Neutrino exchange and asymptotic behaviour of weak interaction cross sections

It is argued that total cross sections cannot increase asymptotically as a power of energy even in the presence of massless particle exchange. Elastic νν scattering is considered as an example. The properties of s- and t-channel partial waves are analysed and it is shown that the above statement is true if the amplitude is bounded by a polynomial in s for s→∞ and t>0 and if its singularity at t=0 is dominated by two-particle exchange.