arXiv2025
We present the first measurement of the missing energy due to nuclear effects in monoenergetic, muon neutrino charged-current interactions on carbon, originating from $K^+ \rightarrow μ^+ ν_μ$ decay at rest ($E_{ν_μ}=235.5$ MeV), performed with the J-PARC Sterile Neutrino Search at the J-PARC Spallation Neutron Source liquid scintillator based experiment. Toward characterizing the neutrino interaction, ostensibly $ν_μn \rightarrow μ^- p$ or $ν_μ$$^{12}\mathrm{C}$ $\rightarrow μ^-$$^{12}\mathrm{N}$, we define the missing energy as the energy transferred to the nucleus ($ω$) minus the kinetic energy of the outgoing proton(s), $E_{m} \equivω-\sum T_p$, and relate this to visible energy in the detector, $E_{m}=E_{ν_μ} (235.5 \mathrm{MeV})-m_μ(105.7 \mathrm{MeV}) + [m_n-m_p (1.3 \mathrm{MeV})] - E_{\mathrm{vis}}$. 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 $(77\pm3)$% pure double-coincidence kaon decay-at-rest signal (621 total events), provides detailed insight into neutrino-nucleus interactions, allowing even the nuclear orbital shell of the struck nucleon to be inferred. The measurement provides an important benchmark for models and event generators at hundreds 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.