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

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

$$\frac{{g{{_\pi ^2}_{{c_o}c_1^*}}}}{{4\pi }}$$