Lattice simulations with G -parity boundary conditions

Christ, N. H.; Kelly, C.; Zhang, D.

doi:10.1103/PhysRevD.101.014506

Title: Lattice simulations with $G$ -parity boundary conditions

Abstract

We discuss $$\textit{G}$$-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 $$\textit{K} → (ππ)_{I=0}$$ 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 multiexponential fits to isolate this as an excited state. We present a formalism for computing hadronic Green’s functions with $$\textit{G}$$-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 16³ × 32 dynamical domain wall ensembles with a 420 MeV pion mass and $$\textit{G}$$-parity boundary conditions in one and two spatial directions.

Authors:

Christ, N. H.;

; Zhang, D.; RBC and UKQCD Collaborations

Publication Date:: 2020-01-21

Research Org.:: Columbia Univ., New York, NY (United States)

Sponsoring Org.:: Intel Corporation; USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR). Scientific Discovery through Advanced Computing (SciDAC)

Contributing Org.:: RBC and UKQCD Collaborations

OSTI Identifier:: 1592805

Alternate Identifier(s):: OSTI ID: 1802296

Grant/Contract Number:: SC0011941

Resource Type:: Published Article

Journal Name:: Physical Review D

Additional Journal Information:: Journal Name: Physical Review D Journal Volume: 101 Journal Issue: 1; Journal ID: ISSN 2470-0010

Publisher:: American Physical Society

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Astronomy & Astrophysics; Physics

Citation Formats


                    Christ, N. H., Kelly, C., Zhang, D., and RBC and UKQCD Collaborations. Lattice simulations with G -parity boundary conditions.  United States: N. p., 2020. 
Web.  doi:10.1103/PhysRevD.101.014506.

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                    Christ, N. H., Kelly, C., Zhang, D., & RBC and UKQCD Collaborations. Lattice simulations with G -parity boundary conditions.  United States.  https://doi.org/10.1103/PhysRevD.101.014506

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                    Christ, N. H., Kelly, C., Zhang, D., and RBC and UKQCD Collaborations. Tue .  
"Lattice simulations with G -parity boundary conditions".  United States.  https://doi.org/10.1103/PhysRevD.101.014506.

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@article{osti_1592805,

  title        = {Lattice simulations with G -parity boundary conditions},

  author       = {Christ, N. H. and Kelly, C. and Zhang, D. and RBC and UKQCD Collaborations},

  abstractNote = {We discuss $\textit{G}$-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 $\textit{K} → (ππ)_{I=0}$ 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 multiexponential fits to isolate this as an excited state. We present a formalism for computing hadronic Green’s functions with $\textit{G}$-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 163 × 32 dynamical domain wall ensembles with a 420 MeV pion mass and $\textit{G}$-parity boundary conditions in one and two spatial directions.},

  doi          = {10.1103/PhysRevD.101.014506},

  journal      = {Physical Review D},

  number       = 1,

  volume       = 101,

  place        = {United States},

  year         = {2020},

  month        = {1}

}

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Title: Lattice simulations with G -parity boundary conditions

Abstract

Citation Formats

2 + 1 flavor domain wall QCD on a ( 2 fm ) 3 lattice: Light meson spectroscopy with L s = 16 journal, July 2007

Volume dependence of the energy spectrum in massive quantum field theories: I. Stable particle states journal, June 1986

Domain wall fermion QCD with the exact one flavor algorithm journal, March 2018

Continuum limit physics from 2 + 1 flavor domain wall QCD journal, April 2011

Continuum limit of B K from 2 + 1 flavor domain wall QCD journal, July 2011

C- and G-periodic QCD at finite temperature journal, May 1992

Axial symmetries in lattice QCD with Kaplan fermions journal, April 1995

Charged hadrons in local finite-volume QED+QCD with C⋆ boundary conditions journal, February 2016

Lattice determination of the K → ( π π ) I = 2 decay amplitude A 2 journal, October 2012

The BlueGene/Q supercomputer conference, December 2012

Domain wall QCD with near-physical pions journal, May 2013

Physical results from 2 + 1 flavor domain wall QCD and SU(2) chiral perturbation theory journal, December 2008

Quenched lattice QCD with domain wall fermions and the chiral limit journal, April 2004

Weak Transition Matrix Elements¶from Finite-Volume Correlation Functions journal, May 2001

First results from 2 + 1 -flavor domain wall QCD: Mass spectrum, topology change, and chiral symmetry with L s = 8 journal, June 2007

The BAGEL assembler generation library journal, December 2009

Exact pseudofermion action for Monte Carlo simulation of domain-wall fermion journal, November 2014

Two-particle states on a torus and their relation to the scattering matrix journal, May 1991

K→ππ decays in a finite volume journal, December 2001

K → π π Δ I = 3 / 2 decay amplitude in the continuum limit journal, April 2015

I = 2 ππ scattering using G-parity boundary condition journal, March 2004

K → ( π π ) I = 2 Decay Amplitude from Lattice QCD journal, April 2012

Volume dependence of the energy spectrum in massive quantum field theories: II. Scattering states journal, June 1986

Standard Model Prediction for Direct C P Violation in K → π π Decay journal, November 2015

Practical all-to-all propagators for lattice QCD journal, November 2005

Title: Lattice simulations with $G$ -parity boundary conditions

$2 + 1$ flavor domain wall QCD on a $(2 fm)^{3}$ lattice: Light meson spectroscopy with $L_{s} = 16$
journal, July 2007

Volume dependence of the energy spectrum in massive quantum field theories: I. Stable particle states
journal, June 1986

Domain wall fermion QCD with the exact one flavor algorithm
journal, March 2018

Continuum limit physics from $2 + 1$ flavor domain wall QCD
journal, April 2011

Continuum limit of $B_{K}$ from $2 + 1$ flavor domain wall QCD
journal, July 2011

C- and G-periodic QCD at finite temperature
journal, May 1992

Axial symmetries in lattice QCD with Kaplan fermions
journal, April 1995

Charged hadrons in local finite-volume QED+QCD with C⋆ boundary conditions
journal, February 2016

Lattice determination of the $K \to (π π)_{I = 2}$ decay amplitude $A_{2}$
journal, October 2012

The BlueGene/Q supercomputer
conference, December 2012

Domain wall QCD with near-physical pions
journal, May 2013

Physical results from $2 + 1$ flavor domain wall QCD and SU(2) chiral perturbation theory
journal, December 2008

Quenched lattice QCD with domain wall fermions and the chiral limit
journal, April 2004

Weak Transition Matrix Elements¶from Finite-Volume Correlation Functions
journal, May 2001

First results from $2 + 1$ -flavor domain wall QCD: Mass spectrum, topology change, and chiral symmetry with $L_{s} = 8$
journal, June 2007

The BAGEL assembler generation library
journal, December 2009

Exact pseudofermion action for Monte Carlo simulation of domain-wall fermion
journal, November 2014

Two-particle states on a torus and their relation to the scattering matrix
journal, May 1991

K→ππ decays in a finite volume
journal, December 2001

$K \to π π$ $Δ I = 3 / 2$ decay amplitude in the continuum limit
journal, April 2015

I = 2 ππ scattering using G-parity boundary condition
journal, March 2004

$K \to (π π)_{I = 2}$ Decay Amplitude from Lattice QCD
journal, April 2012

Volume dependence of the energy spectrum in massive quantum field theories: II. Scattering states
journal, June 1986

Standard Model Prediction for Direct $C P$ Violation in $K \to π π$ Decay
journal, November 2015

Practical all-to-all propagators for lattice QCD
journal, November 2005