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[{"key": "dc.contributor.advisor", "value": "Eskola, Kari J.", "language": null, "element": "contributor", "qualifier": "advisor", "schema": "dc"}, {"key": "dc.contributor.author", "value": "Hyypp\u00e4, Joel Simeon", "language": null, "element": "contributor", "qualifier": "author", "schema": "dc"}, {"key": "dc.date.accessioned", "value": "2025-06-18T10:48:00Z", "language": null, "element": "date", "qualifier": "accessioned", "schema": "dc"}, {"key": "dc.date.available", "value": "2025-06-18T10:48:00Z", "language": null, "element": "date", "qualifier": "available", "schema": "dc"}, {"key": "dc.date.issued", "value": "2025", "language": null, "element": "date", "qualifier": "issued", "schema": "dc"}, {"key": "dc.identifier.uri", "value": "https://jyx.jyu.fi/handle/123456789/103730", "language": null, "element": "identifier", "qualifier": "uri", "schema": "dc"}, {"key": "dc.description.abstract", "value": "Elektroni\u2013positroni-annihilaation hadronituoton kokonaisvaikutusala on yksi hiukkasfysiikan perustavanlaatuisimmista mitattavista suureista. Hadroneiksi annihiloitumisen ja myoneiksi annihiloitumisen vaikutusalojen v\u00e4lisen suhteen, Re+e\u2212, tutkiminen mahdollistaa kvarkkien v\u00e4rivarausten m\u00e4\u00e4r\u00e4n, NC, selvitt\u00e4misen. \n\nT\u00e4ss\u00e4 pro gradu -tutkielmassa Re+e\u2212-suhde lasketaan vahvan kytkinvakion, \u03b1s, ensimm\u00e4isen kertaluvun tarkkuudella. QCD:n h\u00e4iri\u00f6teorialaskelmat johtavat useisiin divergoituviin termeihin. N\u00e4iden regularisoimiseksi lasku tehd\u00e4\u00e4n dimensiossa N = 4 \u2212 2\u03f5. Kokeellisia mittaustuloksia verrataan Re+e\u2212-suhteen analyyttisiin tuloksiin \u03b1s:n ensimm\u00e4isen, toisen ja kolmannen kertaluvun tarkkuudella sek\u00e4 my\u00f6s naiiviin kvarkki-partonimalliin. Z-bosonin massaa k\u00e4ytet\u00e4\u00e4n QCD-skaalaparametrin \u039bNf=5 QCD m\u00e4\u00e4ritt\u00e4miseen viiden kvarkkimaun alueella. QCD-skaalaparametrit \u039bNf=4 QCD ja \u039bNf=3 QCD m\u00e4\u00e4ritet\u00e4\u00e4n vaatimalla \u03b1s:n jatkuvuus raskaiden b- ja c-kvarkkien massakynnyksill\u00e4.\n\nOsa silmukkaintegraaleista vaatii negatiivisen \u03f5:n ja osa positiivisen \u03f5:n, jotta integraalit voidaan laskea niiden suppenemisalueilla. Laskussa tarvitaan my\u00f6s negatiivinen lopputilan invariantti massa q2. N\u00e4iden matemaattinen hyv\u00e4ksytt\u00e4vyys voidaan osoittaa k\u00e4ytt\u00e4m\u00e4ll\u00e4 analyyttista jatkamista. Analyyttista jatkamista k\u00e4ytet\u00e4\u00e4n my\u00f6s kvarkkien itseisenergiakorjausten laskemisessa.\n\nTeoreettisten ja kokeellisten tulosten vertailu osoittaa selv\u00e4sti, ett\u00e4 NC = 3. Parhaiten kokeellisiin mittauksiin sopivat tulokset sijaitsevat nelj\u00e4n ja viiden kvarkkimaun alueilla. Kolmen kvarkkimaun alueella QCD-korjattu Re+e\u2212-suhde asettuu kokeellisten tulosten alapuolelle.", "language": "fi", "element": "description", "qualifier": "abstract", "schema": "dc"}, {"key": "dc.description.abstract", "value": "The total cross section for hadron production in the electron\u2013positron annihilation is one of the most fundamental observables in particle physics. Studing the ratio between the cross sections of the annihilation into hadrons and into muons provides a way to determine the number of quark colour charges NC. This ratio is known as Re+e\u2212.\n\nIn this master\u2019s thesis, the ratio Re+e\u2212 is calculated to the first order in the strong coupling constant \u03b1s. Perturbative QCD calculations will lead to numerous divergent terms. To regularise them, the calculation is done in the dimension N = 4 \u2212 2\u03f5. The experimental data is compared with the analytical results for the ratio Re+e\u2212 to the first, second and third order in \u03b1s and also with the naive quark-parton model. The Z boson mass is used to define the QCD scale parameter \u039bNf=5 QCD for the five quark flavour region. The QCD scale parameters \u039bNf=4 QCD and \u039bNf=3 QCD are defined by requiring the continuity of the \u03b1s at the b and c heavy-quark mass thresholds.\n\nFor the loop integrals, a negative \u03f5 is needed for some integrals and a positive \u03f5 for other integrals to be able to calculate them in their convergence regions. Also, a negative square of the final-state invariant mass q2 is needed. These become mathematically approvable through analytic continuation. Analytic continuation is also used when calculating the quark self-energy corrections.\n\nComparing the theoretical results with the experimental data shows clearly that the experimental evidence supports that NC = 3. The best fitting results are found in the four and five quark flavour regions. In the three quark flavour region, the QCD-corrected ratio Re+e\u2212 lies lower than the experimental results.", "language": "en", "element": "description", "qualifier": "abstract", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Submitted by Paivi Vuorio (paelvuor@jyu.fi) on 2025-06-18T10:48:00Z\nNo. of bitstreams: 0", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Made available in DSpace on 2025-06-18T10:48:00Z (GMT). No. of bitstreams: 0\n Previous issue date: 2025", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.format.extent", "value": "141", "language": null, "element": "format", "qualifier": "extent", "schema": "dc"}, {"key": "dc.language.iso", "value": "eng", "language": null, "element": "language", "qualifier": "iso", "schema": "dc"}, {"key": "dc.rights", "value": "In Copyright", "language": null, "element": "rights", "qualifier": null, "schema": "dc"}, {"key": "dc.subject.other", "value": "R-suhde", "language": null, "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "QCD", "language": null, "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "analyyttinen jatkaminen", "language": null, "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "hadronic ratio", "language": null, "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "R ratio", "language": null, "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "QCD", "language": null, "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "analytic continuation", "language": null, "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.title", "value": "QCD corrections in the hadron production of the electron\u2013positron scattering", "language": null, "element": "title", "qualifier": null, "schema": "dc"}, {"key": "dc.type", "value": "master thesis", "language": null, "element": "type", "qualifier": null, "schema": "dc"}, {"key": "dc.identifier.urn", "value": "URN:NBN:fi:jyu-202506185520", "language": null, "element": "identifier", "qualifier": "urn", "schema": "dc"}, {"key": "dc.contributor.faculty", "value": "Matemaattis-luonnontieteellinen tiedekunta", "language": "fi", "element": "contributor", "qualifier": "faculty", "schema": "dc"}, {"key": "dc.contributor.faculty", "value": "Faculty of Sciences", "language": "en", "element": "contributor", "qualifier": "faculty", "schema": "dc"}, {"key": "dc.contributor.department", "value": "Fysiikan laitos", "language": "fi", "element": "contributor", "qualifier": "department", "schema": "dc"}, {"key": "dc.contributor.department", "value": "Department of Physics", "language": "en", "element": "contributor", "qualifier": "department", "schema": "dc"}, {"key": "dc.contributor.organization", "value": "Jyv\u00e4skyl\u00e4n yliopisto", "language": null, "element": "contributor", "qualifier": "organization", "schema": "dc"}, {"key": "dc.contributor.organization", "value": "University of Jyv\u00e4skyl\u00e4", "language": null, "element": "contributor", "qualifier": "organization", "schema": "dc"}, {"key": "dc.subject.discipline", "value": "Teoreettinen fysiikka", "language": "fi", "element": "subject", "qualifier": "discipline", "schema": "dc"}, {"key": "dc.subject.discipline", "value": "Theoretical Physics", "language": "en", "element": "subject", "qualifier": "discipline", "schema": "dc"}, {"key": "dc.type.coar", "value": "http://purl.org/coar/resource_type/c_bdcc", "language": null, "element": "type", "qualifier": "coar", "schema": "dc"}, {"key": "dc.rights.copyright", "value": "\u00a9 The Author(s)", "language": "fi", "element": "rights", "qualifier": "copyright", "schema": "dc"}, {"key": "dc.rights.accesslevel", "value": "openAccess", "language": null, "element": "rights", "qualifier": "accesslevel", "schema": "dc"}, {"key": "dc.type.publication", "value": "masterThesis", "language": null, "element": "type", "qualifier": "publication", "schema": "dc"}, {"key": "dc.subject.yso", "value": "kvarkit", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "fysiikka", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "hiukkasfysiikka", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "kvanttiv\u00e4ridynamiikka", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "hadronit", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "myonit", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.rights.url", "value": "https://rightsstatements.org/page/InC/1.0/", "language": null, "element": "rights", "qualifier": "url", "schema": "dc"}]
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