IS THE CRONIN’S REPRESENTATION CORRECT FOR THE PENGUIN OPERATOR?

It is shown that the Cronin’s operator, being used for a phenomenological description of non-loptonic K-meson decays within the effective chiral Lagrangian approach with non-linear realization of chiral SU (3)× SU (3) symmetry (so-called, chiral perturbation theory at the hadronic level), cannot be applied to the determination of the Penguin-operator (O5-operator) at the hadronic level. The affirmation is based on the proof of the violation of the low-energy theorem [Formula: see text] which is valid within the framework of the Cronin’s representation. The violation of this low-energy theorem is obtained at the quark level and connected with the account of the low-energy interactions of pions caused by the overlap of wave functions of pions in the |π+π−> state in the low-energy limit p+→0. The chiral transformation properties of the normal-ordered Penguin operator are studied.

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CHIRAL PERTURBATION THEORY AT THE QUARK LEVEL

International Journal of Modern Physics A ◽

10.1142/s0217751x92003355 ◽

1992 ◽

Vol 07 (29) ◽

pp. 7305-7338 ◽

Cited By ~ 29

Author(s):

A.N. IVANOV ◽

M. NAGY ◽

N.I. TROITSKAYA

Keyword(s):

Perturbation Theory ◽

Chiral Perturbation Theory ◽

Final State Interaction ◽

Low Energy ◽

Chiral Perturbation ◽

Final State ◽

Large N ◽

Quark Level ◽

Energy Approximation

The chiral perturbation theory is developed at the quark level within the extended Nambu-Jona-Lasinio model, which we used for the low-energy approximation of QCD in the leading order of the large N expansion. In terms of constituent-quark loop diagrams we analyze all of the main low-energy effects caused by the first order corrections in the current-quark-mass expansions. For the correct description of the η→3π decays we confirm the important role of the final-state interaction quoted by Gasser and Leutwyler.

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THE PROBLEM OF BOSONIZATION OF LOCAL FOUR-QUARK OPERATORS

International Journal of Modern Physics A ◽

10.1142/s0217751x93001375 ◽

1993 ◽

Vol 08 (20) ◽

pp. 3425-3455 ◽

Cited By ~ 15

Author(s):

A. N. IVANOV ◽

N. I. TROITSKAYA ◽

M. NAGY

Keyword(s):

Sum Rules ◽

Final State Interaction ◽

Quark Condensate ◽

S Wave ◽

Chiral Perturbation ◽

Nonlinear Realization ◽

Final State ◽

Penguin Operator ◽

Hadronic Level ◽

Quark Structure

The problem of bosonization of standard local four-quark operators, by involving the penguin operator, with ΔI = 1/2 and ΔS = 1 selection rules, is studied. We show that the well-known Cronin's operator determined within the effective chiral Lagrangian approach with nonlinear realization of chiral SU (3) × SU (3) symmetry (so-called chiral perturbation theory at the hadronic level) can realize the hadronic level description of local four-quark operators with (V − A) × (V − A) quark structure only. Also, it is shown that any attempts to apply Cronin's operator for bosonization of the penguin operator, possessing (V − A) × (V + A) quark structure, are doomed to failure. The latter is explained by the inability of Cronin's operator to describe correctly the s-wave final-state interaction, which is very important for transitions governed by the penguin operator. The asymmetry of quark condensate is calculated. The sign of this asymmetry is opposite to that one assumed in the framework of QCD sum rules.

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QUARK STRUCTURE OF PSEUDOSCALAR MESONS

International Journal of Modern Physics A ◽

10.1142/s0217751x00000082 ◽

2000 ◽

Vol 15 (02) ◽

pp. 159-207 ◽

Cited By ~ 248

Author(s):

THORSTEN FELDMANN

Keyword(s):

High Energy ◽

Wave Functions ◽

Low Energy ◽

Mixing Process ◽

Chiral Perturbation ◽

Fock States ◽

Mixing Parameters ◽

Pseudoscalar Mesons ◽

Energy Application ◽

Quark Structure

I review to which extent the properties of pseudoscalar mesons can be understood in terms of the underlying quark (and eventually gluon) structure. Special emphasis is put on the progress in our understanding of η–η′ mixing. Process-independent mixing parameters are defined, and relations between different bases and conventions are studied. Both, the low-energy description in the framework of chiral perturbation theory and the high-energy application in terms of light-cone wave functions for partonic Fock states, are considered. A thorough discussion of theoretical and phenomenological consequences of the mixing approach will be given. Finally, I will discuss mixing with other states (π0, ηc, …).

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CHIRAL PROPERTIES OF NON-EXOTIC PROCESSES IN K-MESON PHYSICS

Modern Physics Letters A ◽

10.1142/s021773239200183x ◽

1992 ◽

Vol 07 (23) ◽

pp. 2095-2100 ◽

Cited By ~ 4

Author(s):

A. N. IVANOV ◽

M. NAGY ◽

N. I. TROITSKAYA

Keyword(s):

Perturbation Theory ◽

Chiral Perturbation Theory ◽

Quark Mass ◽

Chiral Perturbation ◽

K Meson ◽

First Order ◽

Current Quark Mass ◽

Quark Level ◽

Mass Expansion ◽

Current Quark

The first order corrections in current quark mass expansion are evaluated for the πK-scattering and Kl3-decay amplitudes within Chiral perturbation theory at the quark level. The Ademollo-Gato theorem is discussed.

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Determination of low-energy constants of Wilson chiral perturbation theory

Journal of High Energy Physics ◽

10.1007/jhep05(2013)038 ◽

2013 ◽

Vol 2013 (5) ◽

Cited By ~ 17

Author(s):

Gregorio Herdoíza ◽

◽

Karl Jansen ◽

Chris Michael ◽

Konstantin Ottnad ◽

...

Keyword(s):

Perturbation Theory ◽

Chiral Perturbation Theory ◽

Low Energy ◽

Chiral Perturbation ◽

Energy Constants

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THE K+→π+π0γ(DE) DECAY IN CHIRAL PERTURBATION THEORY AT THE QUARK LEVEL

Modern Physics Letters A ◽

10.1142/s0217732393001331 ◽

1993 ◽

Vol 08 (17) ◽

pp. 1599-1602 ◽

Cited By ~ 3

Author(s):

A.N. IVANOV ◽

M. NAGY ◽

N.I. TROITSKAYA

Keyword(s):

Perturbation Theory ◽

Chiral Perturbation Theory ◽

Dominant Role ◽

Low Energy ◽

Chiral Perturbation ◽

Direct Emission ◽

Low Energies ◽

Quark Level

The probability of the K+→π+π0γ (DE) decay with the direct emission of a photon is calculated. The strong low-energy interactions are accounted for within chiral perturbation theory at the quark level, based on the Extended Nambu-Jona-Lasinio (ENJL) model approximating QCD at low energies. The dominant role of chiral anomalies is confirmed.

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