C1b: $\mathbf{B - \overline{B}}$ mixing, CP violation, and lifetimes

The main focus of project C1b are lifetimes and inclusive decays of B and D mesons. Based on the Heavy Quark Expansion a systematic expansion of the physical quantities are obtained as an expansion in the inverse heavy quark mass. Several matching coefficient are computed to higher order in perturbative QCD and their phenomenological implications are studied.

1. $\mathbf{\Gamma_{12}^q}$ to NNLO for $\mathbf{m_c=0}$
   • will reduce perturbative uncertainty of leading-power contribution to $\Delta \Gamma_s$ from $\sim$10% to $\sim$3%
   • requires solution of new three-loop integral families
2. $\mathbf{\Gamma_{12}^q}$ at order $\mathbf{\alpha_s/m_b}$
   • needed to reduce overall uncertainty in $\Delta \Gamma_q/\Delta M_q$ well below 10\%
3. $\mathbf{\tau(B^+)/\tau(B_d)}$ and $\mathbf{\tau(\Xi_b^0)/\tau(\Xi_b^-)}$ at orders $\mathbf{\alpha_s^2}$ and $\mathbf{\alpha_s/m_b}$
   • tests the formalism (HQE and lattice calculations)
4. Charm hadron lifetimes
   • tests the HQE at order $1/m_Q$
5. $\mathbf{\tau(B_s)/\tau(B_d)}$ and $\mathbf{\tau(\Lambda_b)/\tau(\Xi_b^0)}$
   • probes new physics in penguin coefficients
6. $\mathbf{\Gamma_{12}^q}$ to NNLO at order $\mathbf{m_c^2/m_b^2}$
   • NNLO accuracy for $a_{\text{fs}}^d$, which probes new physics in e.g. $b\to d \bar{q} q$ decays
7. Phenomenological studies
   • devise judicious combinations to reduce hadronic uncertainties
   • propose new observables