Isospin-breaking effects in inclusive hadronic $τ$ data for the muon $(g-2)$ from first principles
Università degli Studi di Milano-Bicocca（米兰比可卡大学）；Istituto Nazionale di Fisica Nucleare (INFN)（意大利国家核物理研究所）；Brookhaven National Laboratory（布鲁海文国家实验室）；Universität Regensburg（雷根斯堡大学）；Lawrence Livermore National Laboratory（劳伦斯利弗莫尔国家实验室）
Mattia Bruno, Taku Izubuchi, Christoph Lehner, Aaron S. Meyer, Julian Parrino, Xin-Yu Tuo
The knowledge of isospin-breaking effects in hadronic $τ$ decays is required for a high-precision determination of the Hadronic-Vacuum-Polarization contribution to $(g-2)_μ$ from experimental $τ$ data. In this work we present a strategy for their calculation in a fully inclusive setup from first-principles Lattice QCD+QED simulations. We separate radiative corrections in three infrared safe classes, which we study individually. We provide analytic expressions for their effects in the initial state and propose a strategy for final-state corrections directly in Euclidean space. We also examine the non-factorizable contributions and highlight the challenges associated with their analytic continuation from Euclidean to Minkowski space. By studying short-distance corrections in the context of momentum schemes, we provide a prescription for the renormalization of the individual terms at first order in the ispospin-breaking parameters.
Recently, the Budapest-Marseille-Wuppertal collaboration achieved sub-percent precision in the evaluation of the lowest-order hadronic vacuum polarization contribution to the muon $g_μ-2$ (arXiv:hep-lat/2002.12347v3). At this level of precision, isospin-symmetric QCD is not sufficient. In this contribution we review how QED and strong-isospin-breaking effects have been included in our work. Isospin breaking is implemented by expanding the relevant correlation functions to second order in the electric charge $e$ and to first order in $m_u-m_d$. The correction terms are then computed using isosp…
We discuss leading isospin breaking effects in the hadronic vacuum polarisation required for the investigation of the hadronic contribution to $(g-2)_μ$. The calculation proceeds by expanding the relevant correlation functions around the isosymmetric limit. Isosymmetric observables are evaluated on gauge ensembles with $N_{f}=2+1$, $O(a)$ improved Wilson fermions and open boundary conditions generated by the CLS effort. Particular emphasis is placed on the relevant quark-disconnected diagrams required for a complete treatment of leading isospin breaking effects in the valence quark sector. We …
First-principles lattice determinations of the Standard Model expectation for the leading order hadronic vacuum polarization contribution to the anomalous magnetic moment of the muon have become sufficiently precise that further improvement requires including strong and electromagnetic isospin-breaking effects. We provide a continuum estimate of the strong isospin-breaking contribution, $a_μ^{SIB}$, using $SU(3)$ chiral perturbation theory. The result is shown to be dominated by resonance-region contributions encoded in a single low-energy constant whose value is known from flavor-breaking had…
We calculate the strong isospin breaking and QED corrections to meson masses and the hadronic vacuum polarization in an exploratory study on a $64\times24^3$ lattice with an inverse lattice spacing of $a^{-1}=1.78$ GeV and an isospin symmetric pion mass of $m_π=340$ MeV. We include QED in an electro-quenched setup using two different methods, a stochastic and a perturbative approach. We find that the electromagnetic correction to the leading hadronic contribution to the anomalous magnetic moment of the muon is smaller than $1\%$ for the up quark and $0.1\%$ for the strange quark, although it s…
There are emerging tensions for theory results of the hadronic vacuum polarization contribution to the muon anomalous magnetic moment both within recent lattice QCD calculations and between some lattice QCD calculations and R-ratio results. In this paper we work towards scrutinizing critical aspects of these calculations. We focus in particular on a precise calculation of Euclidean position-space windows defined by RBC/UKQCD that are ideal quantities for cross-checks within the lattice community and with R-ratio results. We perform a lattice QCD calculation using physical up, down, strange, an…
Hadronic vacuum polarization contribution to $a_μ$ from functional methods with strong and electromagnetic isospin breaking
University of Valencia and CSIC（瓦伦西亚大学和中科院）；Universidad de Huelva（韦尔瓦大学）；Universidad Autónoma de Querétaro（克雷塔罗自治大学）；Justus-Liebig-Universität Gießen（吉森大学）；GSI Helmholtzzentrum für Schwerionenforschung（亥姆霍兹重离子研究中心）；Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional（国立理工学院高级研究中心）
By far the biggest contribution to hadronic vacuum polarization (HVP) arises from the two-pion channel. Its quark-mass dependence can be evaluated by combining dispersion relations with chiral perturbation theory, providing guidance on the functional form of chiral extrapolations, or even interpolations around the physical point. In addition, the approach allows one to estimate in a controlled way the isospin-breaking (IB) corrections that arise from the pion mass difference. As an application, we present an updated estimate of phenomenological expectations for electromagnetic and strong IB co…
The inclusive hadronic decay-rates of the $τ$ lepton are particularly interesting from the phenomenological point of view since they give access to the CKM matrix elements $V_{ud}$ and $V_{us}$. In this talk, we discuss how a recent method for the extraction of smeared spectral densities from Euclidean lattice correlators can be used to obtain a direct lattice determination of inclusive hadronic $τ$ decay rates. We also present preliminary numerical results obtained by applying this method to correlators measured on two gauge ensembles produced by the ETMC with $N_f=2+1+1$ dynamical flavours a…
A determination of the hadronic vacuum polarization contribution to the anomalous magnetic moment of the muon from lattice QCD aiming at a precision of $1\%$ requires to include isospin breaking corrections in the computation. We present a lattice calculation of the QED and strong isospin breaking corrections to the hadronic vacuum polarization with Domain Wall fermions. The results are obtained using quark masses which are tuned such that pion and kaon masses agree with their physical values including isospin breaking corrections.
Comparison of the hadronic vacuum polarization between hadronic $τ$-decay data and lattice QCD
San Francisco State University（旧金山州立大学）；Instituto de Física de São Carlos, Universidade de São Paulo（圣卡洛斯物理研究所，圣保罗大学）；Department of Physics and IFAE-BIST, Universitat Autònoma de Barcelona（巴塞罗那自治大学物理系及IFAE-BIST）；York University（约克大学）；University of Adelaide（阿德莱德大学）；Institut für Kernphysik, Johannes Gutenberg-Universität Mainz（美因茨约翰内斯·古腾堡大学核物理研究所）
Isospin is an almost exact symmetry of strong interactions and the corrections to the isosymmetric limit are, in general, at the percent level. For several hadronic quantities, such as pseudoscalar meson masses or the kaon leptonic and semileptonic decay rates, these effects are of the same order of magnitude of the errors quoted in nowadays lattice calculations and cannot be neglected any longer. In this talk I discuss some recent results for the pseudoscalar meson spectrum obtained by the RM123 Collaboration including isospin breaking corrections in first principles lattice simulations.
Hadronic spectral functions of $τ$ decays have been used in the past to provide an alternative determination of the LO Hadronic Vacuum Polarization relevant for the (g-2) of the muon. Following recent developments and results in Lattice QCD+QED calculations, we explore the possibility of studying the isospin breaking corrections of $τ$ spectral functions for this prediction. We present preliminary results at physical pion mass based on Domain Wall Fermion ensembles generated by the RBC/UKQCD collaboration.
We propose and apply a new approach to determining $|V_{us}|$ using dispersion relations with weight functions having poles at Euclidean (space-like) momentum which relate strange hadronic $τ$ decay distributions to hadronic vacuum polarization functions (HVPs) obtained from lattice QCD. We show examples where spectral integral contributions from the region where experimental data have large errors or do not exist are strongly suppressed but accurate determinations of the relevant lattice HVP combinations remain possible. The resulting $|V_{us}|$ agrees well with determinations from $K$ physic…
Isospin-breaking (IB) effects in the two-pion contribution to hadronic vacuum polarization (HVP) can be resonantly enhanced, if related to the interference of the $ρ(770)$ and $ω(782)$ resonances. This particular IB contribution to the pion vector form factor and thus the line shape in $e^+e^-\to π^+π^-$ can be described by the residue at the $ω$ pole - the $ρ$-$ω$ mixing parameter $ε_ω$. Here, we argue that while in general analyticity requires this parameter to be real, the radiative channels $π^0γ$, $ππγ$, $ηγ$ can induce a small phase, whose size we estimate as $δ_ε=3.5(1.0)^\circ$ by usin…
We study the pion-mass dependence of the two-pion channel in the hadronic-vacuum-polarization (HVP) contribution to the anomalous magnetic moment of the muon $a_μ^\text{HVP}$, by using an Omnès representation for the pion vector form factor with the phase shift derived from the inverse-amplitude method (IAM). Our results constrain the dominant isospin-$1$ part of the isospin-symmetric light-quark contribution, and should thus allow one to better control the chiral extrapolation of $a_μ^\text{HVP}$, required for lattice-QCD calculations performed at larger-than-physical pion masses. In particul…
The anomalous magnetic moment of the muon $a_μ$ and the running of the electromagnetic coupling $α$ play a fundamental role in beyond Standard Model (SM) physics searches. Non-perturbative hadronic contributions to both quantities, which are related to the hadronic vacuum polarization (HVP) function consisting of two electromagnetic currents, are a main source of uncertainty in the SM prediction. We compute the HVP function in lattice QCD+QED applying the time-momentum representation method. We expand the relevant correlation functions around the isosymmetric limit. In particular, we focus on …
We discuss an alternate scheme, or a 'line of constant physics', which can be used when computing isospin breaking corrections to hadronic quantities. We show that within a certain class of schemes one can separate the electromagnetic corrections from the strong isospin breaking corrections at leading order, meaning that within this class scheme-ambiguities are higher order effects.
We present results for the QED and strong isospin breaking corrections to the hadronic vacuum polarization using $N_f=2+1$ Domain Wall fermions. QED is included in an electro-quenched setup using two different methods, a stochastic and a perturbative approach. Results and statistical errors from both methods are directly compared with each other.
The hadronic-vacuum-polarization contribution to the muon anomalous magnetic moment in isospin-symmetric lattice QCD with twisted-mass fermions
University of Cyprus（塞浦路斯大学）；The Cyprus Institute（塞浦路斯研究所）；Johannes Gutenberg-Universität Mainz（美因茨约翰内斯古腾堡大学）；GSI Helmholtz Centre for Heavy Ion Research（GSI重离子研究中心）；Bergische Universität Wuppertal（伍珀塔尔山岳大学）；Università di Roma “Tor Vergata”（罗马托尔维加塔大学）；Istituto Nazionale di Fisica Nucleare（意大利国家核物理研究所）；Rheinische Friedrich-Wilhelms-Universität Bonn（波恩莱茵弗里德里希·威廉大学）；University of Bern（伯尔尼大学）
Isospin is an almost exact symmetry of strong interactions and the corrections to the isosymmetric limit are, in general, at the percent level. For several hadronic quantities relevant for flavour physics phenomenology, such as pseudoscalar meson masses or the kaon leptonic and semileptonic decay rates, these effects are of the same order of magnitude of the uncertainties quoted in current large-scale QCD simulations on the lattice and cannot be neglected anymore. In this contribution I discuss some recent results for the leptonic decay rates of light pseudoscalar mesons obtained by the Soton-…
