We search for the rare B+ -> K+ tau+ tau- decay using data collected by the LHCb detector at a centre-of-mass energy of 13 TeV during the years 2016-2018, corresponding to a total integrated luminosity of 5.4 fb-1. The two tau leptons are reconstructed through their decay, tau -> pi+ pi- pi+ (pi0) nu. We develop a new method to fit the B+ -> K+ tau+ tau- decay chain in order to recover the missing information from the neutrinos and obtain a refitted B mass whose resolution is 100 MeV better than the one obtained with the baseline method used in LHCb. We normalise the branching fraction measurement to the B+ -> D0bar Ds+ decay, where D0bar -> K+ pi- and Ds+ -> K+ K- pi+. The main sources of background in the analysis are the combinatorial and decays of the type, B -> D() D() K+, where the D mesons decay to 3 charged pions and missing particles. The backgrounds are reduced using a set of selections which include a Boosted Decision Tree (BDT). We perform a blind analysis where the B mass distribution and signal yield in data are not seen until all the analysis steps are performed and validated. The expected sensitivity is found to be, BF(B+ -> K+ tau+ tau-) < 3.2\times 10^{-4} at 90% C.L., which has the potential to improve the previous limit.

The LHCb detector has been upgraded in 2019-2022 where a new tracking detector, the Scintillating Fibre (SciFi) tracker, was introduced. We perform the data quality control of scintillating fibre mats similar to the ones used in the SciFi tracker. In view of the next planned upgrade in the mid 2030s, we also study the possibility of using a clear fibre interface between the SciFi mats and the Silicon Photomultipliers (SiPMs) to allow the cryogenic cooling of the SiPMs during the High Luminosity (HL)-LHC.