Renormalons in electromagnetic annihilation decays of quarkonium

We study the large-order asymptotic behavior of the perturbation series for short-distance coefficients in the NRQCD factorization formulas for the decays J/{psi}{r_arrow}e{sup +}e{sup {minus}} and {eta}{sub c}{r_arrow}{gamma}{gamma}. The short-distance coefficients of the leading matrix elements are calculated to all orders in the large-N{sub f} limit. We find that there is a universal Borel resummable renormalon associated with the cancellation of the Coulomb singularity in the short-distance coefficients. We verify that the ambiguities in the short-distance coefficients from the first infrared renormalon are canceled by ambiguities in the nonperturbative NRQCD matrix elements that contribute through relative order v{sup 2}. Our results are used to estimate the coefficients of higher order radiative corrections in the decay rates for J/{psi}{r_arrow}e{sup +}e{sup {minus}}, {eta}{sub c}{r_arrow}{gamma}{gamma}, and J/{psi}{r_arrow}{gamma}{gamma}{gamma}. {copyright} {ital 1998} {ital The American Physical Society}