Recent progress in low energy neutrino scattering physics and its implications for the standard and beyond the standard model physics

Neutrinos continue to provide a testing ground for the structure of the standard model of particle physics as well as hints towards the physics beyond the standard model. Neutrinos of energies spanning over several orders of magnitude, originating in many terrestrial and astrophysical processes, have been detected via various decay and interaction mechanisms. At MeV scales, there has been one elusive process, until a few years ago, known as coherent elastic neutrino-nucleus scattering (CEvNS) that was theoretically predicted over five decades ago but was never observed experimentally. The recent experimental observation of the CEvNS process by the COHERENT collaboration at a stopped pion neutrino source has inspired physicists across many subfields. This new way of detecting neutrinos has vital implications for nuclear physics, highenergy physics, astrophysics, and beyond. CEvNS, being a low-energy process, provides a natural window to study light, weakly-coupled, new physics in the neutrino sector. Leveraging orders of magnitude higher CEvNS cross section, new physics can be searched with relatively small detectors.In this review, we intend to provide the current status of low energy neutrino scattering physics and its implications for the standard and beyond the standard model physics. We discuss low energy sources of neutrinos with a focus on neutrinos from the stopped pions. Stopped pion sources cover energies in the tens of MeVs and are almost optimal for studying CEvNS. Several worldwide experimental programs have been or are being set up to detect CEvNS and new physics signals in the near future with complementary detection technologies and physics goals. We discuss the general formalism of calculating the tree-level CEvNS cross section and the estimated theoretical uncertainties on the CEvNS cross section stemming from different sources. We also discuss the inelastic scattering of tens of MeV neutrinos that have implications for supernova detection in future neutrino experiments. The stopped-pion facilities are also a near-ideal tens of MeV neutrino source to study inelastic neutrino-nucleus cross sections. We discuss how the CEvNS experiments can be used as a testing ground for the Standard Model (SM) weak physics as well as in searching for the Beyond the Standard Model (BSM) physics signals. Any deviation from the SM predicted event rate either with a change in the total event rate or with a change in the shape of the recoil spectrum, could indicate new contributions to the interaction cross-section. The SM implications include the study of weak nuclear form factor and weak mixing angle. The BSM studies include non-standard interactions, neutrino electromagnetic properties, and sterile neutrino searches. Stopped pion facilities are also a copious source of neutral and