Chiral<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>S</mml:mi><mml:mrow><mml:msub><mml:mrow><mml:mi>U</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mo>⊗</mml:mo><mml:mi>S</mml:mi><mml:mrow><mml:msub><mml:mrow><mml:mi>U</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>Gauge-Invariant Dynamics and the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub>

Biswas, S. N.; Dutt, Ranabir; Nanda, P. K.; Pandit, L. K.

doi:10.1103/physrevd.1.1445

Cited by 8 publications

(4 citation statements)

References 23 publications

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“…About the Kl4 decay processes, however, Biswas et al 6 ) have made discussions along the same line of thought, and argued that they have obtained better results for the decay rate than those of the softpion calculations. Moreover, in the limit of exact symmetry, their results are quite different from those of W einberg.…”

Section: Introductionmentioning

confidence: 95%

“…Recently, Biswas et al 6 ) have evaluated Kz 4 -decay form factors using an approximately chiral invariant Lagrangian which includes 1 ± gauge fields with minimal interactions. Their conclusion is that they have obtained better results for the decay rates than those of soft-pion calculations, and that the modification is certainly due to the inclusion of possible vector and axial-vector meson dominance of the currents.…”

Section: Introductionmentioning

confidence: 99%

“…(1), they do not take consideration of SU(3) breaking effects in *> Throughout this paper, we employ the same notation as in Ref. 6). …”

Section: Introductionmentioning

confidence: 99%

“…However, for the sake of simplicity, we leave it unchanged. Performing the diagonalization of axial-vector and pseudoscalar fields and the renormalization for the pseudoscalar fields, 6 ) we obtain relevant strong vertices. Here we only write down the corrected term:…”

Section: Introductionmentioning

confidence: 99%

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A Comment on Chiral Invariant Lagrangian and Soft-Pion Theorems

1971

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1485In the framework of tree approximation, the soft-pion theorems are shown to hold true even in a general case where 1 ± meson fields are contained in the chiral invariant Lagrangian, which is applicable to hard-pion processes. Thus, contrary to the results of Biswas et al. forKl4 decays, we are led to almost the same results as those of the soft-pion technique when re-examining their calculations. § 1. IntroductionRecently, Dashen and W einstein 1 ) have shown that the soft-pion theorem is justified by an assumption that the real world satisfies an approximate chiral symmetry and, moreover, in the symmetry limit the pion behaves as a Goldstone boson. Starting only from the above assumption, they have also derived a phenomenological Lagrangian which, in the tree approximation, must give the same results as the full theory when calculating the leading order in pion momenta of any amplitudes. This Lagrangian is essentially the same as the one proposed by Weinberg and Schwinger et al.,2 ) and the characteristic feature of this Lagrangian is that o-mesons couple with other hadrons only through phenomenological currents built out of the external hadrons.On the other hand, many authors 3 ) have studied low energy phenomena, including hard-pion processes, by means of various approximately chiral invariant Lagrangians which contain explicitly vector (1-) and axial-vector (1 +) · mesons and other hadrons. These are not contained in the framework of the effective Lagrangian derived by Dashen and W einstein. 1 ) In the course of their calculations, they have considered from the outset tree diagrams only, instead of taking account of the whole diagrams.In this respect, there arises a non-trivial question as to whether we can again obtain the soft-pion theorems even when we take an arbitrary chiral invariant Lagrangian explicitly containing 1 ± mesons and calculate tree diagrams only. For the observation of Dashen and Weinstein is that, if the original Lagrangian is solved by calculating the whole diagrams, the results are equivalent in the leading order of pion momenta to those obtained from the phenomenological one in the at Ernst Mayr

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Section: Introductionmentioning

confidence: 95%

Section: Introductionmentioning

confidence: 99%

“…(1), they do not take consideration of SU(3) breaking effects in *> Throughout this paper, we employ the same notation as in Ref. 6). …”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A Comment on Chiral Invariant Lagrangian and Soft-Pion Theorems

1971

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Experimental study of 30 000Ke4decays

et al. 1977

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An experiment on the decay K '-a'a-e'v was performed at the CERN proton synctirutron with sparkchamber and counter techniques. The IS, branching ratio has been measured relative to the T decay. The ax phase-shift difference 6: -61 and the form factors of the hadronic current have been determined as functions of the n a energy. The xa scattering length a : has been evaluated from the phase shifts with a phenomenological model. The results are compared with the theoretical predictions of current algebra and other models.

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