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 TMF, 1991, Volume 86, Number 3, Pages 385–390 (Mi tmf5455)

$\pi a_1$ Transitions and low-energy limit in the linear sigma model

M. K. Volkov, A. A. Osipov

Abstract: The problem of obtaining the correct low-energy limit in the linear sigma model with participation of vector and axial-vector mesons is discussed. In a naive treatment of the tree approximation, for example, in $\pi\pi$ scattering, the diagrams with intermediate scalar and vector mesons may lead to double counting in the scattering lengths. For the case of the scattering amplitudes and the semileptonic decay $\tau\to\nu_\tau 3\pi$ it is shown that this problem can be solved by taking into account $\pi a_1$ transitions at the external ends of the corresponding meson vertices.

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English version:
Theoretical and Mathematical Physics, 1991, 86:3, 265–269

Bibliographic databases:

Citation: M. K. Volkov, A. A. Osipov, “$\pi a_1$ Transitions and low-energy limit in the linear sigma model”, TMF, 86:3 (1991), 385–390; Theoret. and Math. Phys., 86:3 (1991), 265–269

Citation in format AMSBIB
\Bibitem{VolOsi91} \by M.~K.~Volkov, A.~A.~Osipov \paper $\pi a_1$~Transitions and low-energy limit in the linear sigma model \jour TMF \yr 1991 \vol 86 \issue 3 \pages 385--390 \mathnet{http://mi.mathnet.ru/tmf5455} \transl \jour Theoret. and Math. Phys. \yr 1991 \vol 86 \issue 3 \pages 265--269 \crossref{https://doi.org/10.1007/BF01028424} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1991GJ55400008} 

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This publication is cited in the following articles:
1. M. K. Volkov, A. E. Radzhabov, “The Nambu–Jona-Lasinio model and its development”, Phys. Usp., 49:6 (2006), 551–561
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