HQET Sum Rules for Hadronic Matrix Elements and Applications to BSM Scenarios

The Standard Model (SM) remains among the most stringently tested theories in physics, yet it leaves several open questions, including the nature of dark matter and the mechanism behind baryogenesis. Additionally, hadronic uncertainties continue to limit the precision of SM predictions relative to experimental data. To identify potential beyond the Standard Model (BSM) effects, it is essential to refine theoretical predictions through effective field theory (EFT) techniques and accurate treatment of non-perturbative contributions. My research focuses on these challenges using Heavy Quark Effective Theory (HQET) and observables related to heavy quark lifetimes and neutral B-meson mixing.
Investigations of B-mixing and B-hadron lifetimes serve as a sensitive probe of Quantum Chromodynamics (QCD) and offer an indirect window into BSM physics. The heavy quark expansion (HQE) expresses the total decay rate of B-hadrons as a series in inverse powers of the b-quark mass, allowing a systematic separation of short-distance Wilson coefficients from long-distance hadronic matrix elements. These matrix elements often dominate the theoretical uncertainty in key observables, such as the lifetime ratio $\tau (B^+)/\tau (B_d)$ or the decay rate difference $\Delta \Gamma_s$. While lattice QCD offers precision in the long-term, QCD sum rules provide necessary first estimates.
My first main project is computing dimension-six hadronic matrix elements using HQET sum rules, including a complete set of operators involving all BSM Dirac structures. This involves generating three-loop diagrams with a single gluon insertion, performing integration by parts reductions to master integrals, and extracting double discontinuities with advanced complex analysis techniques. An extension of this project will be to determine dimension-seven matrix elements, the dominant source of uncertainty in $\Delta \Gamma_s$, and where current lattice results suffer from very large uncertainties.
In a complementary project, I investigate a BSM framework in which CP-violating oscillations and decays of $B$-mesons into a dark sector simultaneously generate the baryon asymmetry and the dark matter relic abundance. A central requirement of this mechanism is a minimal strength of new baryon number violating $b$-quark decay channels, which can be tested using both inclusive and exclusive observables. On the theory side, I compute the relevant inclusive decay rates and their impact on $B$-hadron lifetimes within the HQE, including one and two-loop contributions that depend on the same non-perturbative inputs that appear in the SM lifetime and mixing analyses. This creates a direct link between the HQET sum-rule determination of $\Delta B = 0$ matrix elements at dimension six and concrete constraints on the viable parameter space in certain $B$-mesogenesis models.