Non-Singlet spin structure function in the valon model and low x scaling behavior of $g_{1}^{NS}$ and $g_1^p$

A next-to-leading order QCD calculation of non-singlet spin structure function, $g_{1}^{NS}$ is presented within the valon representation of Hadrons. In the valon model, it is assumed that a nucleon is composed of three dressed valence quarks: the valons which have their own internal structure, the valence quark with its associated sea quarks and gluons. The results are in good agreement with all available data from SMC, E143, HERMES and with the newly released data from COMPASS experiments. It appears that the small x tail of $g_{1}^{NS}$ can be described by a single Regge-type exchange. The relevant parameter of this exchange is given. Finally we show that the polarized proton structure function has a scaling behavior at small x. The relevant parameters of this behavior are given too.

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