Development of the quality test protocol for the DEPFET pixel detectors and top-quark mass measurement at high energy e$^{+}$e$^{-}$ colliders

The need of explanation to the nature phenomenons are unstoppable and likewise the necessity of new machines to continue discovering them. On this content, several projects, with different approaches, are under being developed. The International Linear Collider (ILC) and the Compact Linear Collider (CLIC) will use electrons and positrons collision, on the energy range from hundreds of GeV to the multi-TeV scale. On the other hand, the SuperKEKB, which uses $e^{+}e^{-}$ interaction at intermediate energies, generating unprecedented luminosities to study the $B\bar{B}$ processes with very high accuracy. The work presented here entered on this content to perform a tiny contribution. The thesis was divided in two main topics. First part is dedicated to the study and development of the DEPFET system. DEPFET is an active pixel technology, characterized by its excellent position reconstruction, its low material budget and low power consumption, which is capable to cope with all the requirement of the future $e^{+}e^{-}$ colliders. For this reason, DEPFET is one of the candidates for the (ILC) and the baseline technology for the Belle II PXD (SuperKEKB). On this content, the DEPFET prototypes for Belle II PXD were presented, likewise, the process of construction of the PXD shell, to contextualize and motivated the development of a quality control protocol using a needles card. The process of design and test of the distinct needles card prototypes were described, together with a proposed testing protocol. This work resulted in a complete setup, with all the mechanical parts, the electronic boards and software, mounted and prepared to be used during the PXD production. The second study is focused on the measurement of the top-quark mass. This part has introduced a new observable, $B(m_{t},\zeta_{S'})$, which uses the cross section of the $t\bar{t}$ radiative events to obtain the mass of the top-quark in the continuum. The study has been performed on $e^{+}e^{-}$ collider scenario, to take advantage of this new environment and, potentially, reach unprecedented sensitivities. A partonic level study was done in order to obtain the maximum potential sensitivity achievable on the ILC-$500$ GeV physics scenario. The calculations was performed, independently, using the ISR and FSR particles and then, combining both processes. Afterwards, to approach towards a realistic study, the hadronization and the basic detector effect were included. Moreover, the study was extended to CLIC-$380$ GeV and ILC-$1000$ GeV. $B(m_{t},\zeta_{S'})$ does not require a specific interaction energy the study of the mass can be done not only over the production threshold but in the continuum, therefore, the mass can be defined on a good renormalization system, being sensitive to its running. On this content, the sensitivity to the running of the top-quaks mass was proved. Finally, the study of the systematic errors were performed and a method to minimize its effect was proposed. The results obtained proved that the resolution of $B(m_{t},\zeta_{S'})$ are way below the methods currently used in hadron colliders and in the same order of the threshold measurements on the ILC.