We introduce and examine the analytic properties of the three electromagnetic transition form factors of the Sigma*-Lambda hyperon transition. In the first part of the thesis, we discuss the interaction Lagrangian for the hyperons at hand. We calculate the decay rate of the Dalitz decay Sigma* Lambda -> e+e- in the one-photon approximation in terms of the form factors, as well as the differential cross section of the scattering e+e- -> Sigma*bar Lambda in the one-photon approximation. In the second part of the thesis, we build up the machinery for calculation of the form factors using dispersion relations, performing an analytic continuation from the timelike, q2 > 0, to the spacelike, q2 < 0, region of the virtual photon invariant mass q2. Due to an anomalous cut in the triangle diagram arising from a two-pion saturation of the photon-hyperon vertex, there is an additional term in the dispersive integral. We use the scalar three-point function as a model for the examination of the dispersive approach with the anomalous cut. The one-loop diagram is calculated both directly and using dispersion relations. After comparison of the two methods, they are found to coincide when the anomalous contribution is added to the dispersive integral in the case of the octet Sigma exchange. By examination of the branch points of the logarithm in the discontinuity, we deduce the structure of the Riemann surface of the unitarity cut and present trajectories of the branch points. The result of our analysis of the analytic structure yields a correct dispersive relation for the electromagnetic transition form factors. This opens the way for the calculation of these form factors in the low-energy region for both space- and timelike q2. As an outlook, we present preliminary calculations for the hyperon-pion scattering amplitude using the unitarity and the anomalous contribution in a once-subtracted dispersion relation. Finally we present the corresponding preliminary unsubtracted dispersive calculations for the form factors.
| Identifer | oai:union.ndltd.org:UPSALLA1/oai:DiVA.org:uu-392236 |
| Date | January 2019 |
| Creators | Vitos, Timea |
| Publisher | Uppsala universitet, Kärnfysik |
| Source Sets | DiVA Archive at Upsalla University |
| Language | English |
| Detected Language | English |
| Type | Student thesis, info:eu-repo/semantics/bachelorThesis, text |
| Format | application/pdf |
| Rights | info:eu-repo/semantics/openAccess |
| Relation | FYSAST ; FYSMAS1099 |
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