Model-independent extraction of form factors and |𝑉𝑐⁢𝑏| in ¯𝐵 →𝐷⁢ℓ−⁢¯𝜈ℓ with hadronic tagging at BABAR

Using the entire BABAR ϒ⁡(4⁢𝑆) dataset, the first two-dimensional unbinned angular analysis of the semileptonic decay ¯ 𝐵 →𝐷⁢ℓ−⁢ ¯ 𝜈 ℓ is performed, employing hadronic reconstruction of the tag-side 𝐵 meson from ϒ⁡(4⁢𝑆) →𝐵⁢ ¯ 𝐵 . Here, ℓ denotes the light charged leptons 𝑒 and 𝜇. A novel data-driven signal-background separation procedure with minimal dependence on simulation is developed. This procedure preserves all multidimensional correlations present in the data. The expected sin2⁡𝜃ℓ dependence of the differential decay rate in the Standard Model is demonstrated, where 𝜃ℓ is the lepton helicity angle. Including input from the latest lattice QCD calculations and previously available experimental data, the underlying form factors are extracted using both model-independent (BGL) and dependent (CLN) methods. Comparisons with lattice calculations show flavor SU(3) symmetry to be a good approximation in the 𝐵(𝑠) →𝐷(𝑠) sector. Using the BGL results, the CKM matrix element |𝑉𝑐⁢𝑏| =(41.09 ±1.16) ×10−3 and the Standard Model prediction of the lepton-flavor universality violation variable ℛ⁡(𝐷) =0.300 ±0.004, are extracted. The value of |𝑉𝑐⁢𝑏| from ¯ 𝐵 →𝐷⁢ℓ−⁢ ¯ 𝜈 ℓ tends to be higher than that extracted using ¯ 𝐵 →𝐷*⁢ℓ−⁢ ¯ 𝜈 ℓ. The Standard Model ℛ⁡(𝐷) calculation is at a 1.97⁢𝜎 tension with the latest HFLAV experimental average.