### Towards a nonperturbative calculation of weak Hamiltonian Wilson coefficients

Here, we propose a method to compute the Wilson coefficients of the weak effective Hamiltonian to all orders in the strong coupling constant using Lattice QCD simulations. We perform our calculations adopting an unphysically light weak boson mass of around 2 GeV. We demonstrate that systematic errors for the Wilson coefficients C

_{1}and C_{2}, related to the current-current four-quark operators, can be controlled and present a path towards precise determinations in subsequent works.- Publication Date:

- Report Number(s):
- BNL-205731-2018-JAAM

Journal ID: ISSN 2470-0010; PRVDAQ

- Grant/Contract Number:
- SC0012704

- Type:
- Published Article

- Journal Name:
- Physical Review D

- Additional Journal Information:
- Journal Volume: 97; Journal Issue: 7; Journal ID: ISSN 2470-0010

- Publisher:
- American Physical Society (APS)

- Research Org:
- Brookhaven National Laboratory (BNL), Upton, NY (United States)

- Sponsoring Org:
- USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)

- Contributing Orgs:
- RBC and UKQCD Collaborations

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; standard model; lattice; QCD; GeV; decay; Wilson; NNLO; EFT; coupling; Hamiltonian; axial; wilson; boson; quark

- OSTI Identifier:
- 1434187

- Alternate Identifier(s):
- OSTI ID: 1440345

```
Bruno, Mattia, Lehner, Christoph, and Soni, Amarjit.
```*Towards a nonperturbative calculation of weak Hamiltonian Wilson coefficients*. United States: N. p.,
Web. doi:10.1103/PhysRevD.97.074509.

```
Bruno, Mattia, Lehner, Christoph, & Soni, Amarjit.
```*Towards a nonperturbative calculation of weak Hamiltonian Wilson coefficients*. United States. doi:10.1103/PhysRevD.97.074509.

```
Bruno, Mattia, Lehner, Christoph, and Soni, Amarjit. 2018.
"Towards a nonperturbative calculation of weak Hamiltonian Wilson coefficients". United States.
doi:10.1103/PhysRevD.97.074509.
```

```
@article{osti_1434187,
```

title = {Towards a nonperturbative calculation of weak Hamiltonian Wilson coefficients},

author = {Bruno, Mattia and Lehner, Christoph and Soni, Amarjit},

abstractNote = {Here, we propose a method to compute the Wilson coefficients of the weak effective Hamiltonian to all orders in the strong coupling constant using Lattice QCD simulations. We perform our calculations adopting an unphysically light weak boson mass of around 2 GeV. We demonstrate that systematic errors for the Wilson coefficients C1 and C2, related to the current-current four-quark operators, can be controlled and present a path towards precise determinations in subsequent works.},

doi = {10.1103/PhysRevD.97.074509},

journal = {Physical Review D},

number = 7,

volume = 97,

place = {United States},

year = {2018},

month = {4}

}