Standard Model Prediction for Direct CP Violation in K→ππ Decay

Bai, Z.; Blum, T.; Boyle, P. A.; Christ, N. H.; Frison, J.; Garron, N.; Izubuchi, T.; Jung, C.; Kelly, C.; Lehner, C.; Mawhinney, R. D.; Sachrajda, C. T.; Soni, A.; Zhang, D.

doi:10.1103/PhysRevLett.115.212001

Title: Standard Model Prediction for Direct $C P$ Violation in $K \to π π$ Decay

Abstract

In this paper, we report the first lattice QCD calculation of the complex kaon decay amplitude A₀ with physical kinematics, using a 32³ x 64 lattice volume and a single lattice spacing a, with 1/a = 1.3784(68) GeV. We find Re(A₀) = 4.66(1.00)(1.26) x 10^-7 GeV and Im(A₀) = -1.90(1.23)(1.08) x 10^-11 GeV, where the first error is statistical and the second systematic. The first value is in approximate agreement with the experimental result: Re(A₀) = 3.3201(18) x 10^-7 GeV, while the second can be used to compute the direct CP-violating ratio Re(ϵ'/ϵ) = 1.38(5.15)(4.59) x 10^-4, which is 2.1σ below the experimental value 16.6(2.3) x 10^-4. Finally, the real part of A₀ is CP conserving and serves as a test of our method while the result for Re(ϵ'/ϵ) provides a new test of the standard model theory of CP violation, one which can be made more accurate with increasing computer capability.

Authors:

Bai, Z. ^[1]; Blum, T. ^[2]; Boyle, P. A. ^[3]; Christ, N. H. ^[1]; Frison, J. ^[3]; Garron, N. ^[4]; Izubuchi, T. ^[5]; Jung, C. ^[6]; Kelly, C. ^[7]; Lehner, C. ^[6]; Mawhinney, R. D. ^[1]; Sachrajda, C. T. ^[8]; Soni, A. ^[6]; Zhang, D. ^[1]

Columbia Univ., New York, NY (United States). Physics Dept.
Univ. of Connecticut, Storrs, CT (United States). Physics Dept.
Univ. of Edinburgh, Scotland (United Kingdom). School of Physics. SUPA
Plymouth Univ. (United Kingdom). School of Computing & Mathematics
Brookhaven National Lab. (BNL), Upton, NY (United States). Physics Dept. RIKEN-BNL Research Center
Brookhaven National Lab. (BNL), Upton, NY (United States). Physics Dept.
Brookhaven National Lab. (BNL), Upton, NY (United States). RIKEN-BNL Research Center
Univ. of Southampton (United Kingdom). School of Physics and Astronomy

Publication Date:: Tue Nov 17 00:00:00 EST 2015

Research Org.:: Columbia Univ., New York, NY (United States); Brookhaven National Laboratory (BNL), Upton, NY (United States); Univ. of Edinburgh, Scotland (United Kingdom)

Sponsoring Org.:: USDOE Office of Science (SC), High Energy Physics (HEP); Science and Technology Facilities Council (STFC) (United Kingdom); Japan Society for the Promotion of Science (Japan); Leverhulme Trust (United Kingdom)

Contributing Org.:: RBC and UKQCD Collaborations; Univ. of Connecticut, Storrs, CT (United States); Plymouth Univ. (United Kingdom); Univ. of Southampton (United Kingdom)

OSTI Identifier:: 1354688

Alternate Identifier(s):: OSTI ID: 1226179

Report Number(s):: BNL-113786-2017-JA
Journal ID: ISSN 0031-9007; KA2401012

Grant/Contract Number:: AC02-98CH10886; AC02-06CH11357; SC0011941; FG02-92ER41989; ST/L000296/1; ST/G000557/1; ST/L000458/1; ST/J000329/1; ST/H008845/1; ST/K000411/1; ST/K005804/1; ST/K005790/1; 26400261; RPG-2014-118

Resource Type:: Accepted Manuscript

Journal Name:: Physical Review Letters

Additional Journal Information:: Journal Volume: 115; Journal Issue: 21; Journal ID: ISSN 0031-9007

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; lattice; QCD; HET; kinematics; kaon; decay; GeV; CP; violation

Citation Formats


                    Bai, Z., Blum, T., Boyle, P. A., Christ, N. H., Frison, J., Garron, N., Izubuchi, T., Jung, C., Kelly, C., Lehner, C., Mawhinney, R. D., Sachrajda, C. T., Soni, A., and Zhang, D. Standard Model Prediction for Direct CP Violation in K→ππ Decay.  United States: N. p., 2015. 
Web.  doi:10.1103/PhysRevLett.115.212001.

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                    Bai, Z., Blum, T., Boyle, P. A., Christ, N. H., Frison, J., Garron, N., Izubuchi, T., Jung, C., Kelly, C., Lehner, C., Mawhinney, R. D., Sachrajda, C. T., Soni, A., & Zhang, D. Standard Model Prediction for Direct CP Violation in K→ππ Decay.  United States.  https://doi.org/10.1103/PhysRevLett.115.212001

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                    Bai, Z., Blum, T., Boyle, P. A., Christ, N. H., Frison, J., Garron, N., Izubuchi, T., Jung, C., Kelly, C., Lehner, C., Mawhinney, R. D., Sachrajda, C. T., Soni, A., and Zhang, D. Tue .  
"Standard Model Prediction for Direct CP Violation in K→ππ Decay".  United States.  https://doi.org/10.1103/PhysRevLett.115.212001.  https://www.osti.gov/servlets/purl/1354688.

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@article{osti_1354688,

  title        = {Standard Model Prediction for Direct CP Violation in K→ππ Decay},

  author       = {Bai, Z. and Blum, T. and Boyle, P. A. and Christ, N. H. and Frison, J. and Garron, N. and Izubuchi, T. and Jung, C. and Kelly, C. and Lehner, C. and Mawhinney, R. D. and Sachrajda, C. T. and Soni, A. and Zhang, D.},

  abstractNote = {In this paper, we report the first lattice QCD calculation of the complex kaon decay amplitude A0 with physical kinematics, using a 323 x 64 lattice volume and a single lattice spacing a, with 1/a = 1.3784(68) GeV. We find Re(A0) = 4.66(1.00)(1.26) x 10-7 GeV and Im(A0) = -1.90(1.23)(1.08) x 10-11 GeV, where the first error is statistical and the second systematic. The first value is in approximate agreement with the experimental result: Re(A0) = 3.3201(18) x 10-7 GeV, while the second can be used to compute the direct CP-violating ratio Re(ϵ'/ϵ) = 1.38(5.15)(4.59) x 10-4, which is 2.1σ below the experimental value 16.6(2.3) x 10-4. Finally, the real part of A0 is CP conserving and serves as a test of our method while the result for Re(ϵ'/ϵ) provides a new test of the standard model theory of CP violation, one which can be made more accurate with increasing computer capability.},

  doi          = {10.1103/PhysRevLett.115.212001},

  journal      = {Physical Review Letters},

  number       = 21,

  volume       = 115,

  place        = {United States},

  year         = {Tue Nov 17 00:00:00 EST 2015},

  month        = {Tue Nov 17 00:00:00 EST 2015}

}

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We report on the first realistic ab initio calculation of a hadronic weak decay, that of the amplitude A₂ for a kaon to decay into two π mesons with isospin 2. We find ReA₂=(1.436±0.063_stat±0.258_syst)10^-8 GeV in good agreement with the experimental result and for the hitherto unknown imaginary part we find ImA₂=-(6.83±0.51_stat±1.30_syst)10^-13 GeV. Moreover combining our result for ImA₂ with experimental values of ReA₂, ReA0, and ϵ'/ϵ, we obtain the following value for the unknown ratio ImA₀/ReA₀ within the standard model: ImA₀/ReA₀=-1.63(19)_stat(20)_syst×10^-4. One consequence of these results is that the contribution from ImA₂ to the direct CP violation parameter ϵ'more »« less
https://doi.org/10.1103/PhysRevLett.108.141601
Exclusive semileptonic $B_{s} \to K ℓ ν$ decays on the lattice

Journal Article Flynn, J. M. ; Hill, R. C. ; Jüttner, A. ; ... - Physical Review. D.

Semore »« less
https://doi.org/10.1103/PhysRevD.107.114512
Long-distance contribution to $ε_{K}$ from lattice QCD

Journal Article Bai, Ziyuan ; Christ, Norman H. ; Karpie, Joseph M. ; ... - Physical Review. D.

A lattice QCD approach to the calculation of the long-distance contributions to ϵ_K is presented. This parameter describes indirect CP violation in K → ππ decay. While the short-distance contribution to ϵ_K can be accurately calculated in terms of standard model parameters and a single hadronic matrix element, B_K, there is a long-distance part which is estimated to be approximately 5% of the total and is more difficult to determine. A method for determining this small but phenomenologically important contribution to ϵ_K using lattice QCD is proposed and a complete exploratory calculation of the contribution is presented. This exploratory calculation uses an unphysical light quark mass corresponding to a 339 MeV pion mass and an unphysical charm quark mass of 968 MeV, expressed in themore »« less
https://doi.org/10.1103/PhysRevD.109.054501
Time-dependent analysis of $B^{0} \to K_{S}^{0} π^{-} π^{+} γ$ decays and studies of the $K^{+} π^{-} π^{+}$ system in $B^{+} \to K^{+} π^{-} π^{+} γ$ decays

Journal Article del Amo Sanchez, P. ; Lees, J. P. ; Poireau, V. ; ... - Physical Review D

Wemore »« less
Cited by 12
https://doi.org/10.1103/PhysRevD.93.052013

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Title: Standard Model Prediction for Direct C P Violation in K→ππ Decay

Abstract

Citation Formats

Emerging Understanding of the Δ I = 1 / 2 Rule from Lattice QCD journal, April 2013

Measurements of direct CP violation, CPT symmetry, and other parameters in the neutral kaon system journal, January 2003

Weak transition matrix elements from finite-volume correlation functions text, January 2000

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

ππ scattering journal, June 2001

Application of chiral perturbation theory to K→2π decays journal, November 1985

Review of Particle Physics journal, August 2014

Theory of the CP -violating parameter ɛ ′ / ɛ journal, January 2000

Review of Particle Physics text, January 2008

Kaon matrix elements and CP violation from quenched lattice QCD: The 3-flavor case journal, December 2003

K to π π decay amplitudes from lattice QCD journal, December 2011

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

Theoretical status of ε′/ε journal, May 2001

C P -Violation in the Renormalizable Theory of Weak Interaction journal, February 1973

Axial symmetries in lattice QCD with Kaplan fermions text, January 1994

Review of Particle Physics text, January 2012

A precision measurement of direct CP violation in the decay of neutral kaons into two pions text, January 2002

Calculation of K → π π decay amplitudes with improved Wilson fermion action in lattice QCD journal, October 2015

Weak Decays Beyond Leading Logarithms text, January 1995

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

A general method for non-perturbative renormalization of lattice operators journal, July 1995

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

K → ππ decay amplitudes from the lattice journal, May 2003

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

A dispersive treatment of $$K_{\ell 4}$$ K ℓ 4 decays journal, April 2015

Weak decays beyond leading logarithms journal, October 1996

Charge conjugation, a new quantum numberG, and selection rules concerning a nucleon-antinucleon system journal, April 1956

Covariant approximation averaging text, January 2014

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

Charge Conjugation, a New Quantum Number G, and Selection Rules Concerning a Nucleon-Antinucleon System book, January 1986

Theoretical status of journal, June 2000

Covariant approximation averaging journal, June 2015

Review of Particle Physics text, January 2018

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

Theoretical status of ε′/ε journal, March 2001

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

Matching factors for Δ S = 1 four-quark operators in RI/SMOM schemes journal, July 2011

with physical final state journal, March 2005

Domain Wall QCD with Near-Physical Pions text, January 2012

The BAGEL assembler generation library journal, December 2009

Evidence for the 2 π Decay of the K 2 0 Meson journal, July 1964

Uncovering CP Violation book, January 2003

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

Erratum: Measurements of direct C P violation, C P T symmetry, and other parameters in the neutral kaon system [Phys. Rev. D 67, 012005 (2003)] journal, October 2004

A General Method for Non-Perturbative Renormalization of Lattice Operators text, January 1994

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

Practical all-to-all propagators for lattice QCD text, January 2005

A precision measurement of direct CP violation in the decay of neutral kaons into two pions journal, September 2002

Right-handed charged currents in the era of the Large Hadron Collider text, January 2017

Probing SUSY with 10 TeV stop mass in rare decays and CP violation of kaon journal, December 2016

Direct CP violation in ${K^0\to\pi\pi}$ : Standard Model Status journal, June 2018

Lattice simulations with G -parity boundary conditions journal, January 2020

Physics beyond colliders at CERN: beyond the Standard Model working group report text, January 2020

FLAG Review 2019: Flavour Lattice Averaging Group (FLAG) journal, February 2020

Consistency checks for two-body finite-volume matrix elements: I. Conserved currents and bound states text, January 2019

Singularity-free next-to-leading order ΔS = 1 renormalization group evolution and ϵ K ′ /ϵK in the Standard Model and beyond journal, December 2016

ε ′ /ε in 331 models journal, March 2016

Supersymmetric Explanation of CP Violation in K →ππ Decays text, January 2016

Violation of lepton flavor and lepton flavor universality in rare kaon decays journal, April 2016

Kaon CP violation and neutron EDM in the minimal left-right symmetric model text, January 2019

Isoscalar ππ Scattering and the σ Meson Resonance from QCD text, January 2017

Supersymmetric Explanation of C P Violation in K → π π Decays journal, August 2016

Lattice simulations with G-parity Boundary Conditions text, January 2019

FLAG Review 2019 text, January 2020

Physics beyond colliders at CERN: beyond the Standard Model working group report journal, December 2019

Direct C P Violation in K → μ + μ − journal, November 2017

Uncovering Mass Generation Through Higgs Flavor Violation text, January 2015

Common explanation to the R K ( * ) , R D ( * ) , and ε ′ / ε anomalies in a 3HDM with right-handed neutrinos and connections to neutrino physics journal, September 2019

From deep inelastic scattering to heavy-flavor semileptonic decays: Total rates into multihadron final states from lattice QCD journal, November 2017

Opportunities for lattice QCD in quark and lepton flavor physics text, January 2019

Uncovering mass generation through Higgs flavor violation journal, February 2016

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

Towards NNLO accuracy for ε′/ε journal, January 2017

Violation of lepton flavor and lepton flavor universality in rare kaon decays text, January 2016

Patterns of flavour violation in models with vector-like quarks journal, April 2017

FLAG Review 2019 text, January 2019

Correlating ε ′ / ε with hadronic B decays via U ( 2 ) 3 flavor symmetry journal, January 2020

Title: Standard Model Prediction for Direct $C P$ Violation in $K \to π π$ Decay

Emerging Understanding of the $Δ I = 1 / 2$ Rule from Lattice QCD
journal, April 2013

Measurements of direct $CP$ violation, $CPT$ symmetry, and other parameters in the neutral kaon system
journal, January 2003

Weak transition matrix elements from finite-volume correlation functions
text, January 2000

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

ππ scattering
journal, June 2001

Application of chiral perturbation theory to K→2π decays
journal, November 1985

Review of Particle Physics
journal, August 2014

Theory of the $CP$ -violating parameter $ɛ^{'} / ɛ$
journal, January 2000

Review of Particle Physics
text, January 2008

Kaon matrix elements and CP violation from quenched lattice QCD: The 3-flavor case
journal, December 2003

$K$ to $π π$ decay amplitudes from lattice QCD
journal, December 2011

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

Theoretical status of ε′/ε
journal, May 2001

C P -Violation in the Renormalizable Theory of Weak Interaction
journal, February 1973

Axial symmetries in lattice QCD with Kaplan fermions
text, January 1994

Review of Particle Physics
text, January 2012

A precision measurement of direct CP violation in the decay of neutral kaons into two pions
text, January 2002

Calculation of $K \to π π$ decay amplitudes with improved Wilson fermion action in lattice QCD
journal, October 2015

Weak Decays Beyond Leading Logarithms
text, January 1995

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

A general method for non-perturbative renormalization of lattice operators
journal, July 1995

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

K → ππ decay amplitudes from the lattice
journal, May 2003

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

A dispersive treatment of $$K_{\ell 4}$$ K ℓ 4 decays
journal, April 2015

Weak decays beyond leading logarithms
journal, October 1996

Charge conjugation, a new quantum numberG, and selection rules concerning a nucleon-antinucleon system
journal, April 1956

Covariant approximation averaging
text, January 2014

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

Charge Conjugation, a New Quantum Number G, and Selection Rules Concerning a Nucleon-Antinucleon System
book, January 1986

Theoretical status of
journal, June 2000

Covariant approximation averaging
journal, June 2015

Review of Particle Physics
text, January 2018

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

Theoretical status of ε′/ε
journal, March 2001

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

Matching factors for $Δ S = 1$ four-quark operators in RI/SMOM schemes
journal, July 2011

with physical final state
journal, March 2005

Domain Wall QCD with Near-Physical Pions
text, January 2012

The BAGEL assembler generation library
journal, December 2009

Evidence for the $2 π$ Decay of the $K_{2}^{0}$ Meson
journal, July 1964

Uncovering CP Violation
book, January 2003

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

Erratum: Measurements of direct $C P$ violation, $C P T$ symmetry, and other parameters in the neutral kaon system [Phys. Rev. D 67, 012005 (2003)]
journal, October 2004

A General Method for Non-Perturbative Renormalization of Lattice Operators
text, January 1994

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

Practical all-to-all propagators for lattice QCD
text, January 2005

A precision measurement of direct CP violation in the decay of neutral kaons into two pions
journal, September 2002

Right-handed charged currents in the era of the Large Hadron Collider
text, January 2017

Probing SUSY with 10 TeV stop mass in rare decays and CP violation of kaon
journal, December 2016

Direct CP violation in ${K^0\to\pi\pi}$ : Standard Model Status
journal, June 2018

Lattice simulations with $G$ -parity boundary conditions
journal, January 2020

Physics beyond colliders at CERN: beyond the Standard Model working group report
text, January 2020

FLAG Review 2019: Flavour Lattice Averaging Group (FLAG)
journal, February 2020

Consistency checks for two-body finite-volume matrix elements: I. Conserved currents and bound states
text, January 2019

Singularity-free next-to-leading order ΔS = 1 renormalization group evolution and ϵ K ′ /ϵK in the Standard Model and beyond
journal, December 2016

ε ′ /ε in 331 models
journal, March 2016

Supersymmetric Explanation of CP Violation in K →ππ Decays
text, January 2016

Violation of lepton flavor and lepton flavor universality in rare kaon decays
journal, April 2016

Kaon CP violation and neutron EDM in the minimal left-right symmetric model
text, January 2019

Isoscalar ππ Scattering and the σ Meson Resonance from QCD
text, January 2017

Supersymmetric Explanation of C P Violation in K → π π Decays
journal, August 2016

Lattice simulations with G-parity Boundary Conditions
text, January 2019

FLAG Review 2019
text, January 2020

Physics beyond colliders at CERN: beyond the Standard Model working group report
journal, December 2019

Direct $C P$ Violation in $K \to μ^{+} μ^{-}$
journal, November 2017

Uncovering Mass Generation Through Higgs Flavor Violation
text, January 2015

Common explanation to the $R_{K^{()}}$ , $R_{D^{()}}$ , and $ε^{'} / ε$ anomalies in a 3HDM with right-handed neutrinos and connections to neutrino physics
journal, September 2019

From deep inelastic scattering to heavy-flavor semileptonic decays: Total rates into multihadron final states from lattice QCD
journal, November 2017

Opportunities for lattice QCD in quark and lepton flavor physics
text, January 2019

Uncovering mass generation through Higgs flavor violation
journal, February 2016

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

Towards NNLO accuracy for ε′/ε
journal, January 2017

Violation of lepton flavor and lepton flavor universality in rare kaon decays
text, January 2016

Patterns of flavour violation in models with vector-like quarks
journal, April 2017

FLAG Review 2019
text, January 2019

Correlating $ε^{'} / ε$ with hadronic $B$ decays via ${U (2)}^{3}$ flavor symmetry
journal, January 2020

Opportunities for Lattice QCD in quark and lepton flavor physics
journal, November 2019

FLAG Review 2019
text, January 2020