Analyticity and Regge asymptotics in virtual Compton scattering on the nucleon

We test the consistency of the data on the nucleon structure functions with analyticity and the Regge asymptotics of the virtual Compton amplitude. By solving a functional extremal problem, we derive an optimal lower bound on themaximum difference between the exact amplitude and the dominant Reggeon contribution for energies. above a certain high value nu(h)(Q(2)). Considering in particular the difference of the amplitudes T-1(inel) (nu, Q(2)) for the proton and neutron, we find that the lower bound decreases in an impressive way when nu(h)(Q(2)) is increased, and represents a very small fraction of the magnitude of the dominant Reggeon. While the method cannot rule out the hypothesis of a fixed Regge pole, the results indicate that the data on the structure function are consistent with an asymptotic behaviour given by leading Reggeon contributions. We also show that the minimum of the lower bound as a function of the subtraction constant S-1(inel) (Q(2)) provides a reasonable estimate of this quantity, in a frame similar, but not identical to the Reggeon dominance hypothesis.

Automated summary

This study examines the consistency of data on nucleon structure functions, analyticity, and Regge asymptotics of the virtual Compton amplitude. By solving a functional extremal problem, an optimal lower bound on the maximum difference between the exact amplitude and dominant Reggeon contribution is derived for high energies above a certain threshold. The results suggest that the data on the structure function are consistent with an asymptotic behavior given by leading Reggeon contributions.