The Rare Decay of the Neutral Pion into a Dielectron
Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
We give a rather self-contained introduction to the rare pion to dielectron decay which in nontrivial leading order is given by a QED triangle loop. We work within the dispersive framework where the imaginary part of the amplitude is obtained via the Cutkosky rules. We derive these rules in detail.
Using the twofold Mellin-Barnes representation for the pion transition form factor, we derive a simple expression for the branching ratio B(π0 e+e-) which we then test for various models. In particular a more recent form factor derived from a Lagrangian for light pseudoscalars and vector mesons inspired by effective field theories.
Comparison with the KTeV experiment at Fermilab is made and we find that we are more than 3σ below the KTeV experiment for some of the form factors. This is in agreement with other theoretical models, such as the Vector Meson Dominance model and the quark-loop model within the constituent-quark framework. But we also find that we can be in agreement with KTeV if we explore some freedom of the form factor not fixed by the low-energy Lagrangian.
Place, publisher, year, edition, pages
2013. , 178 p.
rare pion decay, Mellin transform, Mellin-Barnes representation, dispersive representation, dispersion relation, Kramers-Kronig relations, Cutkosky cutting rules, Feynman Loop diagram calculations
Subatomic Physics Subatomic Physics
IdentifiersURN: urn:nbn:se:uu:diva-211683OAI: oai:DiVA.org:uu-211683DiVA: diva2:668048
Master Programme in Physics
2013-11-07, Å11167, Uppsala, 15:15 (English)
Leupold, Stefan, Prof. Dr.