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Determination of g π∧∑and g π∑∑ Couplings From Adler Conditions

  • R. Prasad
  • C. P. Singh
Conference paper

Abstract

Recently we have derived (1) the PCAC Adler consistency conditions on the invariant amplitudes of the elastic as well as inelastic pion-charrned baryons processes πC0 → πC0, πC1, →πC1, πC0 →πC1 and πC0 →πC*. Numerical evaluations of these conditions with the low- lying intermediate states together with the assumption of unsubtracted form of dispersion relations for the invariant amplitudes yield the various hadronic couplings of charmed baryons. The values of the coupling constants are found as follows:
$$\frac{{g_{\pi {c_o}{c_1}}^2}}{{4\pi }}\, = \,58.3,\,\frac{{g{{_\pi ^2}_c}{{_{_1}}_{{c_1}}}}}{{4\pi }}\, = \,28.6,\,\frac{{g{{_\pi ^2}_{{c_1}c_1^*}}}}{{4\pi }}\, = {\kern 1pt} \,0.034,\,\frac{{g{{_\pi ^2}_c}{{_{_1^*c}}_{_1^*}}}}{{4\pi }}\, = \,1.43,\,$$
if we use
$$\frac{{g{{_\pi ^2}_{{c_o}c_1^*}}}}{{4\pi }}\, = {\kern 1pt} \,0.15$$
(i. e. Γc* = 20 MeV) as input value in the 3um rules. In a later investigation (2), we used superconvergence and finite-energy sum rules to determine these coupling constants and now we find;
$$\frac{{g_{\pi {c_o}{c_1}}^2}}{{4\pi }}\, = \,51.5,\,\frac{{g{{_\pi ^2}_c}{{_{_1}}_{{c_1}}}}}{{4\pi }}\, = \,24.5,\,\frac{{g{{_\pi ^2}_{{c_1}c_1^*}}}}{{4\pi }}\, = {\kern 1pt} \,0.024,\,\frac{{g{{_\pi ^2}_c}{{_{_1^*c}}_{_1^*}}}}{{4\pi }}\, = \,16.4,\,\frac{{g{{_\pi ^2}_c}{{_{_1^*c}}_{_1^*}}}}{{4\pi }}\, = \,6.33\,$$
using again the same input value of
$$\frac{{g{{_\pi ^2}_{{c_o}c_1^*}}}}{{4\pi }}$$

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Copyright information

© D. Reidel Publishing Company 1981

Authors and Affiliations

  • R. Prasad
    • 1
  • C. P. Singh
    • 1
  1. 1.Department of PhysicsBanaras Hindu UniversityIndia

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