Dependence of the Measured Asymmetry a 1 (x)

We propose the new approach for taking into account the Q 2 dependence of measured asymmetry A 1. This approach is based on the similarity of the Q 2 behaviour and the shape of the spin-dependent structure function g 1 (x, Q 2) and spin averaged structure function F 3 (x, Q 2). The analysis is applied on the SMC and E154 experimental data. An experimental study of the nucleon spin structure is realized by measuring of the asymmetry A 1 (x, Q 2) = g 1 (x, Q 2)/F 1 (x, Q 2). The most known theoretical predictions on spin dependent structure function g 1 (x, Q 2) of the nucleon were done by Bjorken 1 and Ellis and Jaffe 2 for the so called first moment value Γ 1 = 1 0 g 1 (x)dx. Studying the properties of g 1 (x, Q 2) and the calculation of the Γ 1 value require the knowledge of structure function g 1 at the same Q 2 in the hole x range. Experimentally asymmetry A 1 is measuring at different values of Q 2 for different x bins. An accuracy of the modern experiments 3,4,5,6 allows to analyze data in the assumption 7 that asymmetry A 1 (x, Q 2) is Q 2 independent (structure functions g 1 and F 1 have the same Q 2 dependence) A 1 (x, Q 2) = A 1 (x) (1) But the precise checking of the Bjorken and Ellis-Jaffe sum rules requires considering the Q 2 dependence of A 1 or g 1. Moreover, the assumption (1) the asymmetry A 1 (x, Q 2) is Q 2 independent does not follow from the theory. On the contrary, the behaviour of F 1 and g 1 as a functions of Q 2 is expected to be different due to the difference between polarized and unpolarized splitting functions. There are several approaches (see 8,9 and its references) how to take into account the Q 2 dependence of A 1. They are based on different approximate solutions of the DGLAP equations. Some of them have been used already by Spin Muon Collaboration (SMC) and E154 Collaboration in the last analyses of experimental data (see 4 and 6 , respectively).