Some very recent computations of $α_{\bar{\rm MS}}(M_Z)$ from $N_f=1+1$ lattice simulations and of the running of the Strong coupling, obtained from the lattice ghost-gluon vertex, over a large momentum window are very briefly reviewed.
We report some preliminary results of our ongoing non-perturbative computation of the twisted 't Hooft running coupling in a particular set-up, using the gradient flow to define the coupling and step scaling techniques to compute it. For the computation we considered a pure gauge SU(3) theory in four dimensions, defined on the lattice on an asymmetrical torus endowed with twisted boundary conditions in a single plane, and related the energy scale of the coupling to an effective size combining the size of the torus and the rank of the gauge group. Additionally, we explore some of the effects of…
We propose to utilize NISQ-era quantum devices to compute short distance quantities in $(2+1)$-dimensional QED and to combine them with large volume Monte Carlo simulations and perturbation theory. On the quantum computing side, we perform a calculation of the mass gap in the small and intermediate regime, demonstrating, in the latter case, that it can be resolved reliably. The so obtained mass gap can be used to match corresponding results from Monte Carlo simulations, which can be used eventually to set the physical scale. In this paper we provide the setup for the quantum computation and sh…
A high precision determination of the strong coupling constant in the MS-bar scheme at the Z-mass scale, using low energy quantities, namely pion/kaon decay constants and masses, as experimental input is presented. The computation employs two different massless finite volume renormalization schemes to non-perturbatively trace the scale dependence of the respective running couplings from a scale of about 200 MeV to 100 GeV. At the largest energies perturbation theory is reliable. At high energies the Schroedinger-Functional scheme is used, while the running at low and intermediate energies is c…
We discuss the theoretical foundations of non-equilibrium Monte Carlo simulations based on Jarzynski's equality and present, as an example of application, the determination of the running coupling in the Schrödinger-functional scheme.
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 o…
We present a lattice determination of the $Λ$ parameter in three-flavor QCD and the strong coupling at the Z pole mass. Computing the nonperturbative running of the coupling in the range from $0.2\,$GeV to $70\,$GeV, and using experimental input values for the masses and decay constants of the pion and the kaon, we obtain $Λ_{\overline{\rm MS}}^{(3)}=341(12)\,$MeV. The nonperturbative running up to very high energies guarantees that systematic effects associated with perturbation theory are well under control. Using the four-loop prediction for $Λ_{\overline{\rm MS}}^{(5)}/Λ_{\overline{\rm MS}…
The determination of quark masses from lattice QCD simulations requires a non-perturbative renormalization procedure and subsequent scale evolution to high energies, where a conversion to the commonly used MS-bar scheme can be safely established. We present our results for the non-perturbative running of renormalized quark masses in Nf=3 QCD between the electroweak and a hadronic energy scale, where lattice simulations are at our disposal. Recent theoretical advances in combination with well-established techniques allows to follow the scale evolution to very high statistical accuracy, and full…
Tensor currents are the only quark bilinear operators lacking a non-perturbative determination of their renormalisation group (RG) running between hadronic and electroweak scales. We develop the setup to carry out the computation in lattice QCD via standard recursive finite-size scaling techniques, and provide results for the RG running of tensor currents in $N_f = 0$ and $N_f = 2$ QCD in the continuum for various Schrödinger Functional schemes. The matching factors between bare and renormalisation group invariant currents are also determined for a range of values of the lattice spacing relev…
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…
In this Letter, we provide a determination of the coupling constant in three-flavor quantum chromodynamics (QCD), $α^{\overline{\mathrm{MS}}}_s(μ)$, for $\overline{\mathrm{MS}}$ renormalization scales $μ\in (1,\,2)$ GeV. The computation uses gauge field configuration ensembles with $\mathcal{O}(a)$-improved Wilson-clover fermions generated by the Coordinated Lattice Simulations (CLS) consortium. Our approach is based on current-current correlation functions and has never been applied before in this context. We convert the results perturbatively to the QCD $Λ$-parameter and obtain $Λ_{\overline…
We evaluate the $Λ$-parameter in the $\overline{\mathrm{MS}}$ scheme for the pure SU(3) gauge theory with the twisted gradient flow (TGF) method. A running coupling constant $g_{\mathrm{TGF}}^2(1/L)$ is defined in a finite volume box with size of $L^4$ with the twisted boundary condition. This defines the TGF scheme. Using the step scaling method for the TGF coupling with lattice simulations, we can evaluate the $Λ$-parameter non-perturbatively in the TGF scheme. In this paper we determine the dimensionless ratios, $Λ_{\mathrm{TGF}}/\sqrtσ$ and $r_{0}Λ_{\mathrm{TGF}}$ together with the $Λ$-par…
We report on our ongoing computation of the perturbative running of the Yang-Mills coupling using gradient flow techniques. In particular, we use the gradient flow method with twisted boundary conditions to perform a perturbative expansion of the expectation value of the Yang-Mills energy density up to fourth order in the coupling at finite flow time. We regularise the resulting integrals using dimensional regularisation, and reproduce the universal coefficient of the 1/ε term in the relation between bare and renormalised couplings. The computation of the finite part leading to a determination…
We study the Renormalisation Group (RG) running of the quark mass, for $N_f=3$ QCD with Wilson fermions in a mixed action setup, with standard Schrödinger Functional (SF) boundary conditions for sea quarks and chirally rotated Schrödinger Functional ($χ$SF) boundary conditions for valence quarks. This necessitates the tuning of the boundary factor $z_f(g_0^2)$ of the $χ$SF valence action, in order to ensure that QCD symmetries are fully recovered in the continuum. The properties of this novel setup are monitored through the ratios $Z_S/Z_P$ and $Σ_S/Σ_P$ of the renormalisation parameters and s…
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）
The progresses in the experimental sector have been the harbinger of the observations of many new hadrons. Very recently, LHCb Collaboration announced the observation of two new $Σ_b(6097)^{\pm}$ states in the $Λ^0_bπ^{\pm}$ invariant mass distribution, which are considered as the excited states of the ground state $Σ^{(*)}_b$ baryon. Though, almost all of the ground state baryons have been observed, having a limited number of excited states observed so far makes them intriguing. Understanding the properties of the excited baryons improve our knowledge on the strong interaction as well as the …
Scale Setting and Strong Coupling Determination in the Gradient Flow Scheme for 2+1 Flavor Lattice QCD
Fakultät für Physik, Universität Bielefeld（比勒费尔德大学物理学院）；Physics Department, Brookhaven National Laboratory（布鲁克海文国家实验室物理系）；Key Laboratory of Quark & Lepton Physics (MOE) and Institute of Particle Physics, Central China Normal University（华中师范大学夸克与轻子物理教育部重点实验室及粒子物理研究所）；Institut für Physik & IRIS Adlershof, Humboldt-Universität zu Berlin（柏林洪堡大学物理学院及IRIS阿德勒斯霍夫研究所）；Institut für Kernphysik, Technische Universität Darmstadt（达姆施塔特工业大学核物理研究所）
The MILC Collaboration has completed production running of electromagnetic effects on light mesons using asqtad improved staggered quarks. In these calculations, we use quenched photons in the noncompact formalism. We study four lattice spacings from $\approx\!0.12\:$fm to $\approx\!0.045\:$fm. To study finite-volume effects, we used six spatial lattice sizes $L/a=12$, 16, 20, 28, 40, and 48, at $a\!\approx\!0.12\:$fm. We update our preliminary values for the correction to Dashen's theorem ($ε$) and the quark-mass ratio $m_u/m_d$.
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）
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 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…
Non-perturbative scale-dependent renormalization problems are ubiquitous in lattice QCD as they enter many relevant phenomenological applications. They require solving non-perturbatively the renormalization group equations for the QCD parameters and matrix elements of interest in order to relate their non-perturbative determinations at low energy to their high-energy counterparts needed for phenomenology. Bridging the large energy separation between the hadronic and perturbative regimes of QCD, however, is a notoriously difficult task. In this contribution we focus on the case of the QCD coupl…
