Probing Neutron Skins with Kaon-Decay-at-Rest Neutrinos: From Coherent to Diffractive Elastic Neutrino–Nucleus Scattering

초록

We investigate coherent elastic neutrino-nucleus scattering (CE$u$NS) induced by pion-decay-at-rest ($\pi$DAR) and kaon-decay-at-rest (KDAR) neutrinos, with emphasis on the transition from strict coherence to the coherent-to-diffractive regime. Organizing CE$u$NS observables in terms of the dimensionless variable $qR$, we show that $\pi$DAR measurements remain largely confined to the near-coherent region for the nuclei considered here, whereas KDAR neutrinos ($E_u=236$ MeV) extend the kinematics into $qR\gtrsim 1$, where recoil spectra begin to develop shape sensitivity to the nuclear weak form factor. Using representative light, medium-mass, and heavy nuclei (${<}^{>}12$C, ${<}^{>}40$Ca, ${<}^{>}48$Ca, and ${<}^{>}208$Pb), we compare Helm and two-parameter Fermi weak-density models and quantify benchmark statistical sensitivities to neutron-skin variations at a J-PARC Sterile Neutrino Search at the J-PARC Spallation Neutron Source (JSNS${<}^{>}2$)-like facility. For a total exposure of 10 ton$\cdot$year and representative KDAR fluences, the one-parameter, stat-only sensitivities improve from about $\Delta R_{np}{<}^{>}(1\sigma )\simeq 0.09$ to 0.02 fm for ${<}^{>}48$Ca and from $\simeq 0.07$ to 0.02 fm for ${<}^{>}208$Pb as the fluence increases. We further perform two-parameter benchmark checks in the Helm and two-parameter Fermi model spaces to quantify how the leading surface-shape nuisance affects the weak-radius inference and its local neutron-skin equivalent. This nuisance produces the largest degradation for ${<}^{>}12$C, moderate degradation for ${<}^{>}40$Ca and ${<}^{>}48$Ca, and only a small effect for ${<}^{>}208$Pb under the detector assumptions adopted here. These results indicate that KDAR-based CE$u$NS can provide a complementary electroweak probe of weak-charge distributions and neutron-surface structure beyond the near-coherent limit, while emphasizing the benchmark and model-dependent scope of the present sensitivity estimates.

키워드