# Status Report on Weak Matrix Element Calculations

## TL;DR

This paper reports on lattice QCD calculations of weak matrix elements, decay constants, and form factors, analyzing systematic errors and providing updated numerical results relevant for particle physics phenomenology.

## Contribution

It presents new lattice simulation results for weak matrix elements and decay constants, with a detailed analysis of systematic uncertainties, improving precision over previous studies.

## Key findings

- Decay constants: f_D=186(29) MeV, f_{D_s}=224(16) MeV
- Bag parameters: B_K=0.67(9), B_8=0.81(1)
- Form factors: T_1=T_2=0.24(1)

## Abstract

This talk presents results of weak matrix elements calculated from simulations done on 170 $32^3 \times 64$ lattices at $\beta = 6.0$ using quenched Wilson fermions. We discuss the extraction of pseudoscalar decay constants $f_\pi$, $f_K$, $f_D$, and $f_{D_s}$, the form-factors for the rare decay $B \to K^* \gamma$, and the matrix elements of the 4-fermion operators relevant to $B_K$, $B_7$, $B_8$. We present an analysis of the various sources of systematic errors, and show that these are now much larger than the statistical errors for each of these observables. Our main results are $f_D=186(29) \MeV$, $f_{D_s}=224(16) MeV$, $T_1=T_2=0.24(1)$, $B_K(NDR, 2\GeV)=0.67(9)$, and $B_8(NDR, 2\GeV)=0.81(1)$.