<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>Δ</mml:mi><mml:mi>I</mml:mi><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:mfrac></mml:math>Rule for Nonleptonic Decays in Asymptotically Free Field Theories

Gaillard, Mary K.; Lee, Benjamin W.

doi:10.1103/physrevlett.33.108

Cited by 831 publications

(404 citation statements)

References 17 publications

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“…It has been known since the early 70s that the bulk of the enhancement must be due to strong interactions at low energies [1]. Therefore a reliable explanation must eventually be based on systematic non-perturbative methods, in particular on lattice QCD [2,3].…”

Section: Introductionmentioning

confidence: 99%

Probing the chiral weak Hamiltonian at finite volumes

Hernández¹,

Laine²

2006

J. High Energy Phys.

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Non-leptonic kaon decays are often described through an effective chiral weak Hamiltonian, whose couplings ("low-energy constants") encode all non-perturbative QCD physics. It has recently been suggested that these low-energy constants could be determined at finite volumes by matching the non-perturbatively measured three-point correlation functions between the weak Hamiltonian and two left-handed flavour currents, to analytic predictions following from chiral perturbation theory. Here we complete the analytic side in two respects: by inspecting how small ("ǫ-regime") and intermediate or large ("p-regime") quark masses connect to each other, and by including in the discussion the two leading ∆I = 1/2 operators. We show that the ǫ-regime offers a straightforward strategy for disentangling the coefficients of the ∆I = 1/2 operators, and that in the p-regime finite-volume effects are significant in these observables once the pseudoscalar mass M and the box length L are in the regime M L < ∼ 5.0. July 20061 pilar.hernandez@ific.uv.es 2

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Section: Introductionmentioning

confidence: 99%

Probing the chiral weak Hamiltonian at finite volumes

Hernández¹,

Laine²

2006

J. High Energy Phys.

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“…Let us rewrite Eq. (5.4) (apart from [Ô m ] sd , which does not contribute to physical kaon decays [3,22]) in the formH…”

Section: Su(3) Classification Of the Effective Theorymentioning

confidence: 99%

“…3 For this purpose, we define correlators involving left-handed flavour currents (this choice is well suited also for a practical implementation of matching computations on the lattice [19,20] …”

Section: Basic Setupmentioning

confidence: 99%

“…The best strategy to do this is to factorise as much as possible the contributions from the different scales, and inspect them one at a time. While QCD corrections from the electroweak scale down can be addressed to a large extent within perturbation theory [3,4], the contribution of the QCD scale can be isolated particularly cleanly with lattice methods, by considering a world with an unphysically light charm quark, as has been recently proposed in Ref. [12].…”

Section: Introductionmentioning

confidence: 99%

“…As the electroweak scale is decoupled through an operator product expansion in the inverse W boson mass, large QCD radiative corrections could arise [3,4], but also physics at the charm quark mass scale of about a GeV [4] or at the "genuine" QCD scale of a few hundred MeV [5] could be involved. Finally final state interactions at the pionic scale of about a hundred MeV have also been discussed as a possible source of the enhancement [6]- [11].…”

Section: Introductionmentioning

confidence: 99%

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Charm mass dependence of the weak Hamiltonian in chiral perturbation theory

Hernández¹,

Laine

2004

J. High Energy Phys.

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Suppose that the weak interaction Hamiltonian of four-flavour SU(4) chiral effective theory is known, for a small charm quark mass m c . We study how the weak Hamiltonian changes as the charm quark mass increases, by integrating it out within chiral perturbation theory to obtain a three-flavour SU(3) chiral theory. We find that the ratio of the SU(3) low-energy constants which mediate ∆I = 1/2 and ∆I = 3/2 transitions, increases rather rapidly with m c , as ∼ m c ln(1/m c ). The logarithmic effect originates from "penguin-type" charm loops, and could represent one of the reasons for the ∆I = 1/2 rule.

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On the Large Nc Expansion in Quantum Chromodynamics

Bardeen

2002

Fortschr. Phys.

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I discuss methods based on the large Nc expansion to study nonperturbative aspects of quantum chromodynamics, the theory of the strong force. I apply these methods to the analysis of weak decay processes and the nonperturbative computation of the weak matrix elements needed for a complete evaluation of these decays in the Standard Model of elementary particle physics. • Introduction.Field theories are frequently studied through a perturbative expansion in the interaction strength or coupling constant. In many cases, a nonperturbative analysis is required to apply these theories in physical situations. The large N expansion is a nonperturbative method of analysis that makes use of particular limits for parameters unrelated to the coupling constant. For example, O(N) spin systems where N is the number of spin components can be studied by mean field methods which become exact in the large N limit. Applications of perturbative QCD, such as the cross-sections for high p_t jets, are greatly simplified using color-ordered amplitudes and a large Nc expansion where Nc is the number of colors, the quantum number associated with the QCD gauge dynamics. The large Nc expansion can also be used to study nonperturbative aspects of quantum chromodynamics with applications to the structure of chiral symmetry breaking and hadronic string theory. More recently, it has been established that there exists a duality between the large N limit of SU(N) supersymmetric Yang-Mills theory and classical supergravity in a higher dimensional space-time. In this talk, I will discuss the nature of the large Nc expansion in QCD and its application to the computation of weak decay amplitudes.• Large Nc expansion in QCD.The large Nc expansion defines a nonperturbative reordering of the QCD coupling constant expansion. Each Feynman diagram can be classified by its dependence on the strong coupling constant, α strong , and the number of colors Nc. In 1974, 't Hooft [1] argued that the structure of the theory simplified in the limit, Nc → ∞ , α strong → 0 , α strong Nc fixed * . The theory is summed to all orders in the rescaled coupling constant, α strong Nc * , with corrections being formally suppressed by powers of 1/Nc. At leading order in this expansion, the gluons are constrained to be in planar Feynman diagrams. Quarks lines form boundaries of the planar surfaces formed by the gluons. In this sense, the structure of large Nc QCD is similar to an open string theory with quarks attached to the ends of the string.

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ΔI=12Rule for Nonleptonic Decays in Asymptotically Free Field Theories

Cited by 831 publications

References 17 publications

Probing the chiral weak Hamiltonian at finite volumes

Probing the chiral weak Hamiltonian at finite volumes

Charm mass dependence of the weak Hamiltonian in chiral perturbation theory

On the Large Nc Expansion in Quantum Chromodynamics

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