Precision Tests of Standard Model at Low Energies with Atoms, Hadrons and Neutrinos

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The Standard Model of elementary particles and fundamental interactions (SM) has been extremely successful in describing and predicting various phenomena in atomic, nuclear and particle physics. Nonetheless this success, there exist numerous indications that physics beyond the Standard Model (BSM) should exist. Precision low-energy tests of SM consists in high-accuracy measurements of SM parameters in the experiments with atoms, nuclei, hadrons and neutrinos. Comparing these measurements to the SM theory predictions one observes or constrains the hypothetical BSM contributions. The precision of modern low-energy experiments probe the BSM contributions due to new particles with masses of 1-10 TeV and are thus comparable or complementary to collider and astrophysical searches. This proposal is dedicated to the extraction of the weak mixing angle from parity-violating electron scattering (PVES) with the Q-Weak and MESA/P2 experiments and parity violation in atoms, extraction of the CKM matrix element V-ud from neutron and nuclear Beta-decay, extraction of neutrino oscillation parameters from short baseline neutrino experiments, extraction of nucleon and nuclear radii from Lamb shift in light muonic atoms and electron scattering, and extraction of properties of Dark Matter particles from direct detection experiments. The common feature of these, otherwise quite different experiments, is the necessity of reliable calculations of SM radiative corrections, in particular, the so-called box graphs that depend on nuclear and hadronic structure and require an inclusion of inclusive nuclear and hadronic intermediate states. At low energy, quantum chromodynamics, the theory of strong interaction, is nonperturbative, and at the moment such contributions cannot be calculated directly from the QCD Lagrangian. To provide box graph calculations at the accuracy level of relevant low-energy precision tests, I propose to use dispersion relations, the method that is based on Lorentz and gauge invariance, unitarity and analyticity. In my previous works I applied this method to Compton scattering with real and virtual photons and to box graph calculations for elastic electron scattering. The scope of this project is the generalization of those studies to the calculation of box diagrams with a photon and a Z(W) and two photons with and without parity violation in arbitrary kinematics, and the generalized Compton process Z(W)+N -> gamma+N underlying the neutrino photon production process. As input to some of dispersion integrals, the electroweak pion production gamma(Z,W)+N -> pi+N amplitudes in a combination with sum rules, effective theories, nuclear effects will be used. This project has a great potential to provide a unified framework for calculating hadronic structure corrections to BSM searches with atoms, electron scattering and beta-decay experiments, neutrino scattering and direct detection Dark Matter experiments.