002812389 001__ 2812389
002812389 005__ 20241113042232.0
002812389 0248_ $$aoai:cds.cern.ch:2812389$$pcerncds:FULLTEXT$$pcerncds:CERN:FULLTEXT$$pcerncds:CERN
002812389 0247_ $$2DOI$$9APS$$a10.1103/PhysRevD.106.114502$$qpublication
002812389 037__ $$9arXiv$$aarXiv:2206.06582$$chep-lat
002812389 037__ $$9arXiv:reportnumber$$aMITP-22-038
002812389 037__ $$9arXiv:reportnumber$$aCERN-TH-2022-098
002812389 035__ $$9arXiv$$aoai:arXiv.org:2206.06582
002812389 037__ $$9arXiv:reportnumber$$aDESY-22-105
002812389 035__ $$9Inspire$$aoai:inspirehep.net:2095867$$d2024-11-12T14:09:47Z$$h2024-11-13T03:00:08Z$$mmarcxml$$ttrue$$uhttps://inspirehep.net/api/oai2d
002812389 035__ $$9Inspire$$a2095867
002812389 041__ $$aeng
002812389 100__ $$aCè, Marco$$uU. Bern, AEC$$uCERN$$vAlbert Einstein Center for Fundamental Physics (AEC) and Institut für Theoretische Physik, Universität Bern, Sidlerstrasse 5, 3012 Bern, Switzerland$$vDepartment of Theoretical Physics, CERN, 1211 Geneva 23, Switzerland
002812389 245__ $$9arXiv$$aWindow observable for the hadronic vacuum polarization contribution to the muon $g-2$ from lattice QCD
002812389 269__ $$c2022-06-13
002812389 260__ $$c2022-12-01
002812389 300__ $$a43 p
002812389 500__ $$9arXiv$$a43 pages, 9 figures, 10 tables; version accepted for publication:
extended discussion of finite-volume corrections. Results and conclusions
unchanged
002812389 520__ $$9APS$$aEuclidean time windows in the integral representation of the hadronic vacuum polarization contribution to the muon <math display="inline"><mi>g</mi><mo>-</mo><mn>2</mn></math> serve to test the consistency of lattice calculations and may help in tracing the origins of a potential tension between lattice and data-driven evaluations. In this paper, we present results for the intermediate time window observable computed using <math display="inline"><mrow><mi mathvariant="normal">O</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">)</mo></mrow></math> improved Wilson fermions at six values of the lattice spacings below 0.1 fm and pion masses down to the physical value. Using two different sets of improvement coefficients in the definitions of the local and conserved vector currents, we perform a detailed scaling study which results in a fully controlled extrapolation to the continuum limit without any additional treatment of the data, except for the inclusion of finite-volume corrections. To determine the latter, we use a combination of the method of Hansen and Patella and the Meyer-Lellouch-Lüscher procedure employing the Gounaris-Sakurai parametrization for the pion form factor. We correct our results for isospin-breaking effects via the perturbative expansion of <math display="inline"><mrow><mi>QCD</mi><mo>+</mo><mi>QED</mi></mrow></math> around the isosymmetric theory. Our result at the physical point is <math display="inline"><msubsup><mi>a</mi><mi>μ</mi><mi>win</mi></msubsup><mo>=</mo><mo stretchy="false">(</mo><mn>237.30</mn><mo>±</mo><mn>0.7</mn><msub><mn>9</mn><mrow><mi>stat</mi></mrow></msub><mo>±</mo><mn>1.2</mn><msub><mn>2</mn><mrow><mi>syst</mi></mrow></msub><mo stretchy="false">)</mo><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>10</mn></mrow></msup></math>, where the systematic error includes an estimate of the uncertainty due to the quenched charm quark in our calculation. Our result displays a tension of <math display="inline"><mrow><mn>3.9</mn><mi>σ</mi></mrow></math> with a recent evaluation of <math display="inline"><msubsup><mi>a</mi><mi>μ</mi><mi>win</mi></msubsup></math> based on the data-driven method.
002812389 520__ $$9arXiv$$aEuclidean time windows in the integral representation of the hadronic vacuum polarization contribution to the muon $g-2$ serve to test the consistency of lattice calculations and may help in tracing the origins of a potential tension between lattice and data-driven evaluations. In this paper, we present results for the intermediate time window observable computed using O($a$) improved Wilson fermions at six values of the lattice spacings below 0.1 fm and pion masses down to the physical value. Using two different sets of improvement coefficients in the definitions of the local and conserved vector currents, we perform a detailed scaling study which results in a fully controlled extrapolation to the continuum limit without any additional treatment of the data, except for the inclusion of finite-volume corrections. To determine the latter, we use a combination of the method of Hansen and Patella and the Meyer-Lellouch-Lüscher procedure employing the Gounaris-Sakurai parameterization for the pion form factor. We correct our results for isospin-breaking effects via the perturbative expansion of QCD+QED around the isosymmetric theory. Our result at the physical point is $a_\mu^{\mathrm{win}}=(237.30\pm0.79_{\rm stat}\pm1.22_{\rm syst})\times10^{-10}$, where the systematic error includes an estimate of the uncertainty due to the quenched charm quark in our calculation. Our result displays a tension of 3.9$\sigma$ with a recent evaluation of $a_\mu^{\mathrm{win}}$ based on the data-driven method.
002812389 540__ $$3preprint$$aCC BY 4.0$$uhttp://creativecommons.org/licenses/by/4.0/
002812389 540__ $$3publication$$aCC BY 4.0$$fSCOAP3$$uhttps://creativecommons.org/licenses/by/4.0/
002812389 542__ $$3publication$$dauthors$$g2022
002812389 595__ $$aCERN-TH
002812389 65017 $$2SzGeCERN$$aParticle Physics - Phenomenology
002812389 65017 $$2SzGeCERN$$aParticle Physics - Lattice
002812389 690C_ $$aCERN
002812389 690C_ $$aARTICLE
002812389 700__ $$aGérardin, Antoine$$uMarseille, CPT$$vAix-Marseille-Université, Université de Toulon, CNRS, CPT, 13288 Marseille, France
002812389 700__ $$avon Hippel, Georg$$uU. Mainz, PRISMA$$vPRISMA+ Cluster of Excellence and Institut für Kernphysik, Johannes Gutenberg-Universität Mainz, 55128 Mainz, Germany
002812389 700__ $$aHudspith, Renwick J.$$uHelmholtz Inst., Mainz$$vHelmholtz-Institut Mainz, Johannes Gutenberg-Universität Mainz, 55128 Mainz, Germany
002812389 700__ $$aKuberski, Simon$$uHelmholtz Inst., Mainz$$uDarmstadt, GSI$$vHelmholtz-Institut Mainz, Johannes Gutenberg-Universität Mainz, 55128 Mainz, Germany$$vGSI Helmholtz Centre for Heavy Ion Research, 64291 Darmstadt, Germany
002812389 700__ $$aMeyer, Harvey B.$$uU. Mainz, PRISMA$$uHelmholtz Inst., Mainz$$vHelmholtz-Institut Mainz, Johannes Gutenberg-Universität Mainz, 55128 Mainz, Germany$$vPRISMA+ Cluster of Excellence and Institut für Kernphysik, Johannes Gutenberg-Universität Mainz, 55128 Mainz, Germany
002812389 700__ $$aMiura, Kohtaroh$$uHelmholtz Inst., Mainz$$uNagoya U. (main)$$vHelmholtz-Institut Mainz, Johannes Gutenberg-Universität Mainz, 55128 Mainz, Germany$$vKEK Theory Center, High Energy Accelerator Research Organization, 1-1 Oho, Tsukuba, Ibaraki 305-0801, Japan
002812389 700__ $$aMohler, Daniel$$uDarmstadt, GSI$$uDarmstadt, Tech. U.$$vInstitut für Kernphysik, Technische Universität Darmstadt, Schlossgartenstrasse 2, D-64289 Darmstadt, Germany$$vGSI Helmholtz Centre for Heavy Ion Research, 64291 Darmstadt, Germany
002812389 700__ $$aOttnad, Konstantin$$uU. Mainz, PRISMA$$vPRISMA+ Cluster of Excellence and Institut für Kernphysik, Johannes Gutenberg-Universität Mainz, 55128 Mainz, Germany
002812389 700__ $$aPaul Srijit$$uU. Mainz, PRISMA$$vPRISMA+ Cluster of Excellence and Institut für Kernphysik, Johannes Gutenberg-Universität Mainz, 55128 Mainz, Germany
002812389 700__ $$aRisch, Andreas$$uJulich, NIC$$vJohn von Neumann-Institut für Computing NIC, Deutsches Elektronen-Synchrotron DESY, Platanenallee 6, 15738 Zeuthen, Germany
002812389 700__ $$aSan José, Teseo$$uU. Mainz, PRISMA$$uHelmholtz Inst., Mainz$$vHelmholtz-Institut Mainz, Johannes Gutenberg-Universität Mainz, 55128 Mainz, Germany$$vPRISMA+ Cluster of Excellence and Institut für Kernphysik, Johannes Gutenberg-Universität Mainz, 55128 Mainz, Germany
002812389 700__ $$aWittig, Hartmut$$uCERN$$uU. Mainz, PRISMA$$uHelmholtz Inst., Mainz$$vDepartment of Theoretical Physics, CERN, 1211 Geneva 23, Switzerland$$vHelmholtz-Institut Mainz, Johannes Gutenberg-Universität Mainz, 55128 Mainz, Germany$$vPRISMA+ Cluster of Excellence and Institut für Kernphysik, Johannes Gutenberg-Universität Mainz, 55128 Mainz, Germany
002812389 773__ $$c114502$$mpublication$$n11$$pPhys. Rev. D$$v106$$xPhys. Rev. D 106, 114502 (2022)$$y2022
002812389 8564_ $$82372890$$s6746$$uhttp://cds.cern.ch/record/2812389/files/AIC_comparison_I0.png$$y00006 Comparison of the isovector and isoscalar contributions (without the charm) using different variations (either using $f_\pi$ or $t_0$ to set the scale, and with both sets of improvement coefficients). The blue point is our final estimate obtained from the rescaling method with the set 1 of improvement coefficients.
002812389 8564_ $$82372891$$s6592$$uhttp://cds.cern.ch/record/2812389/files/AIC_comparison_I1.png$$y00005 Comparison of the isovector and isoscalar contributions (without the charm) using different variations (either using $f_\pi$ or $t_0$ to set the scale, and with both sets of improvement coefficients). The blue point is our final estimate obtained from the rescaling method with the set 1 of improvement coefficients.
002812389 8564_ $$82372892$$s48892$$uhttp://cds.cern.ch/record/2812389/files/extrap_I1.png$$y00003 Left: one typical extrapolation of the isovector contribution using $f_{\rm ch}(\widetilde{y}) = 1/\widetilde{y}$. The data corresponds to the local-conserved discretization of the correlator using the set 1 of improvement coefficients. Error bands are the results from the fit for each of the six lattice spacings. The black line is the chiral extrapolation in the continuum limit. The black point is the result at the physical point. Right: same for the isoscalar contribution but using $f_{\rm ch}(\widetilde{y}) = 0$.
002812389 8564_ $$82372893$$s38360$$uhttp://cds.cern.ch/record/2812389/files/extrap_I0.png$$y00004 Left: one typical extrapolation of the isovector contribution using $f_{\rm ch}(\widetilde{y}) = 1/\widetilde{y}$. The data corresponds to the local-conserved discretization of the correlator using the set 1 of improvement coefficients. Error bands are the results from the fit for each of the six lattice spacings. The black line is the chiral extrapolation in the continuum limit. The black point is the result at the physical point. Right: same for the isoscalar contribution but using $f_{\rm ch}(\widetilde{y}) = 0$.
002812389 8564_ $$82372894$$s16390$$uhttp://cds.cern.ch/record/2812389/files/SU3_I1_fpi.png$$y00001 Continuum extrapolation for the isovector quark contribution at the SU(3)$_{\rm f}$-symmetric point. Left: using $f_{\pi}$-rescaling. Right: with $t_0$ to set the scale. The blue and green points correspond to the two different sets of improvement coefficients (see Section~\ref{sec:lattice}). For clarity, the extrapolated results have been shifted to the left.
002812389 8564_ $$82372895$$s28045$$uhttp://cds.cern.ch/record/2812389/files/mass_shift_I1_z.png$$y00013 Derivatives of the isovector and the strange-connected contributions to the window observable with respect to $X_\pi$. The gray areas illustrate the priors that are used in the global extrapolation.
002812389 8564_ $$82372896$$s13505$$uhttp://cds.cern.ch/record/2812389/files/SU3_charm.png$$y00008 Left panel: study of the continuum extrapolation of the charm quark contribution to $a_\mu^{\rm win}$ at the SU$(3)_{\rm f}$-symmetric point using the local-conserved discretization of the correlation function. The black and green points are obtained using two independent sets of improvement coefficients, as explained in Section~\ref{sec:improvement}. Right panel: Example of a typical extrapolation to the physical point of the charm-quark contribution. The error from the scale setting, which is highly correlated between ensembles, is not shown. The plain lines are obtained from the fit function (\ref{eq:extrapC}) without any cut in the pion mass.
002812389 8564_ $$82372897$$s21382$$uhttp://cds.cern.ch/record/2812389/files/extrap_disc.png$$y00007 Extrapolation to the physical point for the quark-disconnected contribution using \eq{eq:extrapD}. The vertical dashed line represents the physical point in our iso-symmetric QCD setup. The black point is the result of the extrapolation, and the grey band represents the extrapolation to the continuum limit with $X_K=X_K^{\star}$. Points with dashed error bars are not included in the fit.
002812389 8564_ $$82372898$$s17748$$uhttp://cds.cern.ch/record/2812389/files/window_udsc_iso.png$$y00010 Comparison of our results (in units of $10^{-10}$) with other lattice calculations \cite{Blum:2018mom, Aubin:2019usy, Borsanyi:2020mff, Lehner:2020crt, Giusti:2021dvd, Wang:2022lkq, Aubin:2022hgm} in isosymmetric QCD. The four panels on the left show compilations of the individual quark-disconnected, charm, strange and light quark contributions. The total result for $\awin$ in the isosymmetric case is shown in the rightmost panel. Our results are represented by green circles and vertical bands.
002812389 8564_ $$82372899$$s51038$$uhttp://cds.cern.ch/record/2812389/files/extrap_charm.png$$y00009 Left panel: study of the continuum extrapolation of the charm quark contribution to $a_\mu^{\rm win}$ at the SU$(3)_{\rm f}$-symmetric point using the local-conserved discretization of the correlation function. The black and green points are obtained using two independent sets of improvement coefficients, as explained in Section~\ref{sec:improvement}. Right panel: Example of a typical extrapolation to the physical point of the charm-quark contribution. The error from the scale setting, which is highly correlated between ensembles, is not shown. The plain lines are obtained from the fit function (\ref{eq:extrapC}) without any cut in the pion mass.
002812389 8564_ $$82372900$$s29240$$uhttp://cds.cern.ch/record/2812389/files/mass_shift_s_z.png$$y00015 Derivatives of the isovector and the strange-connected contributions to the window observable with respect to $X_\pi$. The gray areas illustrate the priors that are used in the global extrapolation.
002812389 8564_ $$82372901$$s5726$$uhttp://cds.cern.ch/record/2812389/files/window_full_comp.png$$y00011 Comparison of our result for $\awin$ including isospin-breaking corrections with the estimates by ETMC \cite{Giusti:2021dvd}, BMW \cite{Borsanyi:2020mff} and RBC/UKQCD \cite{Blum:2018mom}. The estimate based on the data-driven method of Ref.~\cite{Colangelo:2022vok} is shown in red.
002812389 8564_ $$82372902$$s1412117$$uhttp://cds.cern.ch/record/2812389/files/2206.06582.pdf$$yFulltext
002812389 8564_ $$82372903$$s27550$$uhttp://cds.cern.ch/record/2812389/files/mass_shift_I1_phi4.png$$y00012 Derivatives of the isovector and the strange-connected contributions to the window observable with respect to $X_\pi$. The gray areas illustrate the priors that are used in the global extrapolation.
002812389 8564_ $$82372904$$s27277$$uhttp://cds.cern.ch/record/2812389/files/mass_shift_s_phi4.png$$y00014 Derivatives of the isovector and the strange-connected contributions to the window observable with respect to $X_\pi$. The gray areas illustrate the priors that are used in the global extrapolation.
002812389 8564_ $$82372905$$s16990$$uhttp://cds.cern.ch/record/2812389/files/SU3_I1_t0.png$$y00002 Continuum extrapolation for the isovector quark contribution at the SU(3)$_{\rm f}$-symmetric point. Left: using $f_{\pi}$-rescaling. Right: with $t_0$ to set the scale. The blue and green points correspond to the two different sets of improvement coefficients (see Section~\ref{sec:lattice}). For clarity, the extrapolated results have been shifted to the left.
002812389 8564_ $$82372906$$s12965$$uhttp://cds.cern.ch/record/2812389/files/integrand.png$$y00000 Integrands used to compute the intermediate window $a_\mu^{\rm win}$ for the isovector, isoscalar and charm quark contributions. The isoscalar contribution does not include the charm quark contribution. The data has been obtained on ensemble E250, which has close-to-physical quark masses, using two local vector currents and set~1 of renormalization and improvement coefficients.
002812389 8564_ $$82424458$$s1947055$$uhttp://cds.cern.ch/record/2812389/files/Publication.pdf$$yFulltext
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002812389 980__ $$aARTICLE