Longitudinal Structure Function at Intermediate x and the Gluon Density.pdf

a r X i v : h e p - p h / 9 3 0 2 2 5 7 v 1 1 2 F e b 1 9 9 3 CERN-TH 6785/93 ANL-HEP-PR-93-7 January, 1993 Longitudinal Structure Function at Intermediate x and the Gluon Density Edmond L. Berger1,2 and Ruibin Meng2 1CERN-Geneva 2High Energy Physics Division? Argonne National Laboratory Argonne, IL 60439 Abstract Calculations are presented of the longitudinal structure function FL(x,Q 2). We use next-to-leading order expressions in QCD (O(α2s)) plus parton densities determined previously from global fits to data on deep inelastic lepton scattering, prompt photon production, and bottom quark production. Anticipated data from the DESY ep collider HERA should provide discriminating information on the gluon density, particularly for values of x 0.05. ?Work supported by the U.S. Department of Energy, Division of High Energy Physics, Contract W-31-109-ENG-38. In perturbative quantum chromodynamics(QCD), the longitudinal structure function FL(x,Q 2), measured in deep inelastic lepton scattering, may be expressed to leading order as a sum of integrals over the gluon and quark densities of the nucleon[1]. As usual Q2 is the square of the four-vector momentum exchange, and x is the Bjorken scaling variable. At small values of x, the gluon contribution dominates, and, to fair approximation, FL(x,Q 2) ～= 2αs(Q 2) 3π 1 1.77 x a G( x a ,Q2). (1) Here G(x,Q2) is the gluon density, αs(Q 2) is the QCD coupling strength, and a is a parameter whose value is about 0.4 for FL[2]. Correspondingly, measurement of FL has long been advocated as perhaps the most direct probe of the gluon density at small x. Studies indicate that precise measurements of FL should be feasible at the HERA ep collider at DESY for values of x of order 10?2, or less, and values of Q2 in the range 10 to 100 GeV2[3]. Recently a full next-to-leading order calculation (O(α2s)) in QCD has been published for the deep inelastic structure functions F2 and FL[4]. These analytic expressions allow us to extend the exp