Hunting for B⁺→K⁺τ⁺τ^- decay in the Belle (II) data samples

In recent years, some deviations from the Standard Model (SM) have been observed in semileptonic B meson decays, such as departures from lepton flavour universality in the b → sll and b → cτν transitions quantified by the R_K(*) and R_D(*) ratios. This generated a considerable interest in the flavour physics community: the pattern of anomalies could be explained by New Physics (NP) scenarios predicting large enhancements in the third generation of leptons compared to the first two, as in the b → sττ transition, especially when the NP coupling is proportional to the square of the lepton mass. The current limits for all processes mediated by b → sττ are far from the SM predictions by four orders of magnitude, due to the experimental challenges of reconstructing τ leptons that decay quickly and produce undetectable neutrinos. Consequently, the possibility of large NP-induced enhancements remains unchallenged. An upper limit for the B⁺ → K⁺τ⁺τ^- decay mode has been set by the BaBar experiment, but it has never been searched for by any other experiment. In this work, the search for B⁺ → K⁺τ⁺τ^- is performed in the context of the Belle and Belle II experiments. Due to the presence of up to four neutrinos (missing energy), the B⁺ → K⁺τ⁺τ^- signal cannot be fully reconstructed. At a B factory, e⁺e^- collisions produce Υ(4S) which mostly decay into a pair of B mesons, with a well-known initial state. By fully reconstructing a charged B mesons, we can infer the four momentum of the other B meson, which may decay into K⁺τ⁺τ^-. This technique, called B tagging, effectively mitigates large background contributions in searches involving missing energy. The full reconstruction of hadronic B decays is done using Belle II's exclusive tagging algorithm, employing a network of boosted decision trees trained on Monte Carlo (MC). A significant discrepancy in B-tagging performance between MC and data has been observed, not only being a significant source of systematic uncertainty but also indicating suboptimal training. To address this, a new control procedure, using B → Dπ decays without explicitly reconstructing D mesons, is introduced to calibrate the hadronic B tagging. This provides large statistics, while having a high purity (in contrast to the traditional B → Xlν), also enabling the study of how B decay modelling affects B-tagging performance. By implementing the corresponding corrections to the decay model, the agreement is significantly improved. Furthermore, retraining the B-tagging algorithm with the updated MC simulations increases the background rejection. It is important to note that these efforts and further improvements to the decay model obtained by measuring poorly known hadronic B decays will lead to better performance of hadronic B tagging, benefiting all future searches involving missing energy. After reconstructing the tagged B and the charged tracks from the signal side, events that contain a B⁺ → K⁺τ⁺τ^- are expected to leave no extra energy in the electromagnetic calorimeter (E_ECL). Contamination from beam background photons and neutral clusters arising from hadronic split-off processes degrades the E_ECL resolution. On the other hand, the background mostly composed of semileptonic decays also has low E_ECL. To mitigate the resolution issue and optimise the separation from the background composed mostly of semileptonic B decays, a study of E_ECL is conducted using the control sample of B⁺ → J/ψK⁺ decays. Finally, in the absence of a signal, an upper limit for the branching ratio of the B⁺ → K⁺τ⁺τ^- is derived using combined data sets of Belle and Belle II MC simulations. (author)