We present arguments based on positivity conditions and light-cone analysis for the structure functions $W_4$ and $W_5$ (which occur in neutrino scattering) to conclude that if they scale as ${\nu }^p{W}_{4,5}(\nu , q^2)\to F_{4,5}\left(\xi \right)$, then $p=2\mathrm{}$. We also get the following bound on the scale dimension $l_u$ of the chiral-symmetry-breaking Hamiltonian: $-\left(\frac{5}{2}\right)\ge l_u>-4\mathrm{}$. Further, if we assume that fractional dimensions are not admissible, we get $l_u=-3\mathrm{}$.

• Received 14 June 1973

DOI:https://doi.org/10.1103/PhysRevD.8.3518