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Next-to-leading order corrections to deep inelastic scattering structure functions at small Bjorken-x

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Authors
Hänninen, Henri
Date
2017
Discipline
Teoreettinen fysiikkaTheoretical Physics

 
Syvän epäelastisen sironnan kokeellisia tuloksia on kuvattu onnistuneesti pie- nillä Bjorkenin x:n arvoilla käyttämällä sironnan dipolimallia ja johtavan kerta- luvun valokartiohäiriöteoriaa. On tärkeää selvittää, paraneeko teorian kuvaavuus tutkimalla vaikutuksia korkeampien kertalukujen häiriöteoriasta. Mittaustulosten kuvauksen parantamiseksi tässä työssä johdetaan korjauksia johtavan kertaluvun vaikutusalaan ja rakennefunktioihin häiriöteorian toisessa ker- taluvussa. Tämän toteuttamiseksi esitellään tarvittavassa määrin valokartiokvant- tikenttäteoria, pienen Bjorken-x sironnan dipolimalli ja häiriöteoriaa. Johdettu toi- sen kertaluvun vaikutusalala sisältää pehmeän divergenssin prosessin sisältämien sisäisten gluonien takia. Tämä divergenssi katkaisu-reguloidaan, mistä saadaan äärelliset numeerisesti laskettavat vaikutusalat ja rakennefunktiot. Johdetut toisen kertaluvun korjaukset evaluoidaan numeerisesti ja verrataan tunnettuihin johtavan kertaluvun tuloksiin. Regularisaatio havaitaan toimivaksi, mutta katkaisu ei poista dirvergenssiä täysin ideaalisella tavalla, mikä johtaa koh- tuuttoman suuriin toisen kertaluvun korjauksiin. Tämän seurauksena toisen kerta- luvun vaikutusala ja rakennefunktio tuloksista tulee negatiivisia korkeilla fotonin virtualiteeteilla, mikä on epäfysikaalista. Tämä tulos kertoo, että regularisaatioon tarvitaan huolellisempi lähtestymistapa. ...
 
Experimentally determined Deep Inelastic Scattering structure functions have been successfully described at small Bjorken-x using the dipole picture of the scattering and leading order light cone perturbation theory. It is of interest whether this description can be bettered by studying higher order perturbation theory effects. To improve the description, this work derives corrections to the Deep Inelastic Scattering cross sections and structure functions at next-to-leading order in light cone perturbation theory. To do this the framework of quantum field theory on the light cone is introduced along with necessities of perturbation theory on the light cone and the dipole picture of the scattering. The derived next-to-leading order cross section result has a soft divergence that is regulated with a cut-off, which then yields access to numerically evaluable cross sections and structure functions. The next-to-leading order corrections are evaluated numerically and compared to established leading order results. It is found that while the regularization works, the divergence is over-subtracted leading to inviably large corrections to the leading result. This leads to the next-to-leading order cross section and structure function results becoming negative at high photon virtualities, which is unphysical. This result shows that a more careful approach to the regularization is needed. ...
 
Keywords
sironta
URI

http://urn.fi/URN:NBN:fi:jyu-201703311846

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