τ -Lepton Lifetime Measurement andWorking Point Optimization for the PixelVertex Detector at Belle II

In the Standard Model of Particle Physics, all leptons have the same coupling strength tothe weak interaction. Comparing the theoretical model with experimental observations revealsa slight deviation in the electron branching fraction of τ -lepton decays. However, the precisionof the measurement is limited by the precision of the measured τ -lepton lifetime. This workpresents a novel measurement of the τ -lepton lifetime using a template fitting approach appliedto 3×1-prong τ+τ−decays at Belle II. The decay length is determined in the xy-plane from theprecisely known SuperKEKB interaction point to the 3-prong τ -lepton decay vertex. A robustsoftware framework was developed to unify data processing, validation, and systematic studies, ensuring reproducibility and flexibility for future improvements. The vertex reconstructionachieves a resolution of 31.43 ± 0.01µm, leveraging the precision of the pixel vertex detector.Templates corresponding to different lifetime hypotheses are generated using a re-weightingmethod. The reliability of this approach is confirmed through comparisons with templatesproduced from shifted generator lifetimes and pseudo-data fits. Systematic uncertainties are incorporated into the likelihood fit model via nuisance parameters. To address dominant modelinguncertainties, a dedicated two-dimensional re-weighting strategy was developed, resulting in anexpected total precision of 0.2 fs, including a statistical uncertainty of 0.08 fs and a systematicuncertainty of 0.18 fs. With this, the expected precision of the analysis exceeds the currentworld average by more than a factor of two.In 2023, the Belle II experiment upgraded its pixel vertex detector by replacing the previous single-layer configuration with a new two-layer detector, based on the same sensor design. Optimized sensor working points are crucial for the success of future analyses relyingon precise vertex information with the new two-layer pixel vertex detector. To maximize hitefficiency, dedicated optimization studies were conducted. During pre-commissioning, detailedmulti-parameter source scans were performed to evaluate and tune the sensor settings acrosshalf of the pixel vertex detector modules. These scans identified stable operation points thatsignificantly improved hit efficiency, with gains of up to 14 %, and mitigated effects such ascluster anomalies in under-depleted modules. Simplified high-voltage scans with all pixel vertexdetector modules were subsequently performed, resulting in suitable operating parameters thatalso serve as starting values for future in-situ calibration during beam collisions. Early datafollowing the resumption of beam operations in 2024 revealed individual module improvementsof up to 8 % from refined operation parameters.