Speaker
Description
Neutral $B$ meson mixing and $B$ meson lifetimes are theory-side parametrised in terms of $\Delta B=2$ and 0 four-quark operators which can be determined by calculating weak decay matrix elements using lattice QCD.
While calculations of $\Delta B=2$ mixing matrix elements are standard, matrix elements with $\Delta B=0$ for extracting lifetimes suffer from complications in standard renormalisation procedures.
Here dimension-6 four-quark operators mix with operators of lower mass dimension using standard renormalisation procedures and, moreover, quark-line disconnected diagrams contribute.
We present work detailing the idea to use fermionic gradient flow to non-perturbatively renormalise $\Delta B=0,2$ matrix elements, later to be combined with perturbative input in order to develop renormalisation+matching-to-$\overline{\rm MS}$ procedures for these operators.
The well-studied $\Delta B=2$ matrix elements governing $B$ mixing are first considered to test and validate the method before turning the focus to the quark-line connected $\Delta B=0$ matrix elements.