Study of flavour-changing neutral current and charged current B meson decays

Searching for new physics (NP) beyond the Standard Model (SM) of Particle Physics is one of the primary goals of high energy physics studies. Precision measurements of weak decays of $b$-hadrons provide indirect probes of NP. The LHCb experiment has observed some deviations from the SM predictions in the decay rates, angular distributions and lepton flavour universality (LFU) tests in a series of $b \to s \ell^{+}\ell^{-}$ decays mediated by flavour changing neutral current (FCNC) transitions. The B factories have also found hints of violation of LFU in $b\to c l \bar{\nu}_l $ decays mediated by flavour changing charged current (FCCC) transitions. These anomalous results in B meson decays with leptons in the final states may indicate the existence of NP, and have motivated our studies in the following two aspects. On the experimental side, we focus on studies of FCNC processes, including a sensitivity study for measurement of time-dependent CP violation in the decay $B^0_s \to \phi \mu^+\mu^-$ using the huge data sample to be collected by the upgraded LHCb detector, and a search for the rare decay $B^0 \to \phi \mu^+\mu^-$ using the current available LHCb data set. On the theoretical side, we explore possible NP effects in $\bar{B}\to D^{(*)}\ell^-\bar{\nu}_\ell$ processes in both model-independent and model-dependent ways. The decay $B^0_s \to \phi \mu^+\mu^-$ proceeds via a FCNC $\bar{b} \to \bar{s} \mu^+ \mu^-$ transition and is sensitive to contribution of new particles entering the loop process. The time-dependent CP violation in this decay can be used as a probe for NP, in addition to its decay rate and angular observables. Its branching fraction is found to be on the low side compared with the current SM prediction. The measured angular observables are broadly consistent with the SM predictions. So far, there has been no experimental study of time-dependent CP violation in the decay $B^0_s \to \phi \mu^+\mu^-$ yet. In the next ten (twenty) years, the LHCb experiment with an upgraded detector will accumulate about 50 (300) fb$^{-1}$ of proton-proton collision data, which will provide great opportunities to perform precision study of time-dependent CP violation in the decay $B^0_s \to \phi \mu^+\mu^-$. In order to fully exploit the power of the decay $B^0_s \to \phi \mu^+\mu^-$ in probing NP, we perform the first simulation study and sensitivity analysis of time-dependent CP violation measurement in this decay. We identify a set of CP violation observables and explore the possibility to simplify the formalism for time-dependent angular analysis. We generate simulation samples corresponding to 9 fb$^{-1}$, 50 fb$^{-1}$ and 300 fb$^{-1}$ to assess sensitivity of these observables in both the full and simplified formalisms. We find that a data sample of 300 fb$^{-1}$ will provide the opportunity to measure time-dependent CP violation in the decay $B^0_s \to \phi \mu^+\mu^-$ with a better-than 10$\%$ precision, similar to the currently achieved precision in the decay $B^0_s \to J/\psi(\to \mu^+\mu^-) \phi$, which is the golden channel for CP violation study. These findings can provide important information for the planning of CP violation study in rare $B$ meson decays at the upgraded LHCb experiment. The decay $B^0\to \phi \mu^+\mu^-$ is a very rare process mediated by a $\bar{b}\to \bar{d}$ transition, which could be significantly affected by NP contributions. In the SM, the dominant contribution comes from $\omega-\phi$ mixing, which leads to a branching fraction of the order of $10^{-11}$ -- $10^{-10}$. So far, there is no reported experimental study of this decay. We perform the first search for this process using the proton-proton collision data collected by the LHCb experiment at centre-of-mass energies of 7 TeV, 8 TeV and 13 TeV, corresponding to an integrated luminosity of 9 fb$^{-1}$. In the analysis, the $\phi$, $J/\psi$ and $\psi(2S)$ resonance regions are removed from the $q^2=m^2(\mu^+\mu^-)$ spectrum. The decay $B^0_s\to \phi \mu^+ \mu^-$ is used for normalization, of which around 2000 signal candidates are reconstructed. No significant signal of the very rare decay $B^0\to \phi \mu^+\mu^-$ is observed, and the ratio of its branching fraction to that of the decay $B^0_s\to \phi \mu^+ \mu^-$ is estimated to be less than $4.4\times 10^{-3}$ at a 90$\%$ credible level, excluding the $\phi$ and charmonium regions in the dimuon spectrum. Assuming a phase space decay model for the decay $B^0 \to \phi \mu^+\mu^-$ and using the latest measurement of $\mathcal{B}(B^0_s \to \phi\mu^+\mu^-)$ by the LHCb collaboration, the upper limit on the branching fraction $\mathcal{B}(B^0 \to \phi\mu^+\mu^-)$ in the full $q^2$ range is evaluated to be $3.2 \times 10^{-9}$ at a 90$\%$ credible level. The $\bar{B}\to D^{(*)}\ell^-\bar{\nu}_\ell (\ell=\tau, \mu, e)$ decays are mediated by $b \to c \ell^-\bar{\nu}_\ell$ transitions. Certain NP models, such as charged Higgs or Leptoquark models, may affect these tree-level FCCC processes. Several flavour experiments have measured the ratios of the branching fractions of $\bar{B}\to D^{(*)}\tau^-\bar{\nu}_\tau$ and $\bar{B}\to D^{(*)}\ell^-\bar{\nu}_\ell (\ell=\mu,e)$ decays, denoted $R(D^{(*)})$. Part of the results exhibited some inconsistency with the SM predictions, which have inspired a lot of theoretical studies. We analyze the $\bar{B}\to D^{(*)}\ell^-\bar{\nu}_\ell (\ell=\tau, \mu, e)$ decays both in a model-independent way and in specific G(221) models with LFU, and explore the impacts of NP on the (differential) branching fractions, branching fraction ratios, lepton spin asymmetries and forward-backward asymmetries. After using the measured branching fractions of these processes to constrain the relevant NP parameters, we find that the constrained parameters leave some room for significant NP effects on the lepton spin asymmetries and lepton forward-backward asymmetries. We expect the LHCb and Belle II experiments to perform precision measurements of these observables.