The required improvement in aμHVP will only be possible if issues like the details of the RC for the hadronic cross section data used as well as systematic errors and correlations can be addressed successfully. It also requires a good knowledge of the dynamics for hadronic final states. We will systematically compare the results with an independent method to predict aμHVP by using Lattice QCD, which is the focus of DOE Muon g-2 Theory Initiative. We have proposed and will pursue in this project a novel direct HVP determination in muon-electron elastic scattering or Bhabha process at flavor factories. Feasibility studies of such an experiment at CERN have just started; it will require a new level of precision for RC and multiple scattering effects. Hadronic Light-by-Light (HLbL) [Task 2.2] contribution to (g-2)μ consists of the coupling of four photons by intermediate hadronic states. This object has complicated Lorentz structure, so it is much more complicated that HVP which is given just by one dispersion relation. We will pursue the proposed data driven approach based on developed dispersion relations, which use as the input differential distributions of several hadronic and radiative processes. The goal is to minimize model dependencies in the predictions and to give a reliable estimate of the experimental and theoretical uncertainties for HLbL contribution with the precision required for the new g-2 measurement. The main contribution to HLbL is from the single-meson exchanges, which have as a subpart the neutral pseudoscalar meson transition form factors. Relevant experiments are carried out and planned worldwide, and coordinating these efforts and providing knowledge data base for interpretation and use of the results is the goal of this JRA.

Precise determination of the weak mixing angle with PVES and Vud from beta decay [Task 1.1]: the relevant corrections are the electroweak (EW) boxes that involve an exchange of two gauge vector bosons V = γ, Z, W between the lepton and the hadronic system of interest. While pure electroweak corrections (of which the γ-Z mixing, the analogue of the vacuum polarization from the previous two tasks, is an important part) can be reliably evaluated at 10-4 level, the accuracy of EW boxes calculations is more difficult to control. Recent works showed the importance of a reliable calculation of the γZ-box for the extraction of the weak mixing angle from PVES on a free proton, which is the subject of the P2@MESA experiment in Mainz. MESA will also use the C-12 target with the same detector system. The γW-box is the main nonexperimental source of uncertainty in extracting Vud from nuclear β-decays. Since Vud is the dominant contribution to the unitarity constraint of the first row of the CKM matrix, reducing the uncertainty of the γW-box is of utmost importance. The dispersion integrals for the EW boxes require knowledge of γZ and γW interference inelastic structure functions in the resonance region and beyond. Constructing this input in a close collaboration of theory and experiment, and providing reliable and controlled uncertainty estimates of the EW boxes is the goal of this subproject.

Determination of the neutrino properties [Task 1.2]: in accelerator-based experiments, meson and photon production channels contribute a background for extraction of neutrino oscillation parameters. An ambitious experimental program to test the three-generation paradigm, establish the order of mass eigenstates and investigate CP violation includes existing (NOνA, T2K) and future (DUNE, T2HK) accelerator based experiments. The proposed combined theoretical and experimental study of meson production with neutrino beam is a necessary ingredient to confirm hypothetic nonstandard neutrino oscillations within neutrino experiments, the results of the analysis will serve as input in the calculation of the electroweak boxes and may prove crucial to better constrain calculations of nuclear matrix elements for neutrinoless double β decay experiments.

**Work Package**: 21

**Lead beneficiary**: JGU MAINZ - Germany

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