Summary
The transformation between current and constituent quarks is considered in view of the checking of the contributions, through PCAC, of the Σ*-resonances to the reactions K−p → π0Λ* (with negative parity) and the decays Σ* → K−p and Σ* → π0Λ*. Both the Σ*’s and Λ*’s under consideration are classified in the 70,L=1 representation. In our model only one parameter is left, contrary to what happens in pure group-theoretical approach. The predictions are almost independent of its value and in good agreement with experiment.
Riassunto
Si considerano le trasformazioni tra quark di corrente e quark costituenti in vista del controllo dei contributi, attraverso la PCAC, delle risonanze Σ* alle reazioni K−p→π0Λ* (con parità negativa) ed ai decadimenti Σ* → K−p e Σ* → π0Λ*. Si classificano sia i Σ* che i Λ* presi in considerazione nella rappresentazione 70,L=1. Si lascia nel nostro modello un solo parametro, contrariamente a ciò che avviene in un accostamento puro di teoria dei gruppi. Le previsioni sono quasi indipendenti dal suo valore ed in buon accordo con gli esperimenti.
Реэюме
Рассматривается преобраэование между токовыми и составляюшими кварками с целью проверки вкладов, череэ PCAC, Σ*-реэонансов в реакции K−p→π0Λ* (с отрицательной четностью) и распады Σ*→K−p и Σ*→π0Σ*. Рассматриваемые Σ* и Λ* классифицируются в представлении 70,L=1. В нащей модели остается только один параметр, в отличие от подхода с испольэованием теории групп. Полученные предскаэания почти не эависят от величины зтого параметра и хорощо согласуются с зкспериментом.
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Some confidence on the reliability of eqs. (2.2) may be achieved by comparing the two different expressions one can get for the decay amplitudes of the K-π resonances: \(\begin{gathered} \frac{{m_{K*(1420)}^2 - m_\pi ^2 }}{{f_\pi }}\left\langle {K^{* - } (14} \right.20)|Q_5^{K^ - } |\left. {\pi ^0 } \right\rangle = \frac{{m_{K*(1420)}^2 - m_\pi ^2 }}{{f_\pi }}\left\langle {K^{* - } (14} \right.20)|Q_5^{K^ - } |\left. {K^ - } \right\rangle , \hfill \\ \frac{{m_{K*(1420)}^2 - m_\pi ^2 }}{{f_\pi }}\left\langle {K^{* - } (14} \right.20)|Q_5^{K^ - } |\left. {\pi ^0 } \right\rangle = \frac{{m_{K*(1420)}^2 - m_\pi ^2 }}{{f_\pi }}\left\langle {K^{* - } (14} \right.20)|Q_5^{K^ - } |\left. {K^ - } \right\rangle , \hfill \\ \end{gathered} \). These two equalities imply, respectively, taking inspiration from a previous work (16) for theSU 3 breaking of the axial charges: \(\frac{{f_K }}{{f_K }}\left\{ \begin{gathered} \frac{{0.78}}{{0.55}}\,\,\frac{{0.64}}{{0.75}} = 1.18, \hfill \\ \frac{{1.96}}{{1.74}}\,\,1.2\quad = 1.36, \hfill \\ \end{gathered} \right.\) rather consistently and in agreement with the experimental values. Always from ref. (16) we see that theSU 3 breaking in the matrix elements 〈Σ * i |Q K−5 |p〉 and in thef K/f π-ratio just compensate. So here we shall not consider them both.
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Buccella, F., Savoy, C.A. & Sorba, P. Current quarks, constituent quarks and the reactions K−p → π0Λ*. Nuov Cim A 31, 277–293 (1976). https://doi.org/10.1007/BF02729732
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DOI: https://doi.org/10.1007/BF02729732