Measurements of the $B$ meson production cross-sections at LHCb

Quantum Chromodynamics (QCD), one of the most fundamental components of the Standard Model theory of Particle Physics, is dedicated to describe the strong interactions among quarks and gluons. For the $B$ meson production cross-sections in hadron-hadron collisions, perturbative QCD (pQCD) calculations are available at next-to-leading order (NLO) and with the fixed-order plus next-to-leading logarithms (FONLL) approximations. Measuring $B$ meson production cross-sections at the Large Hadron Collider (LHC) is of great importance to test the pQCD calculations. The LHCb detector is a single-arm forward spectrometer. It collects the physical information of the products in proton-proton collisions at the LHC. The differential and total production cross-sections of $B$ mesons (including $B^+$, $B^0$ and $B_s^0$) in proton-proton collisions at $\sqrt{s}=7\,{\rm TeV}$ are studied using 35${\rm pb}^{-1}$ of data in 2010 and 370${\rm pb}^{-1}$ of data in 2011 collected by the LHCb detector, and reported in this dissertation. The total cross-sections are measured to be \begin{equation} \begin{array}{rcl} \sigma(B^+, 0<p_{\rm T}<40{\rm GeV}/c,2.0<y<4.5) &=& 41.4\pm1.4\,({\rm stat.})\pm3.2\,({\rm syst.})\,{\rm \mu b} (2010), \\ \sigma(B^+, 0<p_{\rm T}<40{\rm GeV}/c,2.0<y<4.5) &=& 41.6\pm0.3\,({\rm stat.})\pm2.7\,({\rm syst.})\,{\rm \mu b} (2011), \\ \sigma(B^0, 2<p_{\rm T}<40{\rm GeV}/c, 2.0<y<4.5) &=& 32.3\pm0.4\,({\rm stat.})\pm2.4\,({\rm syst.})\,{\rm \mu b} (2011), \\ \sigma(B^0_s, 0<p_{\rm T}<40{\rm GeV}/c,2.0<y<4.5) &=& 7.9\pm0.2\,({\rm stat.})\pm2.5\,({\rm syst.})\,{\rm \mu b}(2011). \end{array} \nonumber \end{equation} The numbers in the brackets indicate the year during which the data sample was collected. These results are in good agreement with FONLL theoretical predictions. The $B^+_c$ meson, composed of two different heavy flavor quarks $\overline{b}$ and $c$, has not been well studied experimentally up to now. Using data collected by the LHCb detector in 2011, the production ratio is measured to be \begin{equation} \frac{\sigma\left(B^+_c\right) \times {\cal B} \left( B^+_c\rightarrow J/\psi\pi^+ \right)}{\sigma\left(B^+\right) \times {\cal B}\left( B^+\rightarrow J/\psi K^+ \right)} =0.72 \pm 0.10 \,({\rm stat.})\pm 0.08\,({\rm syst.})\%,\nonumber \end{equation} where $\sigma$ is the production cross-section in the range $4<p_{\rm T}<100{\rm GeV}/c$ and $2.5<\eta<4.5$ and ${\cal B}$ is the branching ratio. This result may shed light on the production mechanism of doubly flavored hadrons.