Relativistic corrections to the exclusive decays of C-even bottomonia into S-wave charmonium pairs

Within the nonrelativistic quantum chromodynamics (NRQCD) factorization formalism, we compute the relativistic corrections to the exclusive decays of bottomonia with even charge conjugation parity into S-wave charmonium pairs at leading order in the strong coupling constant. Relativistic corrections are resummed for a class of color-singlet contributions to all orders in the charm-quark velocity v_c in the charmonium rest frame. Almost every process that we consider in this work has negative relativistic corrections ranging from -20 to -35%. Among the various processes, the relativistic corrections of the next-to-leading order in v_c to the decay rate for χ_b2→η_c(mS)+η_c(nS) with m, n=1 or 2 are very large. In every case, the resummation of the relativistic corrections enhances the rate in comparison with the next-to-leading-order results. We compare our results with available predictions based on the NRQCD factorization formalism. The NRQCD predictions are significantly smaller than those based on the light-cone formalism by 1 or 2 orders of magnitude.