$B\to D_1(2420)$ and $B\to D_1^{\prime }(2430)$ form factors from QCD light-cone sum rules

Abstract

We perform the first calculation of form factors in the semileptonic decays $B\to D_1(2420)\ell {\nu }_{\ell }$ and $B\to D_1^{\prime }(2430)\ell {\nu }_{\ell }$ 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 $B\to D_1(2420)\ell {\nu }_{\ell }$ 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 $D_1^{\prime }$-meson decay constants and predict the lepton-flavour universality ratios $R(D_1)$ and $R(D_1^{\prime })$.

Comments: 30 pages, 2 figures, published version