Mohamed, Ali

This thesis presents a systematic investigation of heavy hadron lifetimes, focusing on the $B$ mesons, as a probe of both Standard Model (SM) dynamics and possible effects of physics beyond the SM (BSM). Within the framework of the Heavy Quark Expansion (HQE), we compute, at leading order in QCD, the complete dimension-seven two-quark contributions, corresponding to the $1/m_b^4$ corrections, for the CKM-favoured non-leptonic decays $b\to c\bar{u}d$ and $b\to c\bar{c}s$, providing the full analytical expressions for the corresponding Wilson coefficients. These results, which reveal new matrix elements unique to non-leptonic decays, lay the foundation for future numerical studies and refined SM lifetime predictions. Having extended the SM calculation to the next order in the HQE, we turn to the dimension-six Darwin contribution, whose sizeable numerical impact in the SM motivates its generalization to a model-independent BSM framework. In particular, we derive, at leading order in QCD, the Wilson coefficients up to and including the dimension-six two-quark (Darwin) operators, corresponding to the $1/m_b^3$ corrections in the HQE, for non-leptonic decays induced by a general effective Hamiltonian. We further determine the previously missing dimension-six four-quark weak-annihilation contribution induced by the same general operator basis. Since the SM QCD-penguin operators are contained within this basis, our calculation also yields, as a special case, the previously missing dimension-five and dimension-six contributions induced by the SM QCD-penguin operators, thereby further improving the theoretical precision of HQE predictions. Finally, we explore the phenomenological implications of the $B$-Mesogenesis model, which links the matter–antimatter asymmetry of the universe and dark matter to exotic $B$-meson decays. The model is tested through both inclusive and exclusive decay channels: the inclusive analysis, performed within the HQE, quantifies the impact of these new decay modes on the total decay rates and the lifetime ratios $\tau(B^+)/\tau(B_d)$ and $\tau(B_s)/\tau(B_d)$, while the exclusive analysis employs light-cone sum rules to calculate the branching fraction for the exclusive decay $B^+\to p\psi$, involving a proton and a dark-sector fermion in the final state. By comparing our predictions with experimental limits from BaBar, Belle, and Belle II, we constrain specific effective operators of the model. Furthermore, by examining power-suppressed terms, we identify regions in the dark-sector mass parameter space where subleading effects exceed the leading dimension-three contributions—offering new insight into the applicability of the operator product expansion within the HQE. Together, these studies advance the theoretical understanding of heavy-hadron lifetimes, strengthen the bridge between precision flavour physics and physics beyond the SM, and open new avenues for probing the interplay between heavy-quark dynamics and the dark sector.

Mohamed, Ali

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