First Measurement of Missing Energy Due to Nuclear Effects in Monoenergetic Neutrino Charged Current Interactions

We present the first measurement of the missing energy due to nuclear effects in monoenergetic, muon neutrino charged-current interactions on carbon, originating from K⁺ → μ⁺ ν_μ decay-at-rest (Eν_μ=235.5 MeV), performed with the JSNS² liquid scintillator based experiment. Towards characterizing the neutrino interaction, ostensibly ν_μ n → μ⁻ p or ν_μ¹²C$ $→ μ^-¹²N, and in analogy to similar electron scattering based measurements, we define the missing energy as the energy transferred to the nucleus (ω) minus the kinetic energy of the outgoing proton(s), Eₘ ≡ ω-∑ Tₚ, and relate this to visible energy in the detector, Eₘ=Eν_μ~(235.5~MeV)-m_μ~(105.7~MeV) - Eᵥᵢₛ. The missing energy, which is naively expected to be zero in the absence of nuclear effects (e.g. nucleon separation energy, Fermi momenta, and final-state interactions), is uniquely sensitive to many aspects of the interaction, and has previously been inaccessible with neutrinos. The shape-only, differential cross section measurement reported, based on a (77±3)% pure double-coincidence KDAR signal (621 total events), provides an important benchmark for models and event generators at 100s-of-MeV neutrino energies, characterized by the difficult-to-model transition region between neutrino-nucleus and neutrino-nucleon scattering, and relevant for applications in nuclear physics, neutrino oscillation measurements, and Type-II supernova studies.