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 the maximum difference between the exact amplitude and the dominant Reggeon contribution for energies \(\nu \) above a certain high value \(\nu _h(Q^2)\). Considering in particular the difference of the amplitudes \(T_1^\text {inel}(\nu , Q^2)\) 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 \(S_1^\text {inel}(Q^2)\) provides a reasonable estimate of this quantity, in a frame similar, but not identical to the Reggeon dominance hypothesis.

我们通过分析和虚拟康普顿振幅的Regge渐近性检验了核子结构函数上数据的一致性。通过解决函数极值问题，对于高于某个特定高值\（\ nu _h（Q ^ 2）\的能量\（\ nu \），我们得出了精确振幅与支配Reggeon贡献之间的最大差的最佳下限。 ）。特别考虑质子和中子的振幅\（T_1 ^ \ text {inel}（\ nu，Q ^ 2）\）的差异，我们发现当\（\ nu _h时，下界以令人印象深刻的方式减小（Q ^ 2）\）增加了，代表了统治雷吉翁星系的一小部分。尽管该方法不能排除固定Regge极点的假设，但结果表明，结构函数数据与Reggeon前导贡献所给出的渐近行为是一致的。我们还表明，下限的最小值是减法常数\（S_1 ^ \ text {inel}（Q ^ 2）\）的函数，它在类似但不相同的帧中提供了对该数量的合理估计。 Reggeon优势假设。