Tensor couplings in dark matter direct detection and muon-to-electron conversion

In recent years, there have been advancements in dark matter direct detectors, as well as experiments that look for violations of charged-lepton flavor through muon-to-electron conversion. While these two beyond the Standard Model (BSM) searches are completely different, both can be treated within the non-relativistic effective field theory (NRET). However, a notable lacuna persists in the literature concerning the incorporation of tensor interactions in NERT. This presentation will address this gap by incorporating tensor amplitudes into the NRET theory using a novel methodology for the decomposition of antisymmetric tensor-type interactions. Specifically, the presentation will focus on the role of tensor interactions in dark matter direct detection and muon-to-electron conversion, providing tensor matrix elements that are essential for those ongoing BSM searches. I will discuss the way those new matrix elements enrich our understanding of new physics interactions, facilitating enhanced experimental interpretations and potential breakthroughs.