Abstract
The s-wave decay amplitude in the nonleptonic decay of baryons is analyzed within heavy baryon chiral perturbation theory in the large-N_c limit at one-loop order, where N_c is the number of color charges. Loop graphs with octet and decuplet intermediate states are systematically incorporated into the analysis and the effects of the decuplet-octet mass difference are accounted for. There are large-N_c cancellations between different one-loop graphs as a consequence of the large-N_c spin-flavor symmetry of QCD baryons. The predictions of large-N_c baryon chiral perturbation theory are in very good agreement both with the expectations from the 1/N_c expansion and with the experimental data.
Highlights
The remarkable success of the 1=N c expansion of QCD—where N c is the number of color charges [1,2]—and its subsequent combination with heavy-baryon chiral perturbation theory [3] to describe several static properties of baryons has been evident over the past two decades.Initially, a 1=N c expansion of the chiral Lagrangian was formulated in Ref. [3]; since the Lagrangian has been useful to evaluate nonanalytic meson-loop corrections to baryon amplitudes in the 1=N c expansion for finite N c .the method was originally applied to compute flavor-27 baryon mass splittings at leading order in chiral perturbation theory [3]
Feynman diagrams for the process under consideration. These diagrams are given by the product of a baryon operator with well-defined transformation properties under the spin-flavor symmetry times a loop integral, which depends nonanalytically on the light quark masses mq
One-loop graphs with intermediate spin-1=2 octet and spin-3=2 decuplet baryon states are analyzed including the full dependence on the decupletoctet baryon mass difference, while at the same time including the cancellations that follow from the large-N c spin-flavor symmetry of baryons
Summary
The remarkable success of the 1=N c expansion of QCD—where N c is the number of color charges [1,2]—. Due to the enormous amount of algebraic calculations involved, it is more appropriate to present first the s-wave amplitude here and to leave the p-wave one for a further paper To this end, one-loop graphs with intermediate spin-1=2 octet and spin-3=2 decuplet baryon states are analyzed including the full dependence on the decupletoctet baryon mass difference, while at the same time including the cancellations that follow from the large-N c spin-flavor symmetry of baryons. [8] are recognized to be present in the current analysis so they are borrowed and adapted to make up the new results At this point, a direct comparison with conventional baryon chiral perturbation theory is performed. In Appendix A all the new operator reductions required are listed whereas in Appendix B all the coefficients that come along with the baryon operators in the several one-loop contributions are provided
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