Higher QCD corrections for inclusive semileptonic B decays

Abstract

In these proceedings we review the calculation of the total decay rate for inclusive 𝐵 → 𝑋 𝑐 ℓ νℓ decays to higher orders in perturbative QCD. The partonic rate is obtained via an asymptotic expansion around the limit 1 − 𝑚 𝑐 /𝑚 𝑏 ≪ 1. The same method can be used to compute kinematic moments in case no experimental cuts are applied, i.e. moments of the differential rate integrated over the whole phase space. We discuss the impact of the 𝑂 (𝛼 3 𝑠 ) corrections on the total semileptonic decay rate and the moments of the dilepton invariant mass 𝑞 2 .

Inclusive $$B\rightarrow X_c \ell {\bar{\nu }}_\ell$$ and $$B\rightarrow X_u \ell {\bar{\nu }}_\ell$$ decays: current status and future prospects

“…These were found to be large. A full calculation of all the α 2 s corrections with a kinematic cut would be necessary to determine the impact of such corrections, which is currently in progress [39]. We do not discuss the result in [75] here in detail as it is based on the same setup as the previous fits in [45] discussed above.…”

“…Note also that the master integrals calculated at NNLO for the partonic decay rate can be also employed in the evaluation of the higher QCD corrections to the 1/m b terms, as was shown for q 2 moments at NLO in [86]. The method employed in [39] can also be applied to calculate the N3LO corrections to moments with cuts if the reduction to master integrals is possible and the system of differential equations can be established. In addition to that it is desirable to study the corrections of order 1/m 3 b in the relation between the bottom quark pole mass and kinetic mass.…”

“…[38]. Analytic expressions for the NNLO corrections to the q 2 spectrum and its moments with cuts have been presented only recently [39]. At N3LO, there are expressions for the moments without cuts in Ref.…”