Unified description of the non-singlet spin dependent structure function $g_1$ incorporating Altarelli-Parisi evolution and the double logarithmic $ln^2(1/x)$ effects at low $x$

A unified equation for the non-singlet spin dependent structure function $g_1^{ns}(x,Q^2)$ which incorporates the complete leading order Altarelli-Parisi evolution at finite $x$ and double logarithmic $ln^2(1/x)$ effects at $x \to 0$ is formulated. The solution of this equation reasonably agrees with the recent data obtained by the Spin Muon Collaboration.

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