Quantum chromodynamics and the nucleon longitudinal structure function

Abstract

The phenomenon of asymptotic freedom together with the theoretical tools of the operator product expansion and renormalisation group allow a systematic and reliable application of perturbative quantum chromodynamics (Q.C.D.) to deep inelastic lepton-hadron scattering. In particular one can study the ratio of the longitudinal to transverse cross-section, R s OE/Qt. Leading order Q.C.D. predictions for R are concluded not to give a satisfactory description of the current data at large X > 0.5. Here we extend this perturbative analysis to include the next to leading order, 0(g+), Q.C.D. contributions. This involves calculating the fourth order contribution to the flavour non-singlet longitudinal coefficient function that appears in the light cone expansion. A technique that regulates the spurious mass-singularities encountered in a consistent manner is discussed, and its use justified through examples utilising the optical theorem. The O((+MS)Q.C.D. expression for the moments of the flavour non-singlet longitudinal structure function is then inverted using a simple technique, allowing a plot of the next to leading order Q.C.D. corrections to the ratio R. Such corrections are found to be small (-12% for X>0.5 ) and it is concluded that to this order of perturbation theory a discrepancybetween theory and experiment still exists.

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