bergner S. Burri J. Finkenrath A. Gasbarro K. Hadjiyiannakou K. Jansen G. Kanwar B. Kostrzewa G. Koutsou K. Ottnad M. Petschlies F. Pittler F. Steffens C. Urbach U. Wenger Department of Physics University of Cyprus 20537 Nicosia Cyprus Computation-based Science and Technology Research Center The Cyprus Institute 20 Konstantinou Kavafi Street 2121 Nicosia Cyprus University of Jena Institute for Theoretical Physics Max-Wien-Platz 1 D-07743 Jena Germany Albert Einstein Center for Fundamental Physics Institute for Theoretical Physics University of Bern Sidlerstrasse 5 CH–3012 Bern Switzerland Bergische Universität Wuppertal Gaußstraße 20 42119 Wuppertal Germany Deutsches Elektronen-Synchrotron DESY Platanenallee 6 15738 Zeuthen Germany High Performance Computing and Analytics Lab Rheinische Friedrich-Wilhelms-Universität Bonn Friedrich-Hirzebruch-Allee 8 D-53115 Bonn Germany PRISMA+ Cluster of Excellence and Institut für Kernphysik Johannes Gutenberg-Universität Mainz Johann-Joachim-Becher-Weg 45 D-55128 Mainz Germany HISKP (Theory) Rheinische Friedrich-Wilhelms-Universität Bonn Nussallee 14-16 D-53115 Bonn Germany Bethe Center for Theoretical Physics Rheinische Friedrich-Wilhelms-Universität Bonn Wegelerstraße 10 D-53115 Bonn Germany

The neutral pion generates the leading pole contribution to the hadronic light-by-light tensor, which is given in terms of the nonperturbative transition form factor Fπ0γγ(q12,q22). Here we present an ab-initio lattice calculation of this quantity in the continuum and at the physical point using twisted-mass lattice QCD. We report our results for the transition form factor parametrized using a model-independent conformal expansion valid for arbitrary spacelike kinematics and compare it with experimental measurements of the single-virtual form factor, the two-photon decay width, and the slope parameter. We then use the transition form factors to compute the pion-pole contribution to the hadronic light-by-light scattering in the muon g−2, finding aμπ0−pole=56.7(3.2)×10−11.

关键词： Lattice field theory Magnetic moment Pions Form factors Ab initio calculations Lattice QCD Path-integral Monte Carlo

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Lattice calculation of the R-ratio smeared with Gaussian kernels

arXiv

引用

arXiv 2022年

作者： Alexandrou, C. Bacchio, S. De Santis, A. Dimopoulos, P. Finkenrath, J. Frezzotti, R. Gagliardi, G. Garofalo, M. Hadjiyiannakou, K. Kostrzewa, B. Jansen, K. Lubicz, V. Petschlies, M. Sanfilippo, F. Simula, S. Tantalo, N. Urbach, C. Wenger, U. Department of Physics University of Cyprus Nicosia20537 Cyprus Computation-based Science and Technology Research Center The Cyprus Institute 20 Konstantinou Kavafi Street Nicosia2121 Cyprus Dipartimento di Fisica INFN Università di Roma Tor Vergata Via della Ricerca Scientifica 1 RomaI-00133 Italy Parma43124 Italy Istituto Nazionale di Fisica Nucleare Sezione di Roma Tre Via della Vasca Navale 84 RomeI-00146 Italy Rheinische Friedrich-Wilhelms-Universität Bonn Nussallee 14-16 Bonn53115 Germany High Performance Computing and Analytics Lab Rheinische Friedrich-Wilhelms-Universität Bonn Friedrich-Hirzebruch-Allee 8 Bonn53115 Germany NIC DESY Platanenallee 6 ZeuthenD-15738 Germany Dipartimento di Matematica e Fisica Università Roma Tre INFN Sezione di Roma Tre Via della Vasca Navale 84 RomeI-00146 Italy Institute for Theoretical Physics Albert Einstein Center for Fundamental Physics University of Bern Sidlerstrasse 5 BernCH-3012 Switzerland

The ratio R(E) of the cross-sections for e+e− → hadrons and e+e− → μ+ μ− is a valuable energy-dependent probe of the hadronic sector of the Standard Model. Moreover, the experimental measurements of R(E) are the inputs of the dispersive calculations of the leading hadronic vacuum polarization contribution to the muon g − 2 and these are in significant tension with direct lattice calculations and with the muon g − 2 experiment. In this talk we discuss the results of our first-principles lattice study of R(E). By using a recently proposed method for extracting smeared spectral densities from Euclidean lattice correlators, we have calculated R(E) convoluted with Gaussian kernels of different widths σ and central energies up to 2.5 GeV. Our theoretical results have been compared with the KNT19 [1] compilation of experimental results smeared with the same Gaussian kernels and a tension (about three standard deviations) has been observed for σ ∼ 600 MeV and central energies around the ρ-resonance peak. © 2022, CC BY.

关键词： Correlators

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Short & intermediate distance HVP contributions to muon g-2: SM (lattice) prediction versus e+e- annihilation data

arXiv

引用

arXiv 2022年

作者： Alexandrou, Constantia Bacchio, Simone Dimopoulos, Petros Finkenrath, Jacob Frezzotti, Roberto Gagliardi, Giuseppe Garofalo, Marco Hadjiyiannakou, Kyriakos Kostrzewa, Bartosz Jansen, Karl Lubicz, Vittorio Petschlies, Marcus Sanfilippo, Francesco Simula, Silvano Urbach, Carsten Wenger, Urs Department of Physics University of Cyprus Nicosia20537 Cyprus Computation-based Science and Technology Research Center The Cyprus Institute 20 Konstantinou Kavafi Street Nicosia2121 Cyprus Parma43124 Italy Dipartimento di Fisica Università di Roma "Tor Vergata" INFN Sezione di Roma Tor Vergata Via della Ricerca Scientifica 1 RomeI-00133 Italy Istituto Nazionale di Fisica Nucleare Sezione di Roma Tre Via della Vasca Navale 84 RomeI-00146 Italy Rheinische Friedrich-Wilhelms-Universität Bonn Nussallee 14-16 Bonn53115 Germany High Performance Computing and Analytics Lab Rheinische Friedrich-Wilhelms-Universität Bonn Friedrich-Hirzebruch-Allee 8 Bonn53115 Germany NIC DESY Platanenallee 6 ZeuthenD-15738 Germany Dipartimento di Matematica e Fisica Università Roma Tre Via della Vasca Navale 84 RomeI-00146 Italy Institute for Theoretical Physics Albert Einstein Center for Fundamental Physics University of Bern Sidlerstrasse 5 BernCH-3012 Switzerland

We present new lattice results of the ETM Collaboration, obtained from extensive simulations of lattice QCD with dynamical up, down, strange and charm quarks at physical mass values, different volumes and lattice spacings, concerning the SM prediction for the so-called intermediate window (W) and short-distance (SD) contributions to the leading order hadronic vacuum polarization (LO-HVP) term of the muon anomalous magnetic moment, aμ. Results for aLOμ−HVP,W and aLOμ−HVP,SD, besides representing a step forward to a complete lattice computation of aLOμ−HVP and a useful benchmark among lattice groups, are compared here with their dispersive counterparts based on experimental data for e+e− into hadrons. The comparison confirms the tension in aLOμ−HVP,W, already noted in 2020 by the BMW Collaboration, while showing no tension in aLOμ−HVP,SD. © 2022, CC BY.

关键词： Magnetic moments

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Time windows of the muon HVP from twisted-mass lattice QCD

arXiv

引用

arXiv 2022年

作者： Alexandrou, C. Bacchio, S. Dimopoulos, P. Finkenrath, J. Frezzotti, R. Gagliardi, G. Garofalo, M. Hadjiyiannakou, K. Kostrzewa, B. Jansen, K. Lubicz, V. Petschlies, M. Sanfilippo, F. Simula, S. Urbach, C. Wenger, U. Department of Physics University of Cyprus Nicosia20537 Cyprus Computation-based Science and Technology Research Center The Cyprus Institute 20 Konstantinou Kavafi Street Nicosia2121 Cyprus Parma43124 Italy Dipartimento di Fisica INFN Università di Roma "Tor Vergata" Via della Ricerca Scientifica 1 RomaI-00133 Italy Istituto Nazionale di Fisica Nucleare Sezione di Roma Tre Via della Vasca Navale 84 RomeI-00146 Italy Rheinische Friedrich-Wilhelms-Universität Bonn Nussallee 14-16 Bonn53115 Germany High Performance Computing and Analytics Lab Rheinische Friedrich-Wilhelms-Universität Bonn Friedrich-Hirzebruch-Allee 8 Bonn53115 Germany NIC DESY Platanenallee 6 ZeuthenD-15738 Germany Dipartimento di Matematica e Fisica Università Roma Tre INFN Sezione di Roma Tre Via della Vasca Navale 84 RomeI-00146 Italy Institute for Theoretical Physics Albert Einstein Center for Fundamental Physics University of Bern Sidlerstrasse 5 BernCH-3012 Switzerland

We present a lattice determination of the leading-order hadronic vacuum polarization (HVP) contribution to the muon anomalous magnetic moment, aHVPμ, in the so-called short and intermediate time-distance windows, aSDμ and aWμ. We employ gauge ensembles produced by the Extended Twisted Mass Collaboration (ETMC) with Nf = 2 + 1 + 1 flavours of Wilson-clover twisted-mass quarks with masses of all the dynamical quark flavours tuned close to their physical values. The simulations are carried out at three values of the lattice spacing equal to ' 0.057, 0.068 and 0.080 fm with spatial lattice sizes up to L ' 7.6 fm. For the short distance window we obtain aSDμ = 69.27 (34) · 10-10, in agreement with the dispersive determination based on experimental e+e- data. For the intermediate window we get instead aWμ = 236.3 (1.3) · 10-10, which is consistent with recent determinations by other lattice collaborations, but disagrees with the dispersive determination at the level of 3.6 σ. Copyright © 2022, The Authors. All rights reserved.

关键词： Magnetic moments

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Inclusive hadronic decay rate of the τ lepton from lattice QCD: the ūs flavour channel and the Cabibbo angle

arXiv

引用

arXiv 2024年

作者： Alexandrou, Constantia Bacchio, Simone De Santis, Alessandro Evangelista, Antonio Finkenrath, Jacob Frezzotti, Roberto Gagliardi, Giuseppe Garofalo, Marco Kostrzewa, Bartosz Lubicz, Vittorio Romiti, Simone Sanfilippo, Francesco Simula, Silvano Tantalo, Nazario Urbach, Carsten Wenger, Urs Department of Physics University of Cyprus Nicosia20537 Cyprus Computation-based Science and Technology Research Center The Cyprus Institute 20 Konstantinou Kavafi Street Nicosia2121 Cyprus Dipartimento di Fisica and INFN Università di Roma Tor Vergata Via della Ricerca Scientifica 1 RomaI-00133 Italy Bergische Universität Wuppertal Gaußstraße 20 Wuppertal42119 Germany Istituto Nazionale di Fisica Nucleare Sezione di Roma Tre Via della Vasca Navale 84 RomeI-00146 Italy Rheinische Friedrich-Wilhelms-Universität Bonn Nussallee 14-16 Bonn53115 Germany High Performance Computing and Analytics Lab Rheinische Friedrich-Wilhelms-Universität Bonn Friedrich-Hirzebruch-Allee 8 Bonn53115 Germany Dipartimento di Matematica e Fisica Università Roma Tre and INFN Sezione di Roma Tre Via della Vasca Navale 84 RomeI-00146 Italy Institute for Theoretical Physics Albert Einstein Center for Fundamental Physics University of Bern Sidlerstrasse 5 BernCH-3012 Switzerland

We present a lattice determination of the inclusive decay rate of the process τ 7→ Xusντ in which the τ lepton decays into a generic hadronic state Xus with ūs flavour quantum numbers. Our results have been obtained in nf = 2+1+1 iso-symmetric QCD with full non-perturbative accuracy, without any OPE approximation and, except for the presently missing long-distance isospin-breaking corrections, include a solid estimate of all sources of theoretical uncertainties. This has been possible by using the Hansen-Lupo-Tantalo method [1] that we have already successfully applied in [2] to compute the inclusive decay rate of the process τ 7→ Xudντ in the ūd flavour channel. By combining our first-principles theoretical results with the presently-available experimental data we extract the CKM matrix element |Vus|, the Cabibbo angle, with a 0.9% accuracy, dominated by the experimental error. Copyright © 2024, The Authors. All rights reserved.

关键词： Quantum theory

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Probing the energy-smeared R-ratio on the lattice

arXiv

引用

arXiv 2022年

作者： Alexandrou, Constantia Bacchio, Simone De Santis, Alessandro Dimopoulos, Petros Finkenrath, Jacob Frezzotti, Roberto Gagliardi, Giuseppe Garofalo, Marco Hadjiyiannakou, Kyriakos Kostrzewa, Bartosz Jansen, Karl Lubicz, Vittorio Petschlies, Marcus Sanfilippo, Francesco Simula, Silvano Tantalo, Nazario Urbach, Carsten Wenger, Urs Department of Physics University of Cyprus Nicosia20537 Cyprus Computation-based Science and Technology Research Center The Cyprus Institute 20 Konstantinou Kavafi Street Nicosia2121 Cyprus Dipartimento di Fisica INFN Università di Roma Tor Vergata Via della Ricerca Scientifica 1 RomaI-00133 Italy Parma43124 Italy Istituto Nazionale di Fisica Nucleare Sezione di Roma Tre Via della Vasca Navale 84 RomeI-00146 Italy Rheinische Friedrich-Wilhelms-Universität Bonn Nussallee 14-16 Bonn53115 Germany High Performance Computing and Analytics Lab Rheinische Friedrich-Wilhelms-Universität Bonn Friedrich-Hirzebruch-Allee 8 Bonn53115 Germany NIC DESY Platanenallee 6 ZeuthenD-15738 Germany Dipartimento di Matematica e Fisica Università Roma Tre INFN Sezione di Roma Tre Via della Vasca Navale 84 RomeI-00146 Italy Institute for Theoretical Physics Albert Einstein Center for Fundamental Physics University of Bern Sidlerstrasse 5 BernCH-3012 Switzerland

We present a first-principles lattice QCD investigation of the R-ratio between the e+e− cross-section into hadrons and that into muons. By using the method of Ref. [1], that allows to extract smeared spectral densities from Euclidean correlators, we compute the R-ratio convoluted with Gaussian smearing kernels of widths of about 600 MeV and central energies from 220 MeV up to 2.5 GeV. Our theoretical results are compared with the corresponding quantities obtained by smearing the KNT19 compilation [2] of R-ratio experimental measurements with the same kernels and, by centring the Gaussians in the region around the ρ-resonance peak, a tension of about three standard deviations is observed. From the phenomenological perspective, we have not included yet in our calculation QED and strong isospin-breaking corrections and this might affect the observed tension. From the methodological perspective, our calculation demonstrates that it is possible to study the R-ratio in Gaussian energy bins on the lattice at the level of accuracy required in order to perform precision tests of the Standard Model. Copyright © 2022, The Authors. All rights reserved.

关键词： Spectral density

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