PRAMANA c Indian Academy of Sciences Vol. 53, No. 4 — journal of October 1999 physics pp. 701–706 The longitudinal structure function and the gluon distribution at low ABHIJEET DAS and A SAIKIA Department of Physics, Gauhati University, Guwahati 781 014, India Department of Physics, Arya Vidyapeeth College, Guwahati 781 016, India MS received 9 April 1999 Abstract. We obtain a relation between the longitudinal structure function , and at small , using the formalism recently reported by one of the authors [2]. We also obtain a relation between , and its slope . This provides us with the determination of the longitudinal structure function from data and hence extract the gluon distribution . Keywords. Longitudinal structure function; gluon distribution; QCD; low . PACS Nos 12.38 Bx; 12.38 Cy 1. Introduction The longitudinal structure function comes as a consequence of the violation of Callan–Gross relation and is defined as In the naive parton model, for spin giving the Callan–Gross relation. How- ever, in the QCD inspired quark-parton model, and is very sensitive to the QCD effects. The QCD prediction for the longitudinal structure function is [1] (1) being the electric charge of the th quark in the unit of proton charge. 701