The PDG 2024 averages for are from inclusive decays and from the exclusive channel

PHYSICS · Multi-part · Fermi University Physics · Scientific Practice & Experimental Methods · Particle Physics & Quantum Fields · Uncertainty in measurement

Symmetry and Flavour, Ch Heavy flavour: charm and beauty decays and the magnitudes of the CKM elements

Problem

The PDG 2024 averages for ∣Vcb∣|V_{cb}| are (42.2±0.5)×10−3(42.2 \pm 0.5)\times10^{-3} from inclusive decays and (39.8±0.6)×10−3(39.8 \pm 0.6)\times10^{-3} from the exclusive channel B→D∗ℓνB \to D^*\ell\nu. Suppose a future lattice calculation of the form factor cuts the exclusive uncertainty to 0.3×10−30.3\times10^{-3}, while both central values stay where they are. ((a)) Treating the two determinations as independent, find by how many standard deviations they would then disagree. ((b)) Name the theoretical input each determination rests on, and say why the smaller error bar would not by itself tell you which value to trust.

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