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Vacuum contributions to the nucleon energy sum rule
Thesis (MSc)--Stellenbosch University, 2024.
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| Format: | Thesis |
| Language: | en_ZA en_ZA |
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Stellenbosch : Stellenbosch University
2024
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| _version_ | 1867613767875952640 |
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| access_status_str | Open Access |
| author | Crowther, Devon Neil |
| author2 | Weigel, Herbert
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| author_browse | Crowther, Devon Neil Weigel, Herbert |
| author_facet | Weigel, Herbert
Crowther, Devon Neil |
| author_sort | Crowther, Devon Neil |
| collection | Thesis |
| dc_rights_str_mv | Stellenbosch University |
| description | Thesis (MSc)--Stellenbosch University, 2024. |
| format | Thesis |
| id | oai:scholar.sun.ac.za:10019.1/130391 |
| institution | Stellenbosch University (South Africa) |
| language | en_ZA en_ZA |
| last_indexed | 2026-06-10T12:41:23.238Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from SUNScholar — Stellenbosch University Repository |
| publishDate | 2024 |
| publishDateRange | 2024 |
| publishDateSort | 2024 |
| publisher | Stellenbosch : Stellenbosch University |
| publisherStr | Stellenbosch : Stellenbosch University |
| record_format | dspace |
| source_str | SUNScholar — Stellenbosch University Repository |
| spelling | oai:scholar.sun.ac.za:10019.1/130391 Vacuum contributions to the nucleon energy sum rule Crowther, Devon Neil Weigel, Herbert Stellenbosch University. Faculty of Science. Dept. of Physics. Quantum field theory -- Models Sum rules (Physics) Quantum chromodynamics Chiral symmetry (Nuclear physics) Nuclear forces (Physics) -- Mathematical models Nambu Jona-Lasinio model Nucleon-nucleon scattering -- Mathematical models UCTD Thesis (MSc)--Stellenbosch University, 2024. ENGLISH 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. AFRIKAANSE 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. Masters 2024-03-01T07:28:37Z 2024-04-26T15:54:17Z 2024-03-01T07:28:37Z 2024-04-26T15:54:17Z 2024-03 Thesis https://scholar.sun.ac.za/handle/10019.1/130391 en_ZA en_ZA Stellenbosch University xiv, v, 79 pages : illustrations application/pdf Stellenbosch : Stellenbosch University |
| spellingShingle | Quantum field theory -- Models Sum rules (Physics) Quantum chromodynamics Chiral symmetry (Nuclear physics) Nuclear forces (Physics) -- Mathematical models Nambu Jona-Lasinio model Nucleon-nucleon scattering -- Mathematical models UCTD Crowther, Devon Neil Vacuum contributions to the nucleon energy sum rule |
| title | Vacuum contributions to the nucleon energy sum rule |
| title_full | Vacuum contributions to the nucleon energy sum rule |
| title_fullStr | Vacuum contributions to the nucleon energy sum rule |
| title_full_unstemmed | Vacuum contributions to the nucleon energy sum rule |
| title_short | Vacuum contributions to the nucleon energy sum rule |
| title_sort | vacuum contributions to the nucleon energy sum rule |
| topic | Quantum field theory -- Models Sum rules (Physics) Quantum chromodynamics Chiral symmetry (Nuclear physics) Nuclear forces (Physics) -- Mathematical models Nambu Jona-Lasinio model Nucleon-nucleon scattering -- Mathematical models UCTD |
| url | https://scholar.sun.ac.za/handle/10019.1/130391 |
| work_keys_str_mv | AT crowtherdevonneil vacuumcontributionstothenucleonenergysumrule |