Measurements of b-hadron lifetimes and the calibration and performance of the LHCb tracking system

The LHCb experiment was designed to perform high precision measurements. The LHCb detector has excellent vertexing, momentum measurement and particle identification capabilities, with a detector geometry and trigger strategy specially adapted for the study of rare decays and $CP$ violation of $b$- and $c$-quarks. For accurate measurements, the detector needs to be perfectly calibrated and its performance monitored to achieve the required performance. The LHCb TELL1 boards are responsible for the acquisition and the pre-processing of the raw data. New effects on signals emitted by the front-end chip, the Beetle, of the Inner Tracker (IT) and Tracker Turicensis (TT) due to the different header configurations are discovered. Strategies to correct for these her effects are proposed and are implemented in the firmware of the IT and TT TELL1 boards. In addition, faster algorithms are developed to perform the calibration of the TELL1 boards and software is developed to perform the full calibration and a monitoring process as a single daily job. The IT and TT hit efficiencies, hit spatial resolutions and signal-over-noise ratios were monitored and measured for the 2011 and 2012 data taking periods using clean samples of $J/\psi$ particles decaying into a muon pair. A novel procedure is proposed to align the LHCb tracking system in the vertical direction ($y$) exploiting the presence of insensitive regions in the tracking system. Using this procedure, it allows to align the IT, the TT and the Outer Tracker (OT), to be aligned vertically with a precision better than 200 $\mu$m. A preliminary analysis of the small dataset recorded in 2010 by LHCb showed great potential to measure $b$-hadron lifetimes in decays with a $J/\psi$ meson in the final state. The trigger system used from 2010 to the middle of 2011 selected $J/\psi$ mesons without any requirement on the distance between the $J/\psi$ decay vertex and the proton proton ($pp$) interaction point, leading to a linear dependence of the reconstruction efficiency as a function of the $b$-hadron decay time. Starting from Summer 2011, a new trigger line was used to select $b$ hadrons with a significantly displaced decay vertex from the $pp$ interaction point into a $J/\psi$. This trigger line exploits the finite flight distance of $b$ hadrons in order to reduce the trigger rate. This displacement requirement introduces additional inefficiencies as a function of the $b$-hadron decay time which is no longer linear. Therefore, a deep understanding of the $b$-hadron decay time efficiency of this new trigger line is required for the measurements of $b$-hadron lifetimes. Analysing the full 1.0 fb$^{-1}$ data sample recorded in 2011, $b$-hadron lifetime measurements are performed for five decay modes: $B^+\to J/\psi K^+$, $B^0\to J/\psi K^{*0}$, $B^0_s\to J/\psi \phi$, $B^0\to J/\psi K^0_S$ and $\Lambda^0_b\to J/\psi \Lambda$. The measured lifetimes in these decay modes are: \begin{align} \tau_{B^+\to J/\psi K^+} & = 1.637 \pm 0.004 \,(\text{stat}) \pm 0.003 \,(\text{syst}) \,\text{ps}, \nonumber\\ \tau_{B^0\to J/\psi K^{*0}} & = 1.524 \pm 0.006 \,(\text{stat}) \pm 0.004 \,(\text{syst}) \,\text{ps}, \nonumber\\ \tau_{B^0\to J/\psi K^0_S} & = 1.415 \pm 0.027 \,(\text{stat}) \pm 0.006 \,(\text{syst}) \,\text{ps}, \nonumber\\ \tau_{B^0_s\to J/\psi \phi} & = 1.499 \pm 0.013 \,(\text{stat}) \pm 0.005 \,(\text{syst}) \,\text{ps}, \nonumber\\ \tau_{\Lambda^0_b\to J/\psi \Lambda} & = 1.480 \pm 0.011 \,(\text{stat}) \pm 0.005 \,(\text{syst}) \,\text{ps}, \nonumber \end{align} which are the world's best measurements and are compatible with theoretical predictions and world averages. From the lifetime measurements in $B^0\to J/\psi K^{*0}$ and $B^0\to J/\psi K^0_S$ decay modes, the ratio of the decay-width difference, $\Delta \Gamma_d$, to the average decay width, $\Gamma_d$, for the $B^0 - \overline{B}^0$ system is measured to be \begin{align} \frac{\Delta \Gamma_d}{\Gamma_d} = -0.044 \pm 0.025 \,(\text{stat}) \pm 0.011 \,(\text{syst}), \nonumber \end{align} which is also compatible with world averages and theoretical predictions.