Large $N$ approach to kaon decays and mixing 28 years later: $\Delta I = 1/2$ rule, $\hat B_K$ and $\Delta M_K$

Buras, Andrzej J.; Gérard, Jean -Marc; Bardeen, William A.

doi:10.1140/epjc/s10052-014-2871-x

Title: Large $$N$$ approach to kaon decays and mixing 28 years later: $$\Delta I = 1/2$$ rule, $$\hat B_K$$ and $$\Delta M_K$$

Abstract

We review and update our results for K → π π decays and K⁰- K¯⁰ mixing obtained by us in the 1980s within an approach based on the dual representation of QCD as a theory of weakly interacting mesons for large N colours. In our analytic approach the dynamics behind the enhancement of ReA₀ and suppression of ReA₂, the so-called ΔI = 1/2 rule for K → π π decays, has a simple structure: the usual octet enhancement through quark-gluon renormalization group evolution down to the scales O(1 GeV) is continued as a meson evolution down to zero momentum scales at which the factorization of hadronic matrix elements is at work. The inclusion of lowest-lying vector meson contributions in addition to the pseudoscalar ones and of Wilson coefficients in a momentum scheme improves significantly the matching between quark-gluon and meson evolutions. In particular, the anomalous dimension matrix governing the meson evolution exhibits the structure of the known anomalous dimension matrix in the quark-gluon evolution. The recent results on ReA₂ and ReA₀ from the RBC-UKQC collaboration give support for our approach. In particular, the signs of the two main contractions found numerically by these authors follow uniquely from our analytic approach.more »« less

Authors:

Buras, Andrzej J. ^[1]; Gérard, Jean -Marc ^[2]; Bardeen, William A. ^[3]

TUM Institute for Advanced Study, Garching (Germany); Technische Univ. Munchen, Garching (Germany)
Univ. catholique de Louvain, Louvain-la-Neuve (Belgium)
Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)

Publication Date:: Tue May 20 00:00:00 EDT 2014

Research Org.:: Fermi National Accelerator Laboratory (FNAL), Batavia, IL (United States)

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

OSTI Identifier:: 1128718

Report Number(s):: FERMILAB-PUB-14-001-T
Journal ID: ISSN 1434-6044; arXiv eprint number arXiv:1401.1385

Grant/Contract Number:: AC02-07CH11359

Resource Type:: Accepted Manuscript

Journal Name:: European Physical Journal. C, Particles and Fields

Additional Journal Information:: Journal Volume: 74; Journal Issue: 5; Journal ID: ISSN 1434-6044

Publisher:: Springer

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Citation Formats


                    Buras, Andrzej J., Gérard, Jean -Marc, and Bardeen, William A. Large $N$ approach to kaon decays and mixing 28 years later: $\Delta I = 1/2$ rule, $\hat B_K$ and $\Delta M_K$.  United States: N. p., 2014. 
Web.  doi:10.1140/epjc/s10052-014-2871-x.

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                    Buras, Andrzej J., Gérard, Jean -Marc, & Bardeen, William A. Large $N$ approach to kaon decays and mixing 28 years later: $\Delta I = 1/2$ rule, $\hat B_K$ and $\Delta M_K$.  United States.  https://doi.org/10.1140/epjc/s10052-014-2871-x

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                    Buras, Andrzej J., Gérard, Jean -Marc, and Bardeen, William A. Tue .  
"Large $N$ approach to kaon decays and mixing 28 years later: $\Delta I = 1/2$ rule, $\hat B_K$ and $\Delta M_K$".  United States.  https://doi.org/10.1140/epjc/s10052-014-2871-x.  https://www.osti.gov/servlets/purl/1128718.

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@article{osti_1128718,

  title        = {Large $N$ approach to kaon decays and mixing 28 years later: $\Delta I = 1/2$ rule, $\hat B_K$ and $\Delta M_K$},

  author       = {Buras, Andrzej J. and Gérard, Jean -Marc and Bardeen, William A.},

  abstractNote = {We review and update our results for K → π π decays and K⁰- K¯⁰ mixing obtained by us in the 1980s within an approach based on the dual representation of QCD as a theory of weakly interacting mesons for large N colours. In our analytic approach the dynamics behind the enhancement of ReA0 and suppression of ReA2, the so-called ΔI = 1/2 rule for K → π π decays, has a simple structure: the usual octet enhancement through quark-gluon renormalization group evolution down to the scales O(1 GeV) is continued as a meson evolution down to zero momentum scales at which the factorization of hadronic matrix elements is at work. The inclusion of lowest-lying vector meson contributions in addition to the pseudoscalar ones and of Wilson coefficients in a momentum scheme improves significantly the matching between quark-gluon and meson evolutions. In particular, the anomalous dimension matrix governing the meson evolution exhibits the structure of the known anomalous dimension matrix in the quark-gluon evolution. The recent results on ReA2 and ReA0 from the RBC-UKQC collaboration give support for our approach. In particular, the signs of the two main contractions found numerically by these authors follow uniquely from our analytic approach. At NLO in 1/N we obtain R = ReA0/ReA2= 16.0±1.5 which amounts to an order of magnitude enhancement over the strict large N limit value √2. QCD penguins contribute at 15% level to this result. We also find B^K = 0.73± 0.02, with the smallness of 1/N corrections to the large N value B^K = 3/4 resulting within our approach from an approximate cancellation between pseudoscalar and vector meson one-loop contributions. We summarize the status of ΔMK in this approach.},

  doi          = {10.1140/epjc/s10052-014-2871-x},

  journal      = {European Physical Journal. C, Particles and Fields},

  number       = 5,

  volume       = 74,

  place        = {United States},

  year         = {Tue May 20 00:00:00 EDT 2014},

  month        = {Tue May 20 00:00:00 EDT 2014}

}

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We show that the symmetric quark model, with Bose quarks or as a three- triplet model with perfect SU(3)''-color symmetry supplemented by current algebra and pion partial conservation of the axial-vector current, provides an alternative to (or suppression beyond) introduction of a P' ''charmed'' quark for banishing abs. value of $delta$S = 2, ΔQ = 0 nonleptonic effects to order Gs. This mechanism is distinguished by the presence of such effects at high energies to order (Gs)² and/or (Gs)(Gt) in the amplitude. Previous estimates using the free three-quartet model for rare decay modes of the K mesons in the Weinberg--Salammore »« less
https://doi.org/10.1103/PhysRevD.12.2869
Epsilon(700) meson and the chemically bond. delta. Ichemically bond = 1/2 rule in kaon decays

Journal Article Volkov, M K ; Ivanov, A N ; Troitskaya, N I - Sov. J. Nucl. Phys. (Engl. Transl.); (United States)

The kaon decays K..-->..2..gamma.., K..-->..2..pi.., and K..-->..3..pi.. are studied. A theoretical basis for the phenomenological chemically bond..delta..Ichemically bond = 1/2 rule is given. The weak interaction is described using the effective Lagrangian found in the standard Kobayashi-Maskawa model including the QCD interaction. The weak vertices take the form of four-quark operators whose low-energy matrix elements are computed in the chiral quark-loop model (CQLM). In this model the decay amplitudes are determined by contact and pole graphs. The latter arise from the exchange of the pseudoscalar mesons ..pi.., eta, and eta' and the scalar meson Epsilon(700). Within the accuracy of themore »« less
Exploring the Quark-Gluon Content of Hadrons: From Mesons to Nuclear Matter

Thesis/Dissertation Matevosyan, Hrayr

Even though Quantum Chromodynamics (QCD) was formulated over three decades ago, it poses enormous challenges for describing the properties of hadrons from the underlying quark-gluon degrees of freedom. Moreover, the problem of describing the nuclear force from its quark-gluon origin is still open. While a direct solution of QCD to describe the hadrons and nuclear force is not possible at this time, we explore a variety of developed approaches ranging from phenomenology to first principle calculations at one or other level of approximation in linking the nuclear force to QCD. The Dyson Schwinger formulation (DSE) of coupled integral equations formore »« less
https://doi.org/10.2172/909580

Full Text Available
Lattice QCD Calculation of Nucleon Structure

Technical Report Liu, Keh-Fei ; Draper, Terrence

It is emphasized in the 2015 NSAC Long Range Plan that "understanding the structure of hadrons in terms of QCD's quarks and gluons is one of the central goals of modern nuclear physics." Over the last three decades, lattice QCD has developed into a powerful tool for ab initio calculations of strong-interaction physics. Up until now, it is the only theoretical approach to solving QCD with controlled statistical and systematic errors. Since 1985, we have proposed and carried out first-principles calculations of nucleon structure and hadron spectroscopy using lattice QCD which entails both algorithmic development and large-scale computer simulation. Wemore »« less
https://doi.org/10.2172/1323029

Full Text Available
Light scalar mesons and charmless hadronic B{sub c}{yields}SP,SV decays in the perturbative QCD approach

Journal Article Liu, Xin ; Xiao, Zhen-Jun - Physical Review. D, Particles Fields

The scalar productions in heavy meson decays can provide a good platform to study not only heavy flavor physics but also their own physical properties in a dramatically different way. In this work, based on the assumption of two-quark structure of the scalars, the charmless hadronic B{sub c}{yields}SP,SV decays (here, S, P, and V denote the light scalar, pseudoscalar, and vector mesons, respectively) are investigated by employing the perturbative QCD (pQCD) factorization approach. In the standard model all these considered B{sub c} meson decays can only occur through the annihilation diagrams. From our numerical evaluations and phenomenological analysis, we findmore »« less
https://doi.org/10.1103/PHYSREVD.82.054029

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Title: Large $$N$$ approach to kaon decays and mixing 28 years later: $$\Delta I = 1/2$$ rule, $$\hat B_K$$ and $$\Delta M_K$$

Abstract

Citation Formats

Hyperons and Heavy Mesons (Systematics and Decay) journal, December 1957

The rule in the large-N limit journal, November 1986

The K → ππ decays in the large-N limit quark evolution journal, January 1987

A consistent analysis of the ΔI = 12 rule for K decays journal, June 1987

The B parameter beyond the leading order of the expansion journal, September 1988

A planar diagram theory for strong interactions journal, April 1974

A two-dimensional model for mesons journal, June 1974

Baryons in the expansion journal, November 1979

Strangeness and the large N-expansion journal, March 1988

Weak decay amplitudes in large Nc QCD journal, April 1989

Phenomenological applications of the expansion journal, July 1989

Asymptotic freedom, light quarks and the origin of the rule in the non-leptonic decays of strange particles journal, March 1977

Chiral perturbation theory and the evaluation of to nonleptonic decays journal, April 1988

The Δ I = 1/2 rule in the chiral limit journal, January 1999

New analysis of the $\Delta I = 1/2$ rule in kaon decays and the $\hat{B}_K$ parameter journal, September 1999

Δ I = 1/2 and epsilon′/epsilon in large- N c QCD journal, May 2003

gauge theories at large journal, May 2013

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

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

Nonleptonic Kaon Decays from Lattice QCD conference, November 2013

The Kaon B-parameter and K-π and K-ππ transition amplitudes on the lattice journal, September 1988

Vector meson effects on hadronic matrix elements book, January 1989

Nonleptonic decays of kaons in the expansion journal, December 1977

Weak meson decays and the expansion journal, July 1982

expansion for exclusive and inclusive charm decays journal, April 1986

Exclusive semileptonic decays of heavy mesons journal, December 1985

Parameters of the six-quark model journal, March 1981

A strategy to study the role of the charm quark in explaining the Delta{I}=1/2 rule journal, November 2004

Chiral-Symmetry Breakdown in Large- N Chromodynamics journal, July 1980

Polychromatic penguins don't fly journal, May 1986

Chiral perturbation theory to one loop journal, November 1984

Nonlinear realization and hidden local symmetries journal, July 1988

Chiral lagrangians for massive spin-1 fields journal, June 1989

Leading and next-to-leading QCD corrections to ɛ-parameter and mixing in the presence of a heavy top quark journal, December 1990

K-K mixing in the standard model journal, September 1985

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

B K using HYP-smeared staggered fermions in N f = 2 + 1 unquenched QCD journal, December 2010

Review of lattice results concerning low-energy particle physics journal, July 2011

ε′/ε in the standard model journal, March 1988

Isospin breaking contributions to ϵ′/ϵ journal, June 1987

Δ I = 1 2 Rule for Nonleptonic Decays in Asymptotically Free Field Theories journal, July 1974

Octet enhancement of non-leptonic weak interactions in asymptotically free gauge theories journal, October 1974

Rare decay modes of the K mesons in gauge theories journal, August 1974

10 - ε′/ε in the Standard Model book, May 2020

Review of lattice results concerning low-energy particle physics text, January 2017

On the Large Nc Expansion in Quantum Chromodynamics book, August 2002

Parameters of the six-quark model journal, February 1981

Review of lattice results concerning low-energy particle physics text, January 2016

Review of lattice results concerning low-energy particle physics text, January 2014

$B_K$ using HYP-smeared staggered fermions in $N_f=2+1$ unquenched QCD text, January 2010

A strategy to study the role of the charm quark in explaining the Delta{I}=1/2 rule text, January 2004

On the Large Nc Expansion in Quantum Chromodynamics text, January 2001

Parameters of the six-quark model journal, March 1981

Nonleptonic decays of kaons in the expansion journal, December 1977

Weak meson decays and the expansion journal, July 1982

Polychromatic penguins don't fly journal, May 1986

Chiral perturbation theory and the evaluation of to nonleptonic decays journal, April 1988

The KL-KS mass difference journal, March 1991

Current-current operator evolution in the chiral limit journal, March 1995

The ΔS = 1 effective hamiltonian including next-to-leading order QCD and QED corrections journal, March 1994

Effective Hamiltonian for non-leptonic decays at NNLO in QCD journal, May 2005

Improved determination of the electroweak penguin contribution to ϵ′/ϵ in the chiral limit journal, February 2003

Next-to-Next-to-Leading-Order Charm-Quark Contribution to the C P Violation Parameter ϵ K and Δ M K journal, March 2012

Clinical outcomes for T1-2N0-1 oral tongue cancer patients underwent surgery with and without postoperative radiotherapy journal, May 2010

Precision computation of the kaon bag parameter text, January 2011

Weakly-induced strong CP-violation text, January 2012

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

The $B_K$ Parameter in the $1/N_c$ Expansion text, January 1995

Leptoquarks meet ε′/ε and rare Kaon processes journal, February 2018

ε ′ /ε in 331 models journal, March 2016

K → ππ and K − π matrix elements of the chromomagnetic operators from Dual QCD journal, July 2018

K → π ν ν ¯ $$ K\to \pi \nu \overline{\nu} $$ and ε′/ε in simplified new physics models journal, November 2015

Improved anatomy of ε′/ε in the Standard Model journal, November 2015

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

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

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

Kaon C P violation and neutron EDM in the minimal left-right symmetric model journal, February 2020

Hyperons and Heavy Mesons (Systematics and Decay)
journal, December 1957

The rule in the large-N limit
journal, November 1986

The K → ππ decays in the large-N limit quark evolution
journal, January 1987

A consistent analysis of the ΔI = 12 rule for K decays
journal, June 1987

The B parameter beyond the leading order of the expansion
journal, September 1988

A planar diagram theory for strong interactions
journal, April 1974

A two-dimensional model for mesons
journal, June 1974

Baryons in the expansion
journal, November 1979

Strangeness and the large N-expansion
journal, March 1988

Weak decay amplitudes in large Nc QCD
journal, April 1989

Phenomenological applications of the expansion
journal, July 1989

Asymptotic freedom, light quarks and the origin of the rule in the non-leptonic decays of strange particles
journal, March 1977

Chiral perturbation theory and the evaluation of to nonleptonic decays
journal, April 1988

The Δ I = 1/2 rule in the chiral limit
journal, January 1999

New analysis of the $\Delta I = 1/2$ rule in kaon decays and the $\hat{B}_K$ parameter
journal, September 1999

Δ I = 1/2 and epsilon′/epsilon in large- N _c QCD
journal, May 2003

gauge theories at large
journal, May 2013

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

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

Nonleptonic Kaon Decays from Lattice QCD
conference, November 2013

The Kaon B-parameter and K-π and K-ππ transition amplitudes on the lattice
journal, September 1988

Vector meson effects on hadronic matrix elements
book, January 1989

Nonleptonic decays of kaons in the expansion
journal, December 1977

Weak meson decays and the expansion
journal, July 1982

expansion for exclusive and inclusive charm decays
journal, April 1986

Exclusive semileptonic decays of heavy mesons
journal, December 1985

Parameters of the six-quark model
journal, March 1981

A strategy to study the role of the charm quark in explaining the Delta{I}=1/2 rule
journal, November 2004

Chiral-Symmetry Breakdown in Large- $N$ Chromodynamics
journal, July 1980

Polychromatic penguins don't fly
journal, May 1986

Chiral perturbation theory to one loop
journal, November 1984

Nonlinear realization and hidden local symmetries
journal, July 1988

Chiral lagrangians for massive spin-1 fields
journal, June 1989

Leading and next-to-leading QCD corrections to ɛ-parameter and mixing in the presence of a heavy top quark
journal, December 1990

K-K mixing in the standard model
journal, September 1985

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

$B_{K}$ using HYP-smeared staggered fermions in $N_{f} = 2 + 1$ unquenched QCD
journal, December 2010

Review of lattice results concerning low-energy particle physics
journal, July 2011

ε′/ε in the standard model
journal, March 1988

Isospin breaking contributions to ϵ′/ϵ
journal, June 1987

$Δ I = \frac{1}{2}$ Rule for Nonleptonic Decays in Asymptotically Free Field Theories
journal, July 1974

Octet enhancement of non-leptonic weak interactions in asymptotically free gauge theories
journal, October 1974

Rare decay modes of the $K$ mesons in gauge theories
journal, August 1974

10 - ε′/ε in the Standard Model
book, May 2020

Review of lattice results concerning low-energy particle physics
text, January 2017

On the Large Nc Expansion in Quantum Chromodynamics
book, August 2002

Parameters of the six-quark model
journal, February 1981

Review of lattice results concerning low-energy particle physics
text, January 2016

Review of lattice results concerning low-energy particle physics
text, January 2014

$B_K$ using HYP-smeared staggered fermions in $N_f=2+1$ unquenched QCD
text, January 2010

A strategy to study the role of the charm quark in explaining the Delta{I}=1/2 rule
text, January 2004

On the Large Nc Expansion in Quantum Chromodynamics
text, January 2001

Parameters of the six-quark model
journal, March 1981

Nonleptonic decays of kaons in the expansion
journal, December 1977

Weak meson decays and the expansion
journal, July 1982

Polychromatic penguins don't fly
journal, May 1986

Chiral perturbation theory and the evaluation of to nonleptonic decays
journal, April 1988

The KL-KS mass difference
journal, March 1991

Current-current operator evolution in the chiral limit
journal, March 1995

The ΔS = 1 effective hamiltonian including next-to-leading order QCD and QED corrections
journal, March 1994

Effective Hamiltonian for non-leptonic decays at NNLO in QCD
journal, May 2005

Improved determination of the electroweak penguin contribution to ϵ′/ϵ in the chiral limit
journal, February 2003

Next-to-Next-to-Leading-Order Charm-Quark Contribution to the $C P$ Violation Parameter $ϵ_{K}$ and $Δ M_{K}$
journal, March 2012

Clinical outcomes for T1-2N0-1 oral tongue cancer patients underwent surgery with and without postoperative radiotherapy
journal, May 2010

Precision computation of the kaon bag parameter
text, January 2011

Weakly-induced strong CP-violation
text, January 2012

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

The $B_K$ Parameter in the $1/N_c$ Expansion
text, January 1995

Leptoquarks meet ε′/ε and rare Kaon processes
journal, February 2018

ε ′ /ε in 331 models
journal, March 2016

K → ππ and K − π matrix elements of the chromomagnetic operators from Dual QCD
journal, July 2018

K → π ν ν ¯ $$ K\to \pi \nu \overline{\nu} $$ and ε′/ε in simplified new physics models
journal, November 2015

Improved anatomy of ε′/ε in the Standard Model
journal, November 2015

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

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

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

Kaon $C P$ violation and neutron EDM in the minimal left-right symmetric model
journal, February 2020

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

Final state interactions in $$K\rightarrow \pi \pi $$ K → π π decays: $$\Delta I=1/2$$ Δ I = 1 / 2 rule vs. $$\varepsilon '/\varepsilon $$ ε ′ / ε
journal, January 2017

Anatomy of $$\varepsilon '/\varepsilon $$ ε ′ / ε beyond the standard model
journal, March 2019