TTP97-05 Two-loop QCD corrections to semileptonic b decays at maximal recoil

TTP97-05 Two-loop QCD corrections to semileptonic b decays at maximal recoil

TTP97-05 Two-loop QCD corrections to semileptonic b decays at maximal recoil

We present a complete ${\cal O}(\alpha_s^2)$ correction to the differential width of the inclusive semileptonic decay $b\to cl\nu_l$ at the kinematical point of vanishing invariant mass of the leptons, $q^2=0$. Together with the recently computed ${\cal O}(\alpha_s^2)$ correction at the upper boundary of the lepton invariant mass spectrum, this new information permits an estimate of the ${\cal O}(\alpha_s^2)$ effect in the total inclusive semileptonic decay width $b\to cl\nu_l$. We argue that the non-BLM part of the ${\cal O}(\alpha_s^2)$ correction gives at most $1\%$ correction to the inclusive semileptonic decay width $b\to cl\nu_l$. This significantly improves the credibility of extracting $|V_{cb}|$ from the inclusive semileptonic decays of the $b$-hadrons.

Andrzej Czarnecki and Kirill Melnikov
Phys. Rev. Lett. 78 3630 1997
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