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

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


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


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Prasad, R., and Singh, C.P.: 1979, Phys. Rev. D20, 256.Google Scholar
  2. 2.
    Prasad, R., and Singh, C.P.: in press, Phys. Rev.Google Scholar
  3. 3.
    Chan, C.H., and Meiere, F.T.: 1968, Phys. Lett. 20, 568.Google Scholar
  4. 4.
    Nagels, M.M. et al.: 1976, Nucl. Phys. B109, 1.ADSCrossRefGoogle Scholar
  5. 5.
    Chan, C.H., and Smalley, L.L.: 1970, Phys. Rev., D2, 2635Google Scholar
  6. 6.
    Singh, C.P.: 1971, Phys. Rev. D4, 270.Google Scholar
  7. 7.
    Engels, J., and Pilkuhn, H.: 1971, Nucl. Phys. B31, 531.ADSCrossRefGoogle Scholar
  8. 8.
    Renner, B., and Zerwas, P.: 1971, Nucl. Phys. B35, 397ADSCrossRefGoogle Scholar
  9. 9.
    Martin, 3.R.: 1966, Nuovo Cimento 43 A, 629.ADSGoogle Scholar
  10. 10.
    Field, R.D., and Jackson, J.D.: 1971, Phys. Rev. D4, 693.Google Scholar
  11. 11.
    Dubricka, S. et al.: 1974, Nucl. Phys. B88, 477.ADSGoogle Scholar

Copyright information

© D. Reidel Publishing Company 1981

Authors and Affiliations

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

Personalised recommendations