C1c: Non-perturbative matrix elements for $\mathrm{B}-$mixing and lifetimes

The project aims at the theoretical description of lifetime and mixing observables of B- mesons by calculating matrix elements of specific four-quark operators of mass dimension six and seven. To achieve this, we will pursue two different approaches. On the one hand, sum rules will be calculated at the three-loop level within the framework of the heavy-quark effective theory (HQET). In the second approach, we will establish a re-normalisation scheme for the relevant operators based on the gradient-flow formalism. The perturbative matching coefficients to the MSbar scheme will be calculated through next-to-next-to-leading order in the strong coupling, while the non-perturbative matrix elements will be determined on the lattice from available gauge configurations.

Sum rules:

• Determination of matrix elements of dimension-7 operators for B meson mixing and lifetimes

Gradient flow

• Perturbative calculation of the flowed matching matrix
• Lattice determination of the flowed matrix elements

Phenomenology

• Study lifetimes and mixing parameter to test the SM and extensions of it