The asymptotic restrictions for the γπ → ππ process

Bolokhov, A.A.; Manashov, A. N.; Vereshagin, V.; Polyakov, M. V.

doi:10.1016/0370-2693(93)91423-k

Cited by 1 publication

(7 citation statements)

References 16 publications

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“…The numerical results obtained in refs. [1,2,8,9,10] for the low energy expansions coefficients of the corresponding amplitudes proved to be in a good agreement with experimental data both in normal and anomalous sectors. Altogether, these results look promising enough and, hence, it makes sense to consider the method used in refs.…”

supporting

confidence: 76%

“…At the same time, Weinberg's results (as well as those derived in refs. [25,26,22,23,30,27,28,24,29,1,2,8,9,10,14,20,21]) clearly demonstrate that it is feasible to analyze the asymptotic behavior degree by degree. Such a way could be only applied if the analytical structure of the amplitude is simple enough.…”

Section: Asymptotic Conditionmentioning

confidence: 91%

“…In the papers [1,2] it was demonstrated that the requirement of "realistic" asymptotic behavior (first suggested by Weinberg [3]), when applied to ππ → ππ and γπ → ππ reactions amplitudes, written in the form dictated by the large-N c limit ( [4,5]) gives rise to certain (infinite) sets of self-consistency conditions for the parameters (masses and coupling constants) of corresponding resonances. It was shown also that the generating equations for those conditions can be presented in the form, clearly displaying the remarkable property which is commonly called as duality (see, for example, [6,7]).…”

mentioning

confidence: 99%

“…Altogether, these results look promising enough and, hence, it makes sense to consider the method used in refs. [1,2,8,9,10] in more detail.…”

mentioning

confidence: 99%

“…The results of the papers [1,2] have been derived in a manner strongly exploiting the high degree of the corresponding amplitudes symmetry, the latter one being caused solely by the symmetry of the considered processes. Such a way, however, could not be used for the consideration of less symmetric reactions.…”

mentioning

confidence: 99%

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Tree-level(π,K)amplitude and analyticity

Vereshagin

1997

Phys. Rev. D

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We consider the tree-level amplitude, describing all 3 channels of the binary (π, K)-reaction, as a meromorphic polynomially bounded function of 3 dependent complex variables. Relying systematically on the Mittag-Leffler theorem, we construct 3 convergent partial fraction expansions, each one being applied in the corresponding domain. Noting, that the mutual intersections of those domains are nonempty, we realize the analytical continuation. It is shown that the necessary conditions to make such a continuation feasible, are the following: 1) The only parameters completely determining the amplitude are the on-shell couplings and masses; 2) These parameters are restricted by a certain (infinite) system of bootstrap equations; 3) The full cross-symmetric amplitude takes the typically dual form, the Pomeron contribution being taken into account; 4) This latter contribution corresponds to a nonresonant background, which, in turn, is expressed in terms of cross-channel resonances parameters.It is demonstrated also, that the Chiral Symmetry provides a unique scale for the mentioned parameters, the resonance saturation effect appearing as a direct consequence of the above results.

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supporting

confidence: 76%