  The low-energy antineutrino- and neutrino-nucleon neutral current elastic
scattering is studied within the framework of the relativistic SU(2) baryon
chiral perturbation theory up to the order of $\mathcal{O}(p^3)$. We have
derived the model-independent hadronic amplitudes and extracted the form
factors from them. It is found that differential cross sections ${{\rm d}
\sigma}/{{\rm d} Q^2}$ for the processes of (anti)neutrino-proton scattering
are in good agreement with the existing MiniBooNE data in the $Q^2$ region
$[0.13,0.20]$ GeV$^2$, where nuclear effects are expected to be negligible. For
$Q^2\leq 0.13$ GeV$^2$, large deviation is observed, which is mainly owing to
the sizeable Pauli blocking effect. Comparisons with the simulation data
produced by the NuWro and GIENE Mento Carlo events generators are also
discussed. The chiral results obtained in this work can be utilized as inputs
in various nuclear models to achieve the goal of precise determination of the
strangeness axial vector form factor, in particular when the low-energy
MicroBooNE data are available in the near future.
