Next-to-leading-logarithm k resummation for B → J/ψ decays
Xin Liu, Hsiang-nan Li, Zhen-Jun Xiao
Abstract
We derive the kT resummation for a transverse-momentum-dependent charmonium wave function, which involves the bottom quark mass mb, the charm quark mass mc, and the charm quark transverse momentum kT, up to the next-to-leading-logarithm (NLL) accuracy under the hierarchy mb≫mc≫kT. The resultant Sudakov factor is employed in the perturbative QCD (PQCD) approach to the Bc→J/ψ transition form factor A0Bc→J/Ψ(0) and the Bc+→J/ψπ+ decay. We compare the NLL resummation effect on these processes with the leading-logarithm one in the literature, and find a (5−10)% enhancement to the form factor A0Bc→J/Ψ(0) and a (10−20)% enhancement to the decay rate BR(Bc+→J/Ψπ+). The improved kT resummation formalism is applicable to the PQCD analysis of heavy meson decays to other charmonia.