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

Abstract

We investigate coherent elastic neutrino--nucleus scattering (CE$ν$NS) induced by pion--decay--at--rest ($π$DAR) and kaon--decay--at--rest (KDAR) neutrinos, with emphasis on the transition from strict coherence to the diffractive regime. Organizing CE$ν$NS observables in terms of the dimensionless variable $qR$, we show that $π$DAR measurements remain confined to the near--coherent region for all nuclei, whereas KDAR neutrinos ($E_ν=236$~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 $1σ$ sensitivities reach $ΔR_{np}^{\,(1 σ)}$ $\simeq0.09$--$0.02$~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$ν$NS as a quantitatively robust and complementary avenue for probing neutron skins and nuclear weak densities beyond the coherent limit.

Figures (7)

• Figure 1: Weak--charge densities $\rho_W(r)$ obtained with the Helm (solid) and two--parameter Fermi (2pF, dashed) parametrizations for $^{12}$C, $^{40}$Ca, $^{48}$Ca, and $^{208}$Pb. Each profile is normalized to the total weak charge $Q_W$ (i.e., $\int d^3r\,\rho_W(r)=Q_W$). The parameter values used in each panel are summarized in Table \ref{['tab:presets']}.
• Figure 2: Weak form factors for $^{12}$C, $^{40}$Ca, $^{48}$Ca, and $^{208}$Pb calculated with the Helm (solid) and two--parameter Fermi (2pF, dashed) parametrizations. Left panels show $|F(q)|^2$ as a function of $qR$, and right panels show $F(q)$ as a function of $q$ (in fm$^{-1}$). Vertical dotted lines indicate the first and second diffraction minima at $qR\simeq4.493$ and $qR\simeq7.725$. Markers in the $^{48}$Ca and $^{208}$Pb right panels indicate the CREX and PREX-II measurements of $F_W(q)$ at their acceptance-averaged momentum transfers (Table \ref{['tab:prex_crex_qR']}).
• Figure 3: Kinematical comparison of KDAR ($E_\nu=236$ MeV) and $\pi$DAR ($E_\nu\simeq30$ MeV) neutrinos. Left panels show $qR$ as a function of the recoil energy $T$ for $^{12}$C, $^{40}$Ca, $^{48}$Ca, and $^{208}$Pb; horizontal dashed lines indicate $qR=1$ and $4.493$. Right panels show the corresponding laboratory scattering angle $\theta(T)$; for each target, dashed lines indicate the angles at which $qR=1$ and $4.493$ are reached. KDAR extends the kinematics to larger $T$ and $qR$, accessing the coherent--to--diffractive transition, while $\pi$DAR events are concentrated in the near--coherent region.
• Figure 4: CE$\nu$NS differential cross sections at KDAR ($E_\nu=236$ MeV) for $^{12}$C, $^{40}$Ca, $^{48}$Ca, and $^{208}$Pb, calculated with the Helm (solid) and two--parameter Fermi (2pF, dashed) weak form factors. Upper axes indicate the corresponding laboratory scattering angle. The spectra peak at low recoil energy and decrease rapidly with $T$; the overall normalization scales as $Q_W^2\propto N^2$, while model--dependent differences appear only at larger $T$, where form--factor suppression becomes significant.
• Figure 5: Same as Fig. \ref{['fig:dsdT KDAR']}, but for $\pi$DAR neutrinos ($E_\nu\simeq30$ MeV). At these lower energies, the recoil spectra are dominated by the near--coherent region where $F(q)\simeq1$, and form--factor suppression (and Helm/2pF differences) becomes noticeable only in the high--recoil tail, especially for heavy targets.