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 $$\Delta M_K$$

Journal Article · Tue May 20 00:00:00 EDT 2014 · European Physical Journal. C, Particles and Fields

DOI:https://doi.org/10.1140/epjc/s10052-014-2871-x· OSTI ID:1128718

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)

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 ΔM_K in this approach.

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

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

Grant/Contract Number:: AC02-07CH11359

OSTI ID:: 1128718

Report Number(s):: FERMILAB-PUB-14-001-T; arXiv eprint number arXiv:1401.1385

Journal Information:: European Physical Journal. C, Particles and Fields, Vol. 74, Issue 5; ISSN 1434-6044

Publisher:: SpringerCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 80 works

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References (64)

Hyperons and Heavy Mesons (Systematics and Decay) Gell-Mann, M.; Rosenfeld, A. H. Annual Review of Nuclear Science, Vol. 7, Issue 1 https://doi.org/10.1146/annurev.ns.07.120157.002203	journal	December 1957
The rule in the large-N limit Bardeen, William A.; Buras, A. J.; Gérard, J. -M. Physics Letters B, Vol. 180, Issue 1-2 https://doi.org/10.1016/0370-2693(86)90150-4	journal	November 1986
The K → ππ decays in the large-N limit quark evolution Bardeen, William A.; Buras, A. J.; Gérard, J. -M. Nuclear Physics B, Vol. 293 https://doi.org/10.1016/0550-3213(87)90091-5	journal	January 1987
A consistent analysis of the ΔI = 12 rule for K decays Bardeen, William A.; Buras, A. J.; Gerard, J. -M. Physics Letters B, Vol. 192, Issue 1-2 https://doi.org/10.1016/0370-2693(87)91156-7	journal	June 1987
The B parameter beyond the leading order of the expansion Bardeen, William A.; Buras, A. J.; Gerard, J. -M. Physics Letters B, Vol. 211, Issue 3 https://doi.org/10.1016/0370-2693(88)90913-6	journal	September 1988
A planar diagram theory for strong interactions Hooft, G. 't Nuclear Physics B, Vol. 72, Issue 3 https://doi.org/10.1016/0550-3213(74)90154-0	journal	April 1974
A two-dimensional model for mesons 't Hooft, G. Nuclear Physics B, Vol. 75, Issue 3 https://doi.org/10.1016/0550-3213(74)90088-1	journal	June 1974
Baryons in the expansion Witten, Edward Nuclear Physics B, Vol. 160, Issue 1 https://doi.org/10.1016/0550-3213(79)90232-3	journal	November 1979
Strangeness and the large N-expansion Buras, Andrzej J. Nuclear Physics A, Vol. 479 https://doi.org/10.1016/0375-9474(88)90452-6	journal	March 1988
Weak decay amplitudes in large Nc QCD Bardeen, William A. Nuclear Physics B - Proceedings Supplements, Vol. 7, Issue 1 https://doi.org/10.1016/0920-5632(89)90566-5	journal	April 1989
Phenomenological applications of the expansion Buras, Andrzej J. Nuclear Physics B - Proceedings Supplements, Vol. 10, Issue 1 https://doi.org/10.1016/0920-5632(89)90066-2	journal	July 1989
Asymptotic freedom, light quarks and the origin of the rule in the non-leptonic decays of strange particles Shifman, M. A.; Vainshtein, A. I.; Zakharov, V. I. Nuclear Physics B, Vol. 120, Issue 2 https://doi.org/10.1016/0550-3213(77)90046-3	journal	March 1977
Chiral perturbation theory and the evaluation of to nonleptonic decays Bijnens, Johan; Guberina, Branko Physics Letters B, Vol. 205, Issue 1 https://doi.org/10.1016/0370-2693(88)90407-8	journal	April 1988
The Δ I = 1/2 rule in the chiral limit Bijnens, Johan; Prades, Joaquim Journal of High Energy Physics, Vol. 1999, Issue 01 https://doi.org/10.1088/1126-6708/1999/01/023	journal	January 1999
New analysis of the $\Delta I = 1/2$ rule in kaon decays and the $\hat{B}_K$ parameter Hambye, T.; Köhler, G. O.; Soldan, P. H. The European Physical Journal C, Vol. 10, Issue 2 https://doi.org/10.1007/s100529900084	journal	September 1999
Δ I = 1/2 and epsilon′/epsilon in large- N _c QCD Hambye, Thomas; Peris, Santiago; Rafael, Eduardo de Journal of High Energy Physics, Vol. 2003, Issue 05 https://doi.org/10.1088/1126-6708/2003/05/027	journal	May 2003
gauge theories at large Lucini, Biagio; Panero, Marco Physics Reports, Vol. 526, Issue 2 https://doi.org/10.1016/j.physrep.2013.01.001	journal	May 2013
$K$ to $π π$ decay amplitudes from lattice QCD Blum, T.; Boyle, P. A.; Christ, N. H. Physical Review D, Vol. 84, Issue 11 https://doi.org/10.1103/PhysRevD.84.114503	journal	December 2011
Lattice determination of the $K \to (π π)_{I = 2}$ decay amplitude $A_{2}$ Blum, T.; Boyle, P. A.; Christ, N. H. Physical Review D, Vol. 86, Issue 7 https://doi.org/10.1103/PhysRevD.86.074513	journal	October 2012
Nonleptonic Kaon Decays from Lattice QCD Christ, Norman H. Proceedings of 2013 Kaon Physics International Conference — PoS(KAON13) https://doi.org/10.22323/1.181.0029	conference	November 2013
The Kaon B-parameter and K-π and K-ππ transition amplitudes on the lattice Gavela, M. B.; Maiani, L.; Petrarca, S. Nuclear Physics B, Vol. 306, Issue 4 https://doi.org/10.1016/0550-3213(88)90439-7	journal	September 1988
Vector meson effects on hadronic matrix elements Gérard, Jean-Marc XXIV International Conference on High Energy Physics https://doi.org/10.1007/978-3-642-74136-4_86	book	January 1989
Nonleptonic decays of kaons in the expansion Fukugita, M.; Inami, T.; Sakai, N. Physics Letters B, Vol. 72, Issue 2 https://doi.org/10.1016/0370-2693(77)90711-0	journal	December 1977
Weak meson decays and the expansion Tadić, Dubravko; Trampetić, Josip Physics Letters B, Vol. 114, Issue 2-3 https://doi.org/10.1016/0370-2693(82)90142-3	journal	July 1982
expansion for exclusive and inclusive charm decays Buras, A. J.; Gérard, J. -M.; Rückl, R. Nuclear Physics B, Vol. 268, Issue 1 https://doi.org/10.1016/0550-3213(86)90200-2	journal	April 1986
Exclusive semileptonic decays of heavy mesons Wirbel, M.; Stech, B.; Bauer, M. Zeitschrift für Physik C Particles and Fields, Vol. 29, Issue 4 https://doi.org/10.1007/BF01560299	journal	December 1985
Parameters of the six-quark model Gaiser, Bradley D.; Tsao, Thomas; Wise, Mark B. Annals of Physics, Vol. 132, Issue 1 https://doi.org/10.1016/0003-4916(81)90269-4	journal	March 1981
A strategy to study the role of the charm quark in explaining the Delta{I}=1/2 rule Giusti, L.; Hernandez, P.; Laine, M. Journal of High Energy Physics, Vol. 2004, Issue 11 https://doi.org/10.1088/1126-6708/2004/11/016	journal	November 2004
Chiral-Symmetry Breakdown in Large- $N$ Chromodynamics Coleman, Sidney; Witten, Edward Physical Review Letters, Vol. 45, Issue 2 https://doi.org/10.1103/PhysRevLett.45.100	journal	July 1980
Polychromatic penguins don't fly Chivukula, R. Sekhar; Flynn, Jonathan M.; Georgi, Howard Physics Letters B, Vol. 171, Issue 4 https://doi.org/10.1016/0370-2693(86)91438-3	journal	May 1986
Chiral perturbation theory to one loop Gasser, J.; Leutwyler, H. Annals of Physics, Vol. 158, Issue 1 https://doi.org/10.1016/0003-4916(84)90242-2	journal	November 1984
Nonlinear realization and hidden local symmetries Bando, Masako; Kugo, Taichiro; Yamawaki, Koichi Physics Reports, Vol. 164, Issue 4-5 https://doi.org/10.1016/0370-1573(88)90019-1	journal	July 1988
Chiral lagrangians for massive spin-1 fields Ecker, G.; Gasser, J.; Leutwyler, H. Physics Letters B, Vol. 223, Issue 3-4 https://doi.org/10.1016/0370-2693(89)91627-4	journal	June 1989
Leading and next-to-leading QCD corrections to ɛ-parameter and mixing in the presence of a heavy top quark Buras, Andrzej J.; Jamin, Matthias; Weisz, Peter H. Nuclear Physics B, Vol. 347, Issue 3 https://doi.org/10.1016/0550-3213(90)90373-L	journal	December 1990
K-K mixing in the standard model Pich, Antonio; de Rafael, Eduardo Physics Letters B, Vol. 158, Issue 6 https://doi.org/10.1016/0370-2693(85)90798-1	journal	September 1985
Continuum limit of $B_{K}$ from $2 + 1$ flavor domain wall QCD Aoki, Y.; Arthur, R.; Blum, T. Physical Review D, Vol. 84, Issue 1 https://doi.org/10.1103/PhysRevD.84.014503	journal	July 2011
$B_{K}$ using HYP-smeared staggered fermions in $N_{f} = 2 + 1$ unquenched QCD Bae, Taegil; Jang, Yong-Chull; Jung, Chulwoo Physical Review D, Vol. 82, Issue 11 https://doi.org/10.1103/PhysRevD.82.114509	journal	December 2010
Review of lattice results concerning low-energy particle physics Colangelo, G.; Dürr, S.; Jüttner, A. The European Physical Journal C, Vol. 71, Issue 7 https://doi.org/10.1140/epjc/s10052-011-1695-1	journal	July 2011
ε′/ε in the standard model Buras, A. J.; Gérard, J. -M. Physics Letters B, Vol. 203, Issue 3 https://doi.org/10.1016/0370-2693(88)90551-5	journal	March 1988
Isospin breaking contributions to ϵ′/ϵ Buras, A. J.; Gerard, J. -M. Physics Letters B, Vol. 192, Issue 1-2 https://doi.org/10.1016/0370-2693(87)91159-2	journal	June 1987
$Δ I = \frac{1}{2}$ Rule for Nonleptonic Decays in Asymptotically Free Field Theories Gaillard, M. K.; Lee, Benjamin W. Physical Review Letters, Vol. 33, Issue 2 https://doi.org/10.1103/PhysRevLett.33.108	journal	July 1974
Octet enhancement of non-leptonic weak interactions in asymptotically free gauge theories Altarelli, G.; Maiani, L. Physics Letters B, Vol. 52, Issue 3 https://doi.org/10.1016/0370-2693(74)90060-4	journal	October 1974
Rare decay modes of the $K$ mesons in gauge theories Gaillard, M. K.; Lee, Benjamin W. Physical Review D, Vol. 10, Issue 3 https://doi.org/10.1103/PhysRevD.10.897	journal	August 1974
10 - ε′/ε in the Standard Model Buras, Andrzej J. Gauge Theories of Weak Decays https://doi.org/10.1017/9781139524100.012	book	May 2020
Review of lattice results concerning low-energy particle physics Aoki, S.; Aoki, Y.; Bečirević, D. Deutsches Elektronen-Synchrotron, DESY, Hamburg https://doi.org/10.3204/pubdb-2017-01363	text	January 2017
On the Large Nc Expansion in Quantum Chromodynamics Bardeen, William A. 100 Years Werner Heisenberg: Works and Impact https://doi.org/10.1002/9783527610853.ch7	book	August 2002
Parameters of the six-quark model Gaiser, Bradley D.; Tsao, Thomas; Wise, Mark B. Annals of Physics, Vol. 131, Issue 2, p. 494 https://doi.org/10.1016/0003-4916(81)90040-3	journal	February 1981
Review of lattice results concerning low-energy particle physics Aoki, S.; Aoki, Y.; Becirevic, D. Deutsches Elektronen-Synchrotron, DESY, Hamburg https://doi.org/10.3204/pubdb-2017-01038	text	January 2016
Review of lattice results concerning low-energy particle physics Wenger, Urs; Colangelo, Gilberto EDP Sciences https://doi.org/10.7892/boris.60235	text	January 2014
$B_K$ using HYP-smeared staggered fermions in $N_f=2+1$ unquenched QCD Bae, Taegil; Jang, Yong-Chull; Jung, Chulwoo arXiv https://doi.org/10.48550/arxiv.1008.5179	text	January 2010
A strategy to study the role of the charm quark in explaining the Delta{I}=1/2 rule Giusti, L.; Hernandez, P.; Laine, M. arXiv https://doi.org/10.48550/arxiv.hep-lat/0407007	text	January 2004
On the Large Nc Expansion in Quantum Chromodynamics Bardeen, William A. arXiv https://doi.org/10.48550/arxiv.hep-ph/0112229	text	January 2001
The KL-KS mass difference Bijnens, Johan; Gérard, Jean-Marc; Klein, Gerhard Physics Letters B, Vol. 257, Issue 1-2 https://doi.org/10.1016/0370-2693(91)90880-y	journal	March 1991
Current-current operator evolution in the chiral limit Fatelo, J. P.; Gérard, J. -M. Physics Letters B, Vol. 347, Issue 1-2 https://doi.org/10.1016/0370-2693(95)00047-o	journal	March 1995
The ΔS = 1 effective hamiltonian including next-to-leading order QCD and QED corrections Ciuchini, M.; Franco, E.; Martinelli, G. Nuclear Physics B, Vol. 415, Issue 2 https://doi.org/10.1016/0550-3213(94)90118-x	journal	March 1994
Effective Hamiltonian for non-leptonic decays at NNLO in QCD Gorbahn, Martin; Haisch, Ulrich Nuclear Physics B, Vol. 713, Issue 1-3 https://doi.org/10.1016/j.nuclphysb.2005.01.047	journal	May 2005
On <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:msub><mml:mi>ϵ</mml:mi><mml:mi>K</mml:mi></mml:msub></mml:math> beyond lowest order in the operator product expansion Buras, Andrzej J.; Guadagnoli, Diego; Isidori, Gino Physics Letters B, Vol. 688, Issue 4-5 https://doi.org/10.1016/j.physletb.2010.04.017	journal	May 2010
Improved determination of the electroweak penguin contribution to ϵ′/ϵ in the chiral limit Cirigliano, Vincenzo; Donoghue, John F.; Golowich, Eugene Physics Letters B, Vol. 555, Issue 1-2 https://doi.org/10.1016/s0370-2693(03)00010-8	journal	February 2003
Next-to-Next-to-Leading-Order Charm-Quark Contribution to the $C P$ Violation Parameter $ϵ_{K}$ and $Δ M_{K}$ Brod, Joachim; Gorbahn, Martin Physical Review Letters, Vol. 108, Issue 12 https://doi.org/10.1103/physrevlett.108.121801	journal	March 2012
Clinical outcomes for T1-2N0-1 oral tongue cancer patients underwent surgery with and without postoperative radiotherapy Shim, Su Jung; Cha, Jihye; Koom, Woong Sub Radiation Oncology, Vol. 5, Issue 1 https://doi.org/10.1186/1748-717x-5-43	journal	May 2010
Precision computation of the kaon bag parameter Durr, S.; Fodor, Z.; Hoelbling, C. arXiv https://doi.org/10.48550/arxiv.1106.3230	text	January 2011
Weakly-induced strong CP-violation Gerard, J. M.; Mertens, P. arXiv https://doi.org/10.48550/arxiv.1206.0914	text	January 2012
A precision measurement of direct CP violation in the decay of neutral kaons into two pions Batley, J. R.; collaboration, Na48 arXiv https://doi.org/10.48550/arxiv.hep-ex/0208009	text	January 2002
The $B_K$ Parameter in the $1/N_c$ Expansion Bijnens, Johan; Prades, Joaquim arXiv https://doi.org/10.48550/arxiv.hep-ph/9502363	text	January 1995

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