Browsing by Author "Crowther, Devon Neil"

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    Vacuum contributions to the nucleon energy sum rule
    (Stellenbosch : Stellenbosch University, 2024-03) Crowther, Devon Neil; Weigel, Herbert ; Stellenbosch University. Faculty of Science. Dept. of Physics.
    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.