I will introduce our IBP package NeatIBP, which automatically generates small-size integration-by-parts (IBP) identities for Feynman integrals. Based on the syzygy and module intersection techniques, the generated IBP identities’ propagator degree is controlled and thus the size of the system of IBP identities is shorter than that generated by the standard Laporta algorithm. Resently, we updated NeatIBP with some new featrues, such as, spanning cut and the reduction interface of NeatIBP and Kira. I will also give some powerful applications of NeatIBP.

Precision measurements involving nuclei are at the cutting edges of nuclear physics and testing the Standard Model (SM) of physics. For instance, precision beta decay measurements have the potential to constrain beyond SM physics at TeV scales. To interpret these experiments, it is crucial to have comparably accurate theoretical predictions of relevant quantities along with an accurate understanding of the underlying nuclear dynamics. In this contribution, I will overview recent calculations of electroweak processes with quantum Monte Carlo (QMC) computational methods used to solve the many-body Schr ̈odinger equation. The QMC approach retains the complexity of many-nucleon dynamics and provides highly accurate results for light nuclei. I will discuss calculations of observable quantities with readily available data–such as beta decay and electromagnetic reactions–used to validate models of nuclear many-body interactions and electroweak currents. I will present QMC calculations of predicted quantities relevant to on-going beta decay experiments and discuss how these results will impact experimental determinations of beyond standard model physics.

We introduce quantum magnetic J-oscillators that operate at zero magnetic field by exploiting nuclear spin-spin J-coupling transitions in molecules. This is achieved by coupling in situ hyperpolarized samples to a programmable digital feedback system that digitizes, delays, and amplifies the sample-generated magnetic field before feeding it back to the sample. Due to the insensitivity of the J-couplings to magnetic field drifts, we achieved coherent J-oscillations lasting over 3000 s, with a linewidth of 337 μHz limited primarily by acquisition time, reaching the Cramér-Rao lower bound in estimating error in frequency measurement [1]. The ability to control the feedback delay and gain enabled us to resolve overlapping resonances, making possible on-demand spectral editing. Application of quantum oscillators was demonstrated on a diverse range of molecules (nitriles, heterocycles, organic acids). The J-oscillators produce highly resolved, sharp spectra, reveal hidden transitions, and may allow distinction of complex mixtures that conventional zero-field NMR [2] cannot resolve. As a result, this approach can expand the scope of zero-field NMR for analytical chemistry, biomolecular characterization, and fundamental physics. [1]. S. Fleischer, S. Lehmkuhl, L. Lohmann, S. Appelt, Approaching the Ultimate Limit in Measurement Precision with RASER NMR. Appl. Magn. Reson. 54 (11), 1241–1270 (2023). [2]. D. A. Barskiy, et al., Zero- to Ultralow-field Nuclear Magnetic Resonance. Prog. Nucl. Magn. Reson. Spectrosc. (2025).