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

^Principal Investigators ^^
|[[https://web.physik.rwth-aachen.de/~harlander|Prof. Robert  Harlander]] | RWTH Aachen University |
| [[ https://www.tp.nt.uni-siegen.de/~lenz/| Prof. Alexander Lenz ]] | Siegen University |
|[[https://www.ttp.kit.edu/memberpages/nierste | Prof. Ulrich Nierste ]] | Karlsruhe Institute of Technology |


==== Subject ====

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.




==== Project Topics ====
**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
 
==== Related publications ====

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