Abstract
The determination of $|V_{cb}|$ using inclusive and exclusive (semi-)leptonic decays exhibits a long-standing tension of varying ${\cal O}(3 \sigma)$ significance. For the inclusive determination the decay rate is expanded in $1/m_b$ using heavy quark expansion, and from moments of physical observables the higher order heavy quark parameters are extracted from experimental data in order to assess $|V_{cb}|$ from the normalisation. The drawbacks are high correlations both theoretically as well as experimentally among these observables. We will scrutinise the inclusive determination in order to add a new and less correlated observable. This observable is related to the decay angle of the charged lepton and can help to constrain the important heavy quark parameters in a new way. It may validate the current seemingly stable extraction of $|V_{cb}|$ from inclusive decays or hints to possible issues, and even may be sensitive to New Physics operators.
Highlights
The higher precision and especially accumulated data of the future Belle-II experiment [38] will be able to make use out of this additional and less correlated observable
For the inclusive determination the decay rate is expanded in 1/mb using heavy quark expansion, and from moments of physical observables the higher order heavy quark parameters are extracted from experimental data in order to assess |Vcb| from the normalisation
For the following discussion to be useful in analysis, we assume that the full event kinematics may be reconstructed experimentally
Summary
For the following discussion to be useful in analysis, we assume that the full event kinematics may be reconstructed experimentally. That can be achieved at (Super-)B-factories [38] with hadronic tag analysis to reconstruct the kinematics including the invisible neutrino momentum This decay kinematics is given by pμB = pμ + pμν + pμxC := qμ + pμxC. 2.2 Differential decay rate The differential rate can be decomposed into the leptonic and hadronic tensor dΓ = 16πG2F |Vcb|2Wμν Lμν dφ ,. The off-shellness of the bottom quark will be mimicked by derivatives of the on-shell delta distribution condition of the hadronic tensor, which occurs at higher orders in the 1/mb expansion This has no impact on the leptonic side, as we can factorise the decay rate according to eq (2.3) and we have dΓ = 16πG2F |Vcb|2Wμν Lμν. The decomposition we have elaborated on in eq (2.10) enables us to calculate the phase-space for the triple differential decay rate in the following subsection
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