Measurement of $\omega$ and $\eta$ mesons via their three pion decay with ALICE in pp collisions at $\sqrt s = 7$ TeV

A Large Ion Collider Experiment (ALICE) is an experiment at the Large Hadron Collider (LHC), focussing on heavy-ion physics, in particular on the so-called Quark-Gluon Plasma (QGP), a state of strongly interacting matter in which quarks and gluons exist as unconfined particles. One way to probe this medium is the measurement of direct photons that escape the medium and can be measured as an excess over a photonic background. Most of this background originates from hadronic decays and precise knowledge of hadron production in a collision, especially the production of neutral mesons, is therefore crucial for such measurements in order to properly describe their background. Furthermore, neutral meson cross sections are used to test and constrain theory predictions of meson production, making production cross section measurements valuable for theory and experiment alike. In this thesis, differential invariant cross sections of $\omega$ and $\eta$ meson production are measured in proton-proton collisions at $\sqrt{s}= 7$ TeV via their decay to $\pi^+\pi^-\pi^0$. For the first time, all available methods to measure photons at mid-rapidity within ALICE are used to reconstruct the $\omega$ meson, allowing to access a wide momentum range. The production cross section of $\eta$ mesons is measured for the first time in the three pion decay channel at this collision energy, serving as a supplement and cross check for the well established $\eta\rightarrow\gamma\gamma$ measurement. The obtained cross sections are found to be consistent with existing measurements at this centre-of-mass energy, as well as reasonably well described by Pythia predictions. Furthermore $\omega/\pi^0$ and $\eta/\pi^0$ ratios are presented, both of which are underestimated by Pythia predictions but mostly consistent with previous measurements.