Relativistic Corrections to the Exclusive Decays of C-even Bottomonia into S-wave Charmonium Pairs

TL;DR

This paper calculates relativistic corrections to the decay rates of C-even bottomonia into S-wave charmonium pairs within NRQCD, revealing significant negative corrections and the importance of resummation, with results differing notably from light-cone predictions.

Contribution

It provides the first comprehensive calculation of relativistic corrections to these decays, including all-orders resummation for certain contributions, and compares NRQCD results with light-cone formalism.

Findings

Relativistic corrections range from -20% to -35%.

Resummation increases decay rate predictions compared to NLO results.

NRQCD predictions are much smaller than light-cone formalism estimates.

Abstract

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 $\chi_{b2}\to \eta_c(mS)+\eta_c(nS)$ 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 an or two orders of magnitudes.