Direct resummation of the leading renormalons in inclusive semileptonic B decay

Abstract

We present a Borel resummation method for the QCD corrections in inclusive, charmless, semileptonic B meson decay. The renormalon contributions are resummed to all orders by employing a bilocal expansion of the Borel transform that accurately accounts for the first infrared renormalons in the Borel plane. The renormalons in the pole mass and the QCD expansion are resummed separately, and a precise relation is obtained between a properly defined pole mass and the ${\bar {\rm MS}}$ mass. The inclusive decay rate is calculated to three loop order using an estimate of the yet unknown NNLO coefficient.