Search for $\mathit{\Lambda_{b}\to K^{-}\mu^{+}}$ at LHCb

In this thesis the search for the decays $\mathit{\Lambda_{b}\to K^{-}\mu^{+}}$ and $\mathit{\Xi_{b}^{\rm 0}\to K^{-}\mu^{+}}$ is presented using the Run~I data of the LHCb experiment. Both decays offer an ansatz to the description of the matter-antimatter asymmetry in our universe and is based on the Sakharov conditions that predict the existence of processes violating the baryon and lepton number conservation. Especially the measured baryon-to-photon ratio $\eta\approx6\cdot10^{-10}$ allows to estimate the probability of such processes in this order of magnitude. In the underlying data set including about $50$ billion recorded $\mathit{\Lambda_{b}}$ decays no signal events are observed and an upper limit on the combined branching fraction is determined at a confidence level of $90\,\%$: $$ \left[{\mathcal B}(\mathit{\Lambda_{b}\to K^{-}\mu^{+}})+{\mathcal B}(\mathit{\Lambda_{b}\to K^{+}\mu^{-}})\right] \times\frac{3.1\cdot10^{-6}}{{\mathcal B}(\mathit{\Lambda_{b}\to p K^{-}})} < 1.95\cdot10^{-9}~. $$ The result is equivalent to the value of $\left[{\mathcal B}(\mathit{\Lambda_{b}\to K^{-}\mu^{+}})+{\mathcal B}(\mathit{\Lambda_{b}\to K^{+}\mu^{-}})\right]$ but excludes the large uncertainty of ${\mathcal B}(\mathit{\Lambda_{b}\to p K^{-}})\approx 3.1\cdot10^{-6}$ that origins from another measurement. In the $\mathit{\Xi_{b}^{\rm 0}\to K^{-}\mu^{+}}$ case the determined upper limit at a confidence level of $90\,\%$ is $$ \frac{f_{\mathit\Xi_{b}^{\rm 0}}}{f_{\mathit\Lambda_{b}}}\times \left[{\mathcal B}(\mathit{\Xi_{b}^{\rm 0}\to K^{-}\mu^{+}})+{\mathcal B}(\mathit{\Xi_{b}^{\rm 0}\to K^{+}\mu^{-}})\right] \times\frac{3.1\cdot10^{-6}}{{\mathcal B}(\mathit{\Lambda_{b}\to p K^{-}})} < 1.25\cdot10^{-9}~, $$ and includes the unknown production ratio of $\mathit{\Xi_{b}}$ to $\mathit{\Lambda_{b}}$. In addition an indication ($\chi=2.7$) for the yet unobserved decay $\mathit{\Xi_{b}^{\rm 0}\to p K^{-}}$ is found with $25\pm10$ signal events.