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 $\mathrm{B}\mathrm{R}({\pi }^{+}\to {\mu }^{+}{\nu }_e)=8.9\times {10}^{-4}$, $\mathrm{B}\mathrm{R}(K^{+}\to {\mu }^{+}{\nu }_e)=3.2\times {10}^{-3}$, improving previous constraints by factors 9 and 1.25, respectively. We also estimate the SBND-PRISM sensitivity to lepton number violating decays, $\mathrm{B}\mathrm{R}({\pi }^{+}\to {\mu }^{+}{\bar{\nu }}_e)=2.1\times {10}^{-3}$ and $\mathrm{B}\mathrm{R}(K^{+}\to {\mu }^{+}{\bar{\nu }}_e)=7.4\times {10}^{-3}$, though not reaching previous BEBC limits. Last, we identify several ways how the SBND collaboration could improve this analysis.