Probing Neutron Skins with KDAR Neutrinos: From Coherent to Diffractive Elastic Neutrino--Nucleus Scattering

Abstract

We investigate coherent elastic neutrino--nucleus scattering (CE$\nu$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 diffractive regime. Organizing CE$\nu$NS observables in terms of the dimensionless variable $qR$, we show that $\pi$DAR measurements remain confined to the near--coherent region for all nuclei, whereas KDAR neutrinos ($E_\nu=236$~MeV) extend the kinematics into $qR\gtrsim1$, where recoil spectra develop genuine 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 examine relevant cross sections and quantify the statistical sensitivity to the neutron skin thickness achievable at a JSNS$^2$--like facility. For a total exposure of 10~ton$\cdot$year and realistic KDAR fluences, projected $1\sigma$ sensitivities reach $\Delta R_{np}^{\,(1 \sigma)}$ $\simeq0.09$--$0.02$~fm for $^{48}$Ca and $\simeq0.07$--$0.02$~fm for $^{208}$Pb as the fluence increases. These sensitivities are competitive with, and complementary to, parity--violating electron--scattering measurements such as CREX and PREX, while relying on an electroweakly clean neutral--current probe with distinct systematic uncertainties. Our results establish KDAR--based CE$\nu$NS as a quantitatively robust and complementary avenue for probing neutron skins and nuclear weak densities beyond the coherent limit.