Bounds which depend only on the vector form factors in quasielastic neutrino reaction

In quasielastic neutrino- (antineutrino-) nucleon reactions, we obtain strict upper bounds for the ratio $R=\frac{\left(\frac{d\sigma }{d\left|q^2\right|}\right(\nu )-\frac{d\sigma }{d\left|q^2\right|}(\bar{\nu }\left)\right)}{\left(\frac{d\sigma }{d\left|q^2\right|}\right(\nu )+\frac{d\sigma }{d\left|q^2\right|}(\bar{\nu }\left)\right)}$ at any neutrino energy $E_{\nu }$ and for the transverse and longitudinal polarizations of the recoil nucleon in the reaction plane at high neutrino energy ($E_{\nu }\gg nucleonmass$) which depend only on the vector form factors. These bounds are constraints to be satisfied by experiments if the conserved-vector-current hypothesis is valid.