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$B\to D_1(2420)$ and $B\to D_1'(2430)$ form factors from QCD light-cone sum rules

We perform the first calculation of form factors in the semileptonic decays $B\!\to\! D_1(2420)\ellν_\ell$ and $B \to D_1^\prime (2430)\ell ν_\ell$ using QCD light-cone sum rules (LCSRs) with $B$-meson distribution amplitudes. In this calculation the $c$-quark mass is finite. Analytical expressions for two-particle contributions up to twist four are obtained. To disentangle the $D_1$ and $D_1^\prime$ contributions in the LCSRs, we suggest a novel approach that introduces a combination of two interpolating currents for these charmed mesons. To fix all the parameters in the LCSRs, we use the two-point QCD sum rules for the decay constants of $D_1$ and $D_1^\prime$ mesons augmented by a single experimental input, that is the $B \to D_1(2420)\ellν_\ell$ decay width. We provide numerical results for all $B\to D_1$ and $B\to D_1^\prime$ form factors. As a byproduct, we also obtain the $D_1$- and $D_1'$-meson decay constants and predict the lepton-flavour universality ratios $R(D_1)$ and $R(D_1')$.