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We make a critical, next-to-leading order, study of the relationship betweenthe longitudinal structure function FL and the gluon distribution proposed inCooper- Sarkar et al. (Z. Phys. C 39:281, 1988; Acta Phys. Pol. B 34:29112003), which is frequently used to extract the gluon distribution from theproton longitudinal structure function at small x. The gluon density isobtained by expanding at particular choices of the point of expansion andcompared with the hard Pomeron behavior for the gluon density. Comparisons withH1 data are made and predictions for the proposed best approach are alsoprovided.

Analysis of the proton longitudinal structure function from the gluon distribution function