Related papers: Hadronic vacuum polarization using gradient flow
The gradient flow in QCD is treated perturbatively through next-to-next-to-leading order in the strong coupling constant. The evaluation of the relevant momentum and flow-time integrals is described, including various means of validation.…
The gradient-flow formalism proves to be a useful tool in lattice calculations of quantum chromodynamics. For example, it can be used as a scheme to renormalize composite operators by inverting the short-flow-time expansion of the…
Over the last decade the gradient flow formalism became an important tool for lattice simulations of Quantum Chromodynamics. It offers remarkable renormalization properties which pave the way for cross-fertilization between perturbative and…
The dispersive approach to quantum chromodynamics is applied to the study of the hadronic vacuum polarization function and associated quantities. This approach merges the intrinsically nonperturbative constraints, which originate in the…
We propose a method to compute the hadronic vacuum polarization function on the lattice at continuous values of photon momenta bridging between the spacelike and timelike regions. We provide two independent demonstrations to show that this…
The QCD coupling appears in the perturbative expansion of the current-current two-point (vacuum polarization) function. Any lattice calculation of vacuum polarization is plagued by several competing non-perturbative effects at small momenta…
We address several aspects of lattice QCD calculations of the hadronic vacuum polarization and the associated Adler function. We implement a representation derived previously which allows one to access these phenomenologically important…
The chromo-magnetic dipole operator is expressed in terms of operators at finite flow time in the gradient-flow formalism. The matching coefficients are evaluated through next-to-next-to-leading order QCD.
The Standard Model prediction for $\mu$-$e$ scattering at Next-to-Next-to-Leading Order (NNLO) contains non-perturbative QCD contributions given by diagrams with a hadronic vacuum polarization insertion in the photon propagator. By taking…
Lattice calculations of hadronic observables are aggravated by short-distance fluctuations. The gradient flow, which can be viewed as a particular realisation of the coarse-graining step of momentum space RG transformations, proves a…
Recent applications of single-scale four-loop tadpoles are briefly reviewed. An algorithm for the evaluation of current correlators based on differential equations is described and applied to obtain high moments of the vacuum polarization…
Normalizing flows can be used to construct unbiased, reduced-variance estimators for lattice field theory observables that are defined by a derivative with respect to action parameters. This work implements the approach for observables…
Over the last decade the gradient flow formalism has become an important tool for lattice simulations of Quantum Chromodynamics. It offers remarkable renormalization properties which pave the way for cross-fertilization between perturbative…
We provide results for the vacuum expectation values of the flowed action density, the quark condensate, and the quark kinetic operator in the gradient-flow formalism. We work in $N_\text{F}$-flavor QCD, keeping the heaviest quark massive…
We study a representation of the hadronic vacuum polarization based on the time-momentum representation of the vector correlator. This representation suggests a way to compute the hadronic vacuum polarization and the associated Adler…
Phenomenological results of equal time, point to point spatial correlation functions of hadronic currents are used to deduce the structure of the QCD vacuum. It is found that a model with only quark condensate is not adequate to explain the…
Non-perturbatively computing the hadronic vacuum polarization at large photon virtualities and making contact with perturbation theory enables a precision determination of the electromagnetic coupling at the $Z$ pole, which enters global…
We discuss the calculation of the leading hadronic vacuum polarization in lattice QCD. Exploiting the excellent quality of the compiled experimental data for the e^+e^- --> hadrons cross-section, we predict the outcome of large-volume…
The precision with which hadronic vacuum polarization (HVP) is obtained determines how accurately important observables, such as the muon anomalous magnetic moment, a_\mu, or the low-energy running of the electromagnetic coupling, \alpha,…
Point-to-point correlation functions of hadron currents in the QCD vacuum are calculated on a lattice and analyzed using dispersion relations, providing physical information down to small spatial separations. Qualitative agreement with…