Lattice simulations with G-parity Boundary Conditions

Abstract

We discuss G-parity lattice boundary conditions as a means to impose momentum on the pion ground state without breaking isospin symmetry. This technique is expected to be critical for the precision measurement of $K\to (\pi \pi {)}_{I=0}$ matrix elements where physical kinematics demands moving pions in the final state and the statistical noise caused by disconnected contributions will make it difficult to use multi-exponential fits to isolate this as an excited state. We present a formalism for computing hadronic Green's functions with G-parity boundary conditions, derive the discretized action and its symmetries, discuss how the strange quark can be introduced and detail techniques for the numerical implementation of these boundary conditions. We demonstrate and test these methods using several $16^3\times 32$ dynamical domain wall ensembles with a $420$ MeV pion mass and G-parity boundary conditions in one and two spatial directions.

arXiv comment76 pages, 11 figures

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Cited by in corpus (5)

• Direct CP violation and the $\Delta I=1/2$ rule in $K\to \pi \pi$ decay from the Standard Model
• Lattice determination of $I=0$ and 2 $\pi \pi$ scattering phase shifts with a physical pion mass
• Isospin 0 and 2 two-pion scattering at physical pion mass using all-to-all propagators with periodic boundary conditions in lattice QCD
• $\Delta I=3/2$ and $\Delta I=1/2$ channels of $K\to \pi \pi$ decay at the physical point with periodic boundary conditions
• Construction of general $N$-body lattice operators with arbitrary momenta