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Chiral symmetry in nucleons
[Thesis]. Manchester, UK: The University of Manchester; 2015.
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Abstract
Chiral perturbation theory allows us to probe the low energy properties of hadrons. In this thesis we have looked at the axial coupling constant (see chapter 4) and baryon number violation (see chapter 5).We calculated the axial coupling constant up to O(p^4) using the extended on mass shell renormalisation scheme in chiral perturbation theory. We also included the decuplet as an explicit degree of freedom. To fit the free parameters in our expression we used a combination of lattice and experimental data.We found that the fourth order corrections were quite large, and we struggled to produce an acceptable fit to the data. We also saw that the running of g_{A}^{pn} with M_\pi predicted by lattice QCD and ChPT at O(p^4) do not agree well. This is likely due to a combination of finite size effects impacting the low pion mass lattice data and the chiral perturbative series converging slowly.For our work on baryon number violation we looked at determining the values of two low-energy constants that appear in the baryon violating chiral Lagrangian. To do this, we matched our expression to lattice data. Previous determinations of the parameters had been done without calculating the effect of loops, ours was the first investigation to see what impact the loop diagrams would have. We found that our determinations of the parameters were in agreement with previous results, suggesting the effect of the loops is small. We also performed a chiral extrapolation, and found that our results were in agreement with previous results that did not account for loop corrections. This suggests that the impact of higher-order corrections is not significant for this baryon-number-violating process.