2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/47751The double logarithmic terms $α_{s} \ln^{2}x $ are important to predict precisely the small $x$ behavior of the spin structure function $g_{1}$. We numerically analyze the evolution of the flavor non-singlet $g_{1}$ including the all-order resummed effect of these terms. It is pointed out that the next-to-leading logarithmic corrections produce an unexpectedly large suppression factor over the experimentally accessible range of $x$ and $Q^{2}$. This implies that the next-to-leading logarithmic contributions are very important in order to obtain a definite prediction.9 pages, ps figures included, sprocl.sty, psfig.sty, and here.sty are required. Invited talk presented at the International Symposium on ``QCD Corrections and New Physics'' October 27-29, 1997 Hiroshima, JapanHigh Energy Physics - Phenomenologytext