The hadronic contribution to the running of the electromagnetic coupling and electroweak mixing angle
Teseo San José, Marco Cè, Antoine Gérardin, Georg von Hippel, Harvey B. Meyer, Kohtaroh Miura, Konstantin Ottnad, Andreas Risch, Jonas Wilhelm, Hartmut Wittig
备注：
9 pages, 3 figures, talk presented at the 38th International Symposium on Lattice Field Theory, 26th-30th July 2021, Zoom/Gather@Massachusetts Institute of Technology
As present and future experiments, on both the energy and precision frontiers, look to identify new physics beyond the Standard Model, we require more precise determinations of fundamental quantities, like the QED and electroweak couplings at various momenta. These can be obtained either entirely from experimental measurements, or from one such measurement at a particular virtuality combined with the couplings' virtuality dependence computed within the SM. Thus, a precise, entirely theoretical determination of the running couplings is highly desirable, even more since the preliminary results of the E989 experiment in Fermilab were published. We give results for the hadronic contribution to the QED running coupling $α(Q^2)$ and weak mixing angle $\sin^2θ_W(Q^2)$ in the space-like energy region $(0, 7]~\text{GeV}^2$ with a total relative uncertainty of $2\%$ at energies $Q^2 \ll 1~\text{GeV}^2$, and $1\%$ at $Q^2 > 1~\text{GeV}^2$.
The dispersive approach to QCD is briefly overviewed and its application to the assessment of hadronic contributions to electroweak observables is discussed.
Dispersive approach to quantum chromodynamics is applied to the assessment of hadronic contributions to electroweak observables. The employed approach merges the corresponding perturbative input with intrinsically nonperturbative constraints, which originate in the respective kinematic restrictions. The evaluated hadronic contributions to the muon anomalous magnetic moment and to the shift of the electromagnetic fine structure constant at the scale of Z boson mass conform with recent assessments of these quantities.
We present a preliminary study of the leading hadronic contribution to the running of the Weinberg angle $θ_{\mathrm{W}}$. The running is extracted from the correlation function of the electromagnetic current with the vector part of the weak neutral current using both the standard time-momentum representation method and the Lorentz-covariant coordinate-space method recently introduced by Meyer. Both connected and disconnected contributions have been computed on $N_{\mathrm{f}}=2+1$ non-perturbatively $O(a)$-improved Wilson fermions configurations from the CLS initiative. Similar covariant coor…
We present results for the hadronic running of the electromagnetic coupling and the weak mixing angle from simulations of lattice QCD with $N_f=2+1$ flavours of $O(a)$-improved Wilson fermions. Using two different discretisations of the vector current, we compute the quark-connected and -disconnected contributions to the hadronic vacuum polarisation (HVP) functions $\barΠ^{γγ}$ and $\barΠ^{Zγ}$ for spacelike squared momenta $Q^2\leq 7$ $\mathrm{GeV}^2$. Our results are extrapolated to the physical point using ensembles at four lattice spacings, with pion masses ranging from 130 to 420 MeV. We …
The electromagnetic coupling $α$ and the electroweak mixing angle $θ_{\mathrm{W}}$ are parameters of the Standard Model (SM) that enter precision SM tests and play a fundamental rôle in beyond SM physics searches. Their values are energy dependent, and non-perturbative hadronic contributions are the main source of uncertainty to the theoretical knowledge of the running with energy. We present a lattice study of the leading hadronic contribution to the running of $α$ and $\sin^2θ_{\mathrm{W}}$. The former is related to the hadronic vacuum polarization (HVP) function of electromagnetic currents,…
The energy dependency (running) of the strength of electromagnetic interactions $α$ plays an important role in precision tests of the Standard Model. The running of the former to the $Z$ pole is an input quantity for global electroweak fits, while the running of the mixing angle is susceptible to the effects of Beyond Standard Model physics, particularly at low energies. We present a computation of the hadronic vacuum polarization (HVP) contribution to the running of these electroweak couplings at the non-perturbative level in lattice QCD, in the space-like regime up to $Q^2$ momentum transfer…
The hadronic contribution to the running of the electroweak gauge couplings
GSI Helmholtz Centre for Heavy Ion Research（GSI重离子研究中心）；CERN（欧洲核子研究中心）；High Energy Accelerator Research Organization (KEK)（高能加速器研究机构）；University of Wuppertal（伍珀塔尔大学）
The quark-connected leading-order hadronic contributions to the running of the electromagnetic fine structure constant, $α_{\rm QED}$, and the weak mixing angle, $θ_W$, are determined by a four-flavour lattice QCD computation with twisted mass fermions. Full agreement of the results with a phenomenological analysis is observed with an even comparable statistical uncertainty. We show that the uncertainty of the lattice calculation is dominated by systematic effects which then leads to significantly larger errors than obtained by the phenomenological analysis.
We introduce a model independent method for the determination of the hadronic contribution to the QED running coupling, $Δα_{\text{HAD}}(M_{Z}^{2})$, requiring no $e^+e^-$ annihilation data as input. This is achieved by calculating the heavy-quark contributions entirely in perturbative QCD, whilst the light-quark resonance piece is determined using available lattice QCD results. Future reduction in the current uncertainties in the latter shall turn this method into a valuable alternative to the standard approach. Subsequently, we find that the precision of current determinations of $Δα_{\text{…
Running of the Electroweak Gauge Couplings from First Principles
Johannes Gutenberg-Universität Mainz（约翰内斯·古腾堡美因茨大学）；GSI Helmholtz Centre for Heavy Ion Research（GSI重离子研究中心）；PRISMA ++ Cluster of Excellence and Institut für Kernphysik, Johannes Gutenberg-Universität Mainz（美因茨大学核物理研究所及PRISMA++卓越集群）；Theoretical Physics Department, CERN（欧洲核子研究中心理论物理部）；Institute of Particle and Nuclear Studies, High Energy Accelerator Research Organization (KEK)（高能加速器研究机构粒子与核研究研究所）；Helmholtz-Institut für Strahlen- und Kernphysik and Bethe Center for Theoretical Physics, Universität Bonn（波恩大学斯特拉斯曼与核物理亥姆霍兹研究所及贝特理论物理中心）；Department of Physics, University of Wuppertal（伍珀塔尔大学物理系）
One possibility for Beyond Standard Model physics is a new strongly-interacting gauge theory. One way to determine if a non-abelian gauge theory is QCD-like or conformal is to measure the running of the renormalized gauge coupling. We define the renormalized coupling from Wilson loop ratios, and measure these ratios via lattice simulations. We test this method in SU(3) pure gauge theory and show some first results for simulations with dynamical fermions in the fundamental representation.
The electromagnetic coupling receives significant contributions to its running from non-perturbative QCD effects. We present an update of a lattice QCD study of the Adler function and of its application to the determination of the running of the QED coupling. We perform a high-statistics computation with two flavours of O$(a)$ improved Wilson fermions in a large range of momentum transfer $Q^2$. The running of the electromagnetic coupling, including contributions from $u$, $d$, $s$ and $c$ valence quarks, is compared to phenomenological determinations at intermediate $Q^2$ values. An extension…
We compute the hadronic running of the electromagnetic and weak couplings in lattice QCD with $N_{\mathrm{f}}=2+1$ flavors of $\mathcal{O}(a)$ improved Wilson fermions. Using two different discretizations of the vector current, we compute the quark-connected and -disconnected contributions to the hadronic vacuum polarization (HVP) functions $\barΠ^{γγ}$ and $\barΠ^{γZ}$ for Euclidean squared momenta $Q^2\leq 7\,\mathrm{GeV}^2$. Gauge field ensembles at four values of the lattice spacing and several values of the pion mass, including its physical value, are used to extrapolate the results to th…
Precision lattice calculation of the hadronic contribution to the running of the electroweak gauge couplings
Helmholtz Institute Mainz, Johannes Gutenberg-Universität Mainz（亥姆霍兹马普研究所，约翰内斯·古腾堡美因茨大学）；GSI Helmholtz Centre for Heavy Ion Research（GSI重离子研究中心）；PRISMA ++ Cluster of Excellence and Institut für Kernphysik, Johannes Gutenberg-Universität Mainz（PRISMA++卓越集群与核物理研究所，约翰内斯·古腾堡美因茨大学）；Theoretical Physics Department, CERN（理论物理部，欧洲核子研究中心）；Institute of Particle and Nuclear Studies, High Energy Accelerator Research Organization (KEK)（粒子与核研究研究所，高能加速器研究机构（KEK））；Department of Physics, University of Wuppertal（物理学系，伍珀塔尔大学）
We determine from first principles the quark mass anomalous dimension in Nf=3 QCD between the electroweak and hadronic scales. This allows for a fully non-perturbative connection of the perturbative and non-perturbative regimes of the Standard Model in the hadronic sector. The computation is carried out to high accuracy, employing massless O(a)-improved Wilson quarks and finite-size scaling techniques. We also provide the matching factors required in the renormalisation of light quark masses from lattice computations with O(a)-improved Wilson fermions and a tree-level Symanzik improved gauge a…
The hadronic contributions to the anomalous magnetic moment of the muon which are relevant for the confrontation between theory and experiment at the present level of accuracy, are evaluated within the same framework: the constituent chiral quark model. This includes the contributions from the dominant hadronic vacuum polarization as well as from the next--to--leading order hadronic vacuum polarization, the contributions from the hadronic light-by-light scattering, and the contributions from the electroweak hadronic $Zγγ$ vertex. They are all evaluated as a function of only one free parameter:…
Hadronic vacuum polarization (HVP) is not only a critical part of the Standard Model (SM) prediction for the anomalous magnetic moment of the muon $(g-2)_μ$, but also a crucial ingredient for global fits to electroweak (EW) precision observables due to its contribution to the running of the fine-structure constant encoded in $Δα^{(5)}_\text{had}$. We find that with modern EW precision data, including the measurement of the Higgs mass, the global fit alone provides a competitive, independent determination of $Δα^{(5)}_\text{had}\big|_\text{EW}=270.2(3.0)\times 10^{-4}$. This value actually lies…
Nonperturbative QCD corrections are important to many low-energy electroweak observables, for example the muon magnetic moment. However, hadronic corrections also play a significant role at much higher energies due to their impact on the running of standard model parameters, such as the electromagnetic coupling. Currently, these hadronic contributions are accounted for by a combination of experimental measurements, effective field theory techniques and phenomenological modeling but ideally should be calculated from first principles. Recent developments indicate that many of the most important …
An accurate and unified description of the non-hadronic electroweak interactions of light- and heavy-mesons is possible when the dressing of quark propagators and the finite size of hadronic bound states is explicitly accounted for.
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 …
