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 BR(π⁺ → μ⁺ νₑ) = 8.9 × 10⁻⁴, BR(K⁺ → μ⁺ νₑ) = 3.2 × 10⁻³, improving previous constraints by factors 9 and 1.25, respectively. We also estimate the SBND-PRISM sensitivity to lepton number violating decays, BR(π⁺ → μ⁺ ν̄ₑ)= 2.1 × 10⁻³ and BR(K⁺ → μ⁺ ν̄ₑ) = 7.4 × 10⁻³, though not reaching previous BEBC limits. Last, we identify several ways how the SBND collaboration could improve this analysis.