The chiral loop expansion of the nonleptonic weak interactions of mesons

Kambor, Joachim; Missimer, John; Wyler, D.

doi:10.1016/0550-3213(90)90236-7

Cited by 208 publications

(318 citation statements)

References 33 publications

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“…This can perhaps most easily be understood by writing ξ in the meson basis and expanding the operators to the third order, whereby it is easy to verify that the very slow ∆I = 3/2 decay K + → π 0 π + is directly proportional to g 27 , while the much faster ∆I = 1/2 decays of K 0 S get a comparable contribution both from g 8 and g 27 . More quantitatively, a leading order analysis [6], supplemented by phenomenologically determined large phase factors [9] in the amplitudes, suggests the well-known values It has been argued that 1-loop corrections in chiral perturbation theory are large [8,10,11], and one can therefore get agreement with experimental data on partial decay widths even with somewhat less differing values of g 8 and g 27 , but a sizeable hierarchy still remains. Eqs.…”

Section: Su(3) Classification Of the Effective Theorysupporting

confidence: 60%

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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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Section: Su(3) Classification Of the Effective Theorysupporting

confidence: 60%

“…Of course, there are other operators with the same symmetries, but a higher order in the chiral expansion: these could either involve more derivatives (a complete collection of such next-to-leading order operators can be found in Ref. [8]), or explicit occurrences of the mass matrix, as in…”

Section: Weak Effective Hamiltonian In Su(4) Chiral Perturbation Theorymentioning

confidence: 99%

Charm mass dependence of the weak Hamiltonian in chiral perturbation theory

Hernández¹,

Laine

2004

J. High Energy Phys.

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“…[60]. The use of partial integration identities allows to reduce the number of operators drastically, leading to the lists commonly used in phenomenology [61]; in our case, however, the use of partial integration identities is not possible, since we consider local operator insertions (i.e.…”

Section: Appendix a Irreducible Representations Of The Valence Groupmentioning

confidence: 99%

“…Instead of a generic operator Orsūv, practical computations of the type in Ref. [60] involve certain factorised forms, like…”

Section: Appendix a Irreducible Representations Of The Valence Groupmentioning

confidence: 99%

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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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Selected Topics on Rare Kaon Processes in the Standard Model and Supergravity

Bilić

Guberina

1994

Fortschr. Phys.

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Rare kaon processes appear to be particularly suitable to study the extensions of the standard model, especially if the possibility for eventual direct evidence becomes unlikely. In this review, we discuss processes that are important as a test of either the standard model or supergravity. Moreover, some of these are important even for both the standard model and for supergravity. Particular attention is paid to the reduction of uncertainties in the calculation, especially the ones coming from the confinement effects. Recent approaches, such as chiral perturbation theory, the large Nc‐expansion, QCD sum rules and lattice QCD, are discussed. This is found to be the best strategy in view of the fact that supersymmetric effects are rather tiny.

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The chiral loop expansion of the nonleptonic weak interactions of mesons

Cited by 208 publications

References 33 publications

Charm mass dependence of the weak Hamiltonian in chiral perturbation theory

Charm mass dependence of the weak Hamiltonian in chiral perturbation theory

Probing the chiral weak Hamiltonian at finite volumes

Selected Topics on Rare Kaon Processes in the Standard Model and Supergravity

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