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Quantum chromodynamics and the nucleon longitudinal structure function

Quantum chromodynamics and the nucleon longitudinal structure function
Quantum chromodynamics and the nucleon longitudinal structure function

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.

University of Southampton
Coulson, Stephen Norman
Coulson, Stephen Norman

Coulson, Stephen Norman (1981) Quantum chromodynamics and the nucleon longitudinal structure function. University of Southampton, Doctoral Thesis.

Record type: Thesis (Doctoral)

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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Published date: 1981

Identifiers

Local EPrints ID: 459844
URI: http://eprints.soton.ac.uk/id/eprint/459844
PURE UUID: 85198518-32b1-4920-a9ec-95861bf9fb81

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Date deposited: 04 Jul 2022 17:19
Last modified: 04 Jul 2022 17:19

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Author: Stephen Norman Coulson

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