A theoretical study of meson transition form factors
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Abstract
This thesis studies the lightest pseudoscalar mesons, pion, eta and eta', through their transition form factors. Describing the underlying structure of hadrons is still a challenging problem in theoretical physics. These form factors, which can be experimentally measured, provide valuable information on the pseudoscalar meson inner structure and are of fundamental interest for describing their elementary interactions. Obtaining a precise description for these form factors has become a pressing subject given their role in one of the finest tests of our understanding of particle physics: the anomalous magnetic moment of the muon. The foreseen experimental precision for this observable challenges the available theoretical descriptions so far.
Still, incorporating the available experimental information into a theoretical framework becomes increasingly difficult as the experimental precision improves, challenging simplified frameworks. In this work, we propose to use the framework of Padé theory in order to precisely describe these form factors in the space-like region, which provides a well-founded mathematically-based and data-driven approach for this task.
The first part of our study is devoted to extract the parameters relevant to our approach using the available single-virtual space-like data. The accuracy of the method, beyond that of previous approaches, has been later confirmed in experiments performed in the low-energy time-like region for the eta and eta' cases. To give consideration to these new results, we incorporated the corresponding data into our analysis. The extension of the formalism to the most general double-virtual case is subsequently discussed, which requires the introduction, for the first time in this context, of Canterbury approximants, the bivariate version of Padé approximants.
As a direct application of our results, the eta-eta' mixing parameters have been extracted from the single-virtual transition form factors. The employed method provides an alternative to the traditional ones, obtaining competitive results while minimizing modeling errors.
Besides, our double-virtual description is employed for describing the rare decays of the pseudoscalar mesons into a lepton pair. The latter process offers an opportunity to test the doubly virtual pseudoscalar mesons transition form factors as well as an opportunity to discuss possible new physics contributions in light of the present discrepancies.
Finally, our approach is used to obtain a precise calculation for the pseudoscalar-pole contribution to the hadronic light-by-light piece of the anomalous magnetic moment of the muon. This includes, for the first time, a systematic error and meets the required precision in foreseen experiments.