Could SBND-PRISM probe lepton flavor violation?

We investigate the possibility of using the Short-Baseline Near Detector (SBND) at Fermilab to constrain lepton flavor violating decays of pions and kaons. We study how to leverage SBND-PRISM, the use of the neutrino beam angular spread to mitigate systematic uncertainties, to enhance this analysis. We show that SBND-PRISM can put stringent limits on the flavor violating branching ratios \(\rm{BR}(\pi^+ \to \mu^+ \nu_e) = 8.9 \times 10^{-4}\), \(\rm{BR}(K^+ \to \mu^+ \nu_e) = 3.2 \times 10^{-3}\), improving previous constraints by factors 9 and 1.25, respectively. We also estimate the SBND-PRISM sensitivity to lepton number violating decays, \(\rm{BR}(\pi^+ \to \mu^+ \overline{\nu}_e)= 2.1 \times 10^{-3}\) and \(\rm{BR}(K^+ \to \mu^+ \overline{\nu}_e) = 7.4 \times 10^{-3}\), though not reaching previous Big European Bubble Chamber (BEBC) limits. Last, we identify several ways how the SBND collaboration could improve this analysis.