Neutrinoless double beta ( \(0\nu \beta \beta \) ) decay is a process where two neutrons in a nucleus are converted into two protons with the emission of two electrons and no neutrinos, thereby violating lepton number conservation by two units. The next generation of \(0\nu \beta \beta \) decay experiments holds the potential to uncover the origin of the neutrino masses and the observed matter-antimatter asymmetry in the universe [1–4]. The observation of this decay would imply that neutrinos are Majorana particles and serve as a probe for several lepton-number-violating (LNV) mechanisms [1, 2], including the standard light-Majorana neutrino exchange. Regardless of the LNV decay mechanism, the interpretation of new physics hinges on an accurate understanding of the underlying nuclear dynamics. Rates of these decays depend not only on unknown parameters associated with BSM physics, but also on nuclear matrix elements that must be obtained from many-body approaches. These matrix elements can vary by a factor of two to three depending on the approach used [3, 4]. Therefore, improving the theoretical description of this process is crucial for the future of fundamental symmetries research. If one assumes that \(0\nu \beta \beta \) decay results come from the exchange of a light Majorana neutrino between two nucleons, then the momentum carried by the neutrino is on the order of 100 MeV/c [3, 5]. Muon captures on nuclei involve momentum transfers on the order of the muon mass, thus placing it in a similar kinematic regime. Therefore, muon capture is a great testing ground to validate models of nuclear electroweak physics that will be relevant to studying \(0\nu \beta \beta \) -decay. Muon capture reactions have been treated extensively from both the theoretical and experimental points of view [6–9] and rates have been obtained in light systems with several methods [10–21]. In the following section, I will briefly review the theory of muon capture in light nuclei and discuss recent QMC calculations of partial muon capture rates on the \(^3\) He and \(^6\) Li ground states.