Vacuum contributions to the nucleon energy sum rule

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dc.contributor.advisorWeigel, Herbert en_ZA
dc.contributor.authorCrowther, Devon Neilen_ZA
dc.contributor.otherStellenbosch University. Faculty of Science. Dept. of Physics.en_ZA
dc.date.accessioned2024-03-01T07:28:37Z
dc.date.accessioned2024-04-26T15:54:17Z
dc.date.available2024-03-01T07:28:37Z
dc.date.available2024-04-26T15:54:17Z
dc.date.issued2024-03
dc.descriptionThesis (MSc)--Stellenbosch University, 2024. en_ZA
dc.description.abstractENGLISH ABSTRACT: Within the Nambu Jona-Lasinio(NJL) chiral soliton model nucleon structure functions were previously explored. One of the structure functions, namely the iso-singlet unpolarized nucleon structure function (IUSF), displayed results that did not agree with experimental data. The simulations described in this pa- per aim to investigate this behaviour of the IUSF. The central means of this investigation is the energy sum rule that relates an integral of the IUSF to the mass of the nucleon. Through this investigation, it was dis- covered that the cut-off constant Λ had not been properly computed in that earlier study. This constant is not a numerical parameter but is fully determined by physical constants, such as the pion mass and pion decay constant. Even though the correction was only minor, the adjusted calculation of the IUSF resulted in a significant problem with the sum rule — a numerical inaccuracy that became more apparent at higher grand spins. These inaccuracies in the sum rule become apparent regardless of the Λ value but were signifcantly more so for the corrected Λ. With the validity of our sum rule in numerical jeopardy, an investigation is launched into why this is so and obtaining the appropriate numerical parameters to fix it. Following this, we investigated the deviation from empirical data exhibited by the IUSF. This was done in two ways, first the numerical parameters that encode the discretisation of the quantum fields were changed, secondly the contribution from the non-solitonic background, which defines the reference energy, was changed to better reflect its spatial invariance. In essence a strong dependence of the IUSF on the treatment of the vacuum subtraction was found.en_ZA
dc.description.abstractAFRIKAANSE OPSOMMING: Voorheen was die Nambu Jona-Lasinio(NJL) chirale solitonmodel is nukleonstruktuurfunksies onder- soek. Een van die struktuurfunksies, die iso-singlet ongepolariseerde nukleonstruktuurfunksie (IUSF), het resultate geleuer wat nie met eksperimentele data ooreenstem nie. In die skripsie, word hierdie gedrag van die IUSF word deur simulasies ondersoek. Die hoof doel leˆ in die energiesomree¨l wat ’n integraal van die IUSF koppel met die massa van die nukleon. Hierdie konstante is nie ’n numeriese parameter nie, maar word ten volle bepaal deur fisiese konstantes, soos die pion massa en verval konstantes. Alhoewel die regstelling slegs minimaal was, het die aangepaste berekening van die IUSF tot ’n beduidende probleem met die somree¨l gelei - ’n numeriese onakkuraatheid wat meer beklemtoon word by hoe¨r grand spins. Hierdie onakkuraathede in die somree¨l is opvallend ongeag die Λ-waarde, maar was aansienlik meer so vir die gekorrigeerde Λ. Met die geldigheid van ons somree¨l in numeriese gevaar, is ’n ondersoek geloods om die oorsprong te vind en die nodige toepaslike numeriese parameters te bepaal. Hierna volg ’n ondersoek van afwyking in empiriese data wat vertoon word deur die IUSF. Dit word op twee maniere gedoen, eerstens die verandering van numeriese parameters wat die diskretisering van die kwantumvelde kodeer, tweedens die bydrae van die nie-solitoniese agtergrond, wat die verwysingsenergie definieer, is verander om die ruimtelike invariansie beter te weerspiee¨l. In wese is ’n sterk afhanklikheid van die IUSF op die hantering van die vakuumaftrekking gevind.af_ZA
dc.description.versionMastersen_ZA
dc.format.extentxiv, v, 79 pages : illustrationsen_ZA
dc.identifier.urihttps://scholar.sun.ac.za/handle/10019.1/130391
dc.language.isoen_ZAen_ZA
dc.language.isoen_ZAen_ZA
dc.publisherStellenbosch : Stellenbosch Universityen_ZA
dc.rights.holderStellenbosch Universityen_ZA
dc.subject.lcshQuantum field theory -- Modelsen_ZA
dc.subject.lcshSum rules (Physics)en_ZA
dc.subject.lcshQuantum chromodynamicsen_ZA
dc.subject.lcshChiral symmetry (Nuclear physics)en_ZA
dc.subject.lcshNuclear forces (Physics) -- Mathematical modelsen_ZA
dc.subject.lcshNambu Jona-Lasinio modelen_ZA
dc.subject.lcshNucleon-nucleon scattering -- Mathematical modelsen_ZA
dc.subject.nameUCTDen_ZA
dc.titleVacuum contributions to the nucleon energy sum ruleen_ZA
dc.typeThesisen_ZA
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