Analytic calculation of two-loop QCD corrections tob→sℓ+ℓ−in the highq2region

Abstract

We present our results for the NNLL virtual corrections to the matrix elements of the operators O1 and O2 for the inclusive process b → sl+l− in the kinematical region q2 > 4mc2, where q2 is the invariant mass squared of the lepton-pair. This is the first analytic two-loop calculation of these matrix elements in the high q2 region. We give the matrix elements as an expansion in mc/mb and keep the full analytic dependence on q2. Making extensive use of differential equation techniques, we fully automatize the expanding of the Feynman integrals in mc/mb. In coincidence with an earlier work where the master integrals were obtained numerically [1], we find that in the high q2 region the αs corrections to the matrix elements sl+l−|O1,2|b calculated in the present paper lead to a decrease of the perturbative part of the q2-spectrum by 10%−15% relative to the NNLL result in which these contributions are put to zero and reduce the renormalization scale uncertainty to ~ 2%.