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Over the last decade, numerical solutions of Quantum Chromodynamics (QCD)using the technique of lattice QCD have developed to a point where they arebeginning to connect fundamental aspects of nuclear physics to the underlyingdegrees of freedom of the Standard Model. In this review, the progress oflattice QCD studies of nuclear matrix elements of electroweak currents andbeyond-Standard-Model operators is summarized, and connections with effectivefield theories and nuclear models are outlined.  Lattice QCD calculations of nuclear matrix elements can provide guidance forlow-energy nuclear reactions in astrophysics, dark matter direct detectionexperiments, and experimental searches for violations of the symmetries of theStandard Model, including searches for additional CP violation in the hadronicand leptonic sectors, baryon-number violation, and lepton-number or flavorviolation. Similarly, important inputs to neutrino experiments seeking todetermine the neutrino-mass hierarchy and oscillation parameters, as well asother electroweak and beyond-Standard-Model processes can be determined. Thephenomenological implications of existing studies of electroweak andbeyond-Standard-Model matrix elements in light nuclear systems are discussed,and future prospects for the field toward precision studies of these matrixelements are outlined.

Nuclear matrix elements from lattice QCD for electroweak and beyond-Standard-Model processes